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Progress in New Cosmologies
Beyond the Big Bang

Progress in New Cosmologies
Beyond the Big Bang
Edited by
Halton C. Arp
Max-Planck Institute for Astrophysics Garching bei Munchen, Germany
C. Roy Keys
Publisher, Apeiron Montreal, Quebec, Canada
and
Konrad Rudnicki
Jagiellonian University Astronomical Observatory Cracow, Poland
Springer Science+ Business Media, LLC

Library of Congress Cataloging in Publication Data

Progress in new cosmologies: beyond the big bang 1 edited by Halton C. Arp, C. Roy Keys,
Konrad Rudnicki.

p. cm. Proceedings of the Thirteenth Cracow Summer School of Cosmology on Progress in New

Cosmologies, held September 7-12, 1992, in L6dz, Poland.

Includes bibliographical references and index. ISBN 978-1-4899-1227-5 ISBN 978-1-4899-1225-1 (eBook) DOI 10.1007/978-1-4899-1225-1 1. Cosmology-Congresses. 2. Astrophysics--Congresses.l. Arp, Ha1ton, C. II. Keys, C. Roy.

III. Rudnicki, Konrad. IV. Cracow Summer School of Cosmology on Progress in New Cos-

mologies (13th: 1992: L6dz, Poland)

QB981.P863 1993

93-42612

523.1---dc20

GP

Proceedings of the Thirteenth Cracow Summer School of Cosmology on Progress in New Cosmologies, held under the auspices of the Omega Foundation and Apeiron, September 7-12, 1992, at the Physics Institute, University of L6dZ, L6dz, Poland
ISBN 978-1-4899-1227-5
©1993 Springer Science+Business Media New York Originally published by P1enum Press, New York in 1993 Softcover reprint of the hardcover 1st edition 1993
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher.

Dedication
In memory of Fritz Zwicky
Some examples of Fritz Zwicky's approach to scientific ideas and hypotheses are given.
I had the opportunity to present the philosophical bases of the scientific methodology of Fritz Zwicky during the Xlth Krakow Summer School of Cosmology "Morphological Cosmology" devoted to the 90th anniversary of his birth (Flin & Duerbeck 1989). On that occasion I discussed the specific Zwickean "Morphological Method" or "Morphological Approach" on the general basis of the Goetheanistic Theory of Knowledge. This paper has been published (Rudnicki 1989}, and consequently I shall not go into great detail here. Nor do I wish to tell the life-story of this great astronomer and cosmologist, since this has been done in a voluminous book by Roland Mueller (1986) and all can read it there. Rather, I wish to mention some selected characteristics of his practical approach to the realm of scientific ideas and hypotheses.
A key to this approach is given in his Morphological Astronomy (Zwicky 1957), where we read the following:
If rain begins to fall on previously dry areas on the earth, the water on the ground will make its way from high levels to low levels in a variety ofways . Some of these ways will be more or less obvious, being predetermined by pronounced mountain formations and valleys, while others will appear more or less at random. Whatever courses are being followed by the first waters, their existence will largely prejudice these chosen by latter floods. A system of ruts will consequently be established which has a high degree ofpermanence. The water rushing to the sea will sift the earth in these ruts and leave the extended layers ofearth outside essentially unexplored. Just as the rains open up the earth here and there, ideas unlock the doors to various aspects of life, fixing the attention of men on some aspects while partly or entirely ignoring others. Once man is in a rut he seems to have the urge to dig even deeper, and what often is most unfortunate, he does not take the excavated debris with him like the waters, but throws it over the edge, thus covering up the unexplored territory and making it impossible for him to see outside his rut. The mud which he is throwing may even hit his neighbors in the eyes, intentionally or unintentionally, and make it difficult for them to see anything at all.
Zwicky, in his astronomical activity, never followed the "predetermined ways." When, according to general opinion, all the single stars, even novae at maximum brightness, were much less luminous than galaxies, he, together with Walter Baade, examined the old observations and organized a systematic search for very lumi-
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Dedication

nous objects, finally proclaiming a new type of single objects-supernovae, which could have the luminosity of entire galaxies. When Edwin Hubble and his followers talked about the uniform background of galaxies and some exceptional agglomerations of them-dusters of galaxies, Zwicky wanted to see whether such uniform background really existed. To check it, he introduced Schmidt cameras into astronomy (the first 8-inch version was in Pasadena on the roof of Robinson Building, followed in 1936 by the 18-inch version on Palomar) and discovered that all the galaxies take part in the clustering. Questioning the prejudice that a galaxy always consists of a nucleus and something around it (a shell, disk or halo), he made a systematic survey of galaxies and discovered compact galaxies, consisting of nucleus alone.
We should also not forget that while most extragalactic astronomers considered the redshifts of extragalactic objects as due to Doppler effect, Zwicky together with Milton Humason always examined other possibilities. To express the possibility of alternatives, he systematically used the expression "symbolic recession veloc-
ity" V., instead of commonly used "radial velocity" V,.. He never fell into another
extreme prejudice, which holds that redshifts are not Doppler in nature. He simply
wanted to explore all possibilities first, so long as they were not excluded by valid scientific arguments.
In general, in his morphological approach he never stuck to one hypothesis (even if it was his own hypothesis), but always worked with entire sets, with continua of hypotheses, and considered all possibilities as long as they remained feasible.
And this is also the aim of our present School of Cosmology. We have to present as many observational facts and as many theoretical hypotheses as possible, and not stick to any single one, as long as alternatives still exist. Of course it is much easier to do research by "digging even deeper" in a wide, "generally accepted" scientific trend. It is easier to get grants, to obtain scientific degrees and honors; yet, in this case, we would merely be following scientific fashion instead of seeking the truth.

References
Flin, P, and Duerbeck, H.W., ed., 1989, Morphological Cosmology (Proceedings, Krakow, Poland 1986) Springer-Verlag.
Mueller, R., 1986, Fritz Zwicky, Verlag Baeschlin. Rudnicki, K., 1989, in: Morphological Cosmology, Flin, P, and Duerbeck, H.W., ed., (Proceed-
ings, Krakow, Poland 1986) Springer-Verlag. Zwicky, F., 1957,.Morphological Astronomy, Springer-Verlag.
Konrad Rudnicki

Foreword
The Hidden Hypotheses Behind the Big Bang
It is quite unavoidable that many philosophical a priori assumptions lurk behind the debate between supporters of the Big Bang and the anti-BB camp. The same battle has been waged in physics between the determinists and the opposing viewpoint. Therefore, by way of introduction to this symposium, I would like to discuss, albeit briefly, the many "hypotheses", essentially of a metaphysical nature, which are often used without being clearly stated.
The first hypothesis is the idea that the Universe has some origin, or origins. Opposing this is the idea that the Universe is eternal, essentially without beginning, no matter how it might change-the old Platonic system, opposed by an Aristotelian view! Or Pope Pius XII or Abbe Lemaitre or Friedmann versus Einstein or Hoyle or Segal, etc.
The second hypothesis is the need for a "minimum of hypotheses"-the simplicity argument. One is expected to account for all the observations with a minimum number of hypotheses or assumptions. In other words, the idea is to "save the phenomena", and this has been an imperative since the time of Plato and Aristotle. But numerous contradictions have arisen between the hypotheses and the facts. This has led some scientists to introduce additional entities, such as the cosmological constant, dark matter, galaxy mergers, complicated geometries, and even a restmass for the photon. Some of the proponents of the latter idea were Einstein, de Broglie, Findlay-Freundlich, and later Vigier and myself.
Very similar to the argument-or rather the postulate-of simplicity is the principle of beauty, a typical Pythagorean concept. A theory of the universe is not adopted because it is "true", but because it fulfills some religious views about the universe, or simply because it is beautiful. Such motivations are not considered scientific, and hence are usually disguised. When this is done, we pay less attention to saving the phenomena, and only concern ourselves with the internal coherence of the theory. One view often expressed by authors is that modern cosmology demands primarily coherence, not proof. We would instead say that coherence is necessary, but not sufficient. Examples of this approach are recent efforts to introduce the superstring theory of space, or to achieve a grand unified theory of forces, which is required not by facts, but by a quest for beauty.
A third hypothesis is the reduction of phenomena in order to save only some facts, which are deemed more important or more cosmologically significant. This hypothesis springs naturally from the belief that all facts in disagreement with a theory are of secondary importance-epiphenomena-that can be easily forgotten. In cosmology, this has led to a neglect of solar physics, even though we know that
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Foreword

solar physics has much to say about, for example, neutrinos, gravity waves, element abundances, etc. This reductionism also leads to ad hoc hypotheses, such as the "cosmological principle", according to which the universe is homogeneous and isotropic-a welcome notion when one is looking for "simple" or "economical" models. Even worse, assessing the "importance" of facts becomes a very subjective exercise, which can lead to a choice of fundamental data that differs from one author to another. For scientists devoted to the "old" classical Big Bang theory, the only items that count are the Hubble shift (which is interpreted as "expansion"), the background radiation (which is called "cosmological") and the abundances of light elements (which are called "primordial"). To scientists dedicated to what I shall call, for the sake of simplicity, the "new Big B~g", the inhomogeneous grouping of galaxies in the universe, the minute traces of inhomogeneity in an almost isotropic background radiation and the obvious young age of many galaxies are arguments that cannot be forgotten, any more than the age of the globular clusters. And finally, of primary importance to the anti Big Bang camp are the evidence of discordant redshifts, the hierarchical distribution of matter in space and the lack of any direct evidence for secular evolution over the last few billion years. Critical writers often assign such evidence greater weight than the three standard arguments offered in support of the Big Bang. Likewise, they tend to regard the background radiation field as not originating from the single, most distant visible shell in the Universe, and reject the notion that element abundances are in any way primordial.
In conclusion, I would issue yet another warning against any type of dogmatism that might give authors who adopt the above hypotheses (or at least some of them) a sense of security, or even certainty, justified only by coherence. As I pointed out earlier, coherence is not sufficient. There is some truth to each of these hypotheses: this is my own working hypothesis! Nevertheless, in cosmology, we are very far from penetrating to the depths of this truth. We must allow ourselves to be guided by more observations-especially of the phenomena now recognized as contradictory-for only observations can illuminate the way for the theoreticians as they strive to achieve a better description of the universe and to learn more of its secrets.
Jean-Claude Peeker College de France

Preface
The present volume contains the proceedings of the 13th Krakow Summer School of Cosmology, which was held in Lodz, Poland from September 7 to 11, 1992. The School was attended by more than 60 astronomers, physicists, students and amateurs. Krakow Summer Schools of Cosmology were originated in Poland by Professors Jan Jerzy Kubikowski, Konrad Rudnicki and Andrzej Zieba in 1968. They take place every second year and are organised in different locations. Their aim is to convey up-to-date, first-hand information about observational and theoretical cosmology to young scientists, graduate students and teachers, as well as to serious amateurs of astronomy, physics and philosophy. The Schools aspire not only to show the current, generally accepted views, but also alternative ones as long as they are based on reliable premises. The first Schools were local in character. Since 1978 they have become international. Each School is devoted to one selected topic. The 13th edition of the School was held under the auspices of Omega Foundation of Lodz and the astronomy and physics journal Apeiron.
To fully appreciate the contents of this volume, we must look back at least to the tum of the century, when a trend began in physics to invest the mathematical laws in which the book of nature had been written since the time of Galileo with an absolute stature, and to restrict the definition of physical reality to laboratory measurement and observation-in short, to reduce the objective world to a series of sense impressions. This trend, of which, ironically, Mach and his followers were among the chief exponents (it will be recalled that Einstein sought to distance himself from Mach's philosophical views), advanced to the point that physics soon found itself relegated to the status of a dialect of mathematics. It became fashionable to seek a single, revelatory equation to describe the Universe, an equation in which, inevitably, time-dependent terms would play a predominant role. Thus, the infinite and eternal universe of the presocratic Greek philosophers, in particular Anaximander, is supplanted by a mathematical cipher wherein the construct "space" is endowed with plastic qualities and mysteriously allowed to expand (or contract) the river of time is made to spring from a source outside of time (the primordial singularity in "spacetime"). So profound has the divorce between the current cosmological model and the empirical evidence become that modem cosmologists must invoke increasingly contrived epicycles ("something foreign and wholly irrelevant" in the immortal words of Copernicus) in order to preserve the Big Bang dogma.
In most textbooks on astronomy, the possibility that the universe might not
have had a beginning is excluded by the very definition given of cosmology. It is hardly surprising that the literature of modem cosmology, which presents the numerous helper hypotheses that have been grafted onto the Big Bang as the quintessence of theoretical acumen, has sought to depict efforts to frame an alternative to· the expanding universe model as a succession of farcical episodes: Einstein
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retracts his cosmological constant with an embarrassed mea culpa; Milne's kinetic cosmology is dismissed a curious fit of whimsy; Hoyle's early investigation of steady state cosmology earns him unrelenting ridicule. Virtually absent from the historical record are the flashes of brilliance that shine like beacons through the darkness of subsequent decades: de Sitter's prediction of "spurious Doppler shifts" in 1917; MacMillan's qualitative description of an energy-conserving static universe (ca. 1920); Eddington's near exact prediction of the 3° K background without expansion (in 1926, and similar work by Nernst, Regener and Finlay-Freundlich); Zwicky's gravitational drag redshifting mechanism (1929), favoured by Hubble as the most plausible explanation of his "apparent velocity" shifts; and de Broglie's quantum tired-light redshift proposal (1962), based on an interaction between the photon's "pilot" wave and the medium of its propagation-to name but a few. The present volume, dedicated to the memory of Fritz Zwicky, is the fruit of efforts to revive this tradition. It may be seen as a continuation of work published in two earlier collections: New Ideas in Astronomy (proceedings of a symposium held in honour of Halton Arp in 1987), and Festschift Vigier (papers presented at a workshop held in Paris in 1990, and published as a special issue of Apeiron).
Many of the papers presented at the 13th Krakow Summer School of Cosmology represented synthetic approaches to a new cosmological model. However, if a few general themes could be distilled from these contributions, the list might include the following: observational contradictions to the Big Bang and the expanding universe, alternatives to the Doppler interpretation of "cosmological" redshifts, problems associated with astrophysical sources and the intergalactic medium and alternatives to conventional theories of gravity.
Exhaustive treatments of observational contradictions associated with the Big Bang are given by Halton Arp, who raises the issue of redshift discrepancies in nearby galaxies and young stars (which show systematically higher redshifts than their older counterparts), Victor Clube, who argues that a newly discovered relationship between apparently diverse classes of object, viz. spiral arms and giant comets, poses grave problems for expansion; and Eric Lerner, whose paper focusses on the incompatibility between the Big Bang and current observations of light elements, as well as the ever-recurring "age of the universe" problem and the nearperfect isotropy of the microwave background. Two relatively recent-yet by no means insignificant-problems are raised by William Napier and Jack Sulentic. Napier presents a detailed account of his tests of the Tifft effect, which demonstrate beyond doubt that redshift periodicities are real, while Sulentic examines the incidence of discordant redshifts in compact groups of galaxies. Miroslaw Zabierowski investigates a hitherto unsuspected case of redshift quantization within the Local Group, and finally, Fred Walker notes that a small sample of spiral galaxies of the same morphological type and absolute magnitude might have the same apparent rotation velocity, contrary to what would be expected if galactic redshifts are due to expansion.
Alternative explanations of the Hubble law are put forward by Amitabha Ghosh, who introduces a velocity-dependent term in the gravitational force law; Eugene Shtyrkov, who suggests that the velocity of light changes as light waves travel through intergalactic space; and Thomas and John Miller, whose investigation of the de Sitter redshift-magnitude relation brings quasars in as close as intermediate-redshift objects. Discussions of specific astrophysical objects are found in papers by Peter Browne, who applies a magnetic vortex tube model to the problem of beams of ultrarelativistic charged particles in active galactic nuclei, and William

Preface

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Peter, E. Griv and Anthony Peratt, who indicate that the Alfven plasma model may explain radio lobes and extragalactic jets from classic double radio sources. Wieslaw Tkaczyk finds that the inhomogeneous spatial distribution of gamma-ray bursts may fit an unconventional cosmology; Svetlana Triphonova and Anatoly Lagutin present a unified cascade model for producing gamma-radiation in active galactic nuclei; and Bogdan Wszolek proposes that dust in the South Coma void may cause additional redshifting in light originating from galaxies beyond the void.
In addition to phenomenologically motivated modifications to the gravity laws proposed by Andre Assis and Amitabha Ghosh (by the addition of a velocity term to the Newtonian force law), David Roscoe discusses a Galilean invariant formalism for gravitational action. Franco Selleri interprets the equations of special relativity in the presence of a fundamental frame, while Henrik Broberg shows that particles can be described as locally confined systems of vacuum energy. Finally, comprehensive new cosmologies are presented by Toivo Jaakkola, whose equilibrium model takes as its point of departure a coupling between gravitation and electromagnetism, and Tom Van Flandern, who describes a universe model deduced from first principles.
Exciting progress is now being made in the subjects of episodic matter creation, understanding of the physics of non-velocity redshifts, the significance of quantized redshifts, more general solutions of the equations of general relativity and the workings of Machian physical laws. Perhaps we have reached the point where we can take on the ultimate challenge of relating the mysterious world of quantum mechanics to the realm of classical physics. It is clear by now that these seminal investigations will by carried out by a small number of researchers working outside the constricting assumptions of conventional astronomy and physics.
The crucial discoveries needed to break away from current dogma will only be communicated in alternative journals, conferences and books such as the present one, where investigators can speak frankly about the fundamental issues. The dissemination of such publications is important, and the future will show, we believe, that real progress depends on a more general and enlightened participation by a large number of people who are concerned with achieving better understanding of our universe.
The editors, on behalf of all the participants, wish to thank the local organizers Wieslaw Tkaczyk of the Physics Department, University of Lodz, and Mieczyslaw Borkowski, Director of Omega Foundation, for making all arrangements for the conference on the ground. We also wish to acknowledge the efforts of local organizing committee members Marcin Tkaczyk, Radoslaw Borkowski, Wojciech Blonski, Tomasz Gierka, Mariola Kubiak, Grzegorz Kociolek, Bozena Mirys and Leszek Wojtczak, as well as the staff of the Physics Institute at University of Lodz, whose dedicated work was crucial to the success of the conference. The material for the proceedings was prepared with invaluable assistance from Svetlana Triphonova. Finally, we would like to express our gratitude to Omega Foundation for generously providing funds for the event, to the participants for delivering excellent manuscripts and to Konrad Rudnicki for forging ahead against all odds.
Halton C. Arp C. Roy Keys Konrad Rudnicki

Contents
Fitting Theory to Observation-From Stars to Cosmology ............................. 1 HaltonArp
Redshift Periodicity in the Local Supercluster .................................................... 29 W.M. Napier and B.N.G. Guthrie
Compact Groups of Galaxies ................................................................................... 49 Jack W. Sulentic
Is there Matter in Voids? .......................................................................................... 67 Bogdan Wszolek
Redshifts and Arp-like Configurations in the Local Group ............................ 71 M. Zabierowski
Are the Galaxies Really Receding?......................................................................... 81 Fred L. Walker
The Case Against the Big Bang............................................................................... 89
Eric J. Lerner
De Sitter Redshift: The Old and the New............................................................ 105 John B. Miller and Thomas E. Miller
Equilibrium Cosmology............................................................................................. 111 Toivo Jaakkola
A Steady-State Cosmology........................................................................................ 153 A.K. T. Assis
Cosmological Principles............................................................................................ 169 Konrad Rudnicki
The Meta Model: A New Deductive Cosmology from First Principles....................................................................................... 177
T. Van Flandern
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Dark Matter, Spiral Arms and Giant Comets ...................................................... 187 S.V.M. Oube
Active Galactic Nuclei: Their Synchrotron and Cerenkov Radiations...................................................................................... 205
P.F. Browne
Computer Simulations of Galaxies......................................................................... 237 W. Peter, E. Griv and A.L. Peratt
Are there Gamma-Ray Burst Sources at Cosmological Distances?................ 249 W. Tkaczyk
Gamma-Ray Emission Regions in AGNs .............................................................. 259 Svetlana Triphonova and Anatoly Lagutin
On the Meaning of Special Relativity if a Fundamental Frame Exists .................................................................... 269
F. Selleri
Galilean Gravitation on a Manifold....................................................................... 285 D.F. Roscoe
Astrophysical and Cosmological Consequences of Velocity-Dependent Inertial Induction................................................ 305
Amitabha Ghosh
A New Interpretation of Cosmological Redshifts: Variable Light Velocity.................................................................................. 327
Eugene I. Shtyrkov
Quantized Vacuum Energy and the Hierarchy of Matter............................... 333 Henrik Broberg
Index............................................................................................................................... 353

Fitting Theory to Observation-From Stars to Cosmology

HaltonArp
Max-Planck-Institut fiir Astrophysik Garching bei Miinchen, Germany
A review of observational contradictions to the conventional interpretation of redshifts as velocities includes new discrepancies in nearby galaxies and also in the young stars they contain. It is established that the strongest empirical relation is between the redshift and age of an object, and that velocities are not significant factors in cosmic redshifts. Expanding universes are, therefore, excluded.
As an example of how a successful theory must incorporate all observational facts, I describe a more general solution of the equations of general relativity. In this solution we do not make the special case assumption that the mass of elementary particles is constant. We solve the more general case where mass is variable, the case which, a priori, is more likely to apply to the universe as a whole. We discuss how this theory predicts all the currently accepted astrophysical observations as well as the "forbidden" data which violate current theory.

Nearby Groups of Galaxies

The current theory of the Big Bang rests entirely on the interpretation of displacements of lines of elements in the spectra of small fuzzy spots in the sky called galaxies. But if we investigate the nearest galaxies to us, the ones we can resolve in detail (and, therefore, know the most about), we immediately encounter irreconcilable contradictions with the expanding universe theory. Figure 1 shows the redshifts of all the major companions relative to the redshift of their dominant galaxy in two of the nearest groups of galaxies. H the redshifts of the companions are due to orbital velocity around the central galaxy, there should be as many negative as positive spectral shifts. Instead, 21 out of 21 of these companions are redshifted positively. This has one chance in two million of happening accidentally and, therefore, proves that these companion galaxies have intrinsic, excess redshifts. (Arp 1987).
There is surprising news, however. A new member has been recently added to our Local (M31) Group. After a lengthy delay, it has been decided that IC342, seen through considerable absorbing material at low galactic latitudes in our own galaxy, is really within the confines of our Local Group. Our Milky Way galaxy is about 0.6 Mpc away from M31. On roughly the other side of M31 from us, IC342 lies about 1.2 Mpc distant from M31. (Madore and Freedman 1992, McCall1989). But this galaxy counted among the M31 Group, as shown in Figure 1, has the highest redshift of all presently accepted Local Group members: c!J.z- +289 km s-1!

Progress in New Cosmologies: Beyond the Big Bang

Edited by H.C. Alp et al., Plenum Press, New York, 1993

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= Figwe 1. Relative redshifts (Az km s·1 ) of all major companion galaxies in two nearest groups
of galaxies. The dominant galaxies in the two groups are M31 (Local Group) and M81 in the
next major group. N represents the approximate number of objects.

·100

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Figure 2. Residual redshifts of nineteen galaxies known to be companions of large galaxies. This announcement of the systematic redshift of companion galaxies appeared in Nature in 1970 (Vol. 25, March 14 1970). The significance then was about one part in a few thousand. Now that the significance has grown to about one chance in 4 million, the effect is not discussed in major journals. (Figure excerpted from Field, Arp and Bahcall1973).

Fitting Theory to Observation

3

The chance now becomes 1 in 4 million that companion galaxies do not have intrinsic redshifts! It is important to note that in 1970, excess redshifts in companion galaxies were routinely announced in Nature magazine, as shown in Table 1 and Figure 2. The significance was then already a part in a few thousand. This result was confirmed by Bottinelli and Gougenheim (1973) and Jaakkola (1973). An independent investigation by Collin-Souffrin, Peeker and Tovmassian (1974) also supported the result, and yielded the important correlation that compact companions tended to be more systematically redshifted than lower surface brightness companions. Today, when the effect has grown to overwhelming significance, there is little likelihood the results and their implications will be discussed in the major professional journals. Establishment astronomers often argue that discordant redshift evidence has had the opportunity to be published and read, but the judgment of astronomers was that it was not significant and, therefore, not worth further discussion. The truth of the matter is that as soon as the consequences for conventional theory were realized it became rapidly more difficult to communicate the evidence. As the evidence grew to overwhelming proportions, discussion shrank to the vanishing point.

Table 1. Differential redshifts in companion galaxies (as of 1970)

Dominant galaxy M31
M81
NGC 5128
M51 Atlas 48 Atlas 58 Atlas 82 Atlas 86 Atlas 87 • Corrected later to +57 (km s·').

Companion galaxy
M32 NGC 205 NGC 185 M33
M82 NGC 185 NGC 3077 IC 2574 HOII
NGC 5102 NGC 5236 NGC 5253 NGC 5068
NGC 5195 Companion Companion Companion Companion Companion

Differential redshift (km s·1)
+85 +62 +58 +57
+234 +58 -104* +91
+215
+77 +64 -42 +139
+109 -120
+60 +90 +23 +180

As a result, younger astronomers are not aware of the fact that companion galaxies are systematically redshifted, and they try to apply completely incorrect dynamical calculations to their data (which show the effect also). One of many examples of this can be seen in a paper by Vader and Chaboyer (1992).
The systematic redshift of companions, of course, has now been established in every group tested out to the limit of applicable redshift surveys; Arp and Sulentic (1985) measured over 100 galaxies in more than 40 different groups with

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Figure 3. The number of companion galaxies as a function of their redshift with respect to the central galaxy (From Arp and Sulentic 1985). The preferred values of redshift previously found in independent galaxy samples by W. Tifft are marked by arrows.

the Arecibo radio telescope and tested a total of 160 galaxies in groups with dominant galaxies as faint as apparent magnitude 11.8. Overwhelming evidence was found that the companions are systematically redshifted, as shown in Figure
3. Later M. Geller and J. Huchra at the Center for Astrophysics (CFA) tested their
surveys and reported no effect. R. Brent Tully also reported no effect in groups he had picked out. But when a team of astronomers from Trieste (Girardi et al. 1990) analyzed this same Geller-Huchra and Tully data, they found a strong confirmation of the systematic redshift excess of companion galaxies in groups. Figure 4 here shows the significance of their excess numbers greater than velocity difference zero for the Geller-Huchra (GH) data.
It is instructive to note that even though Girardi et al. proposed an explanation that avoided intrinsic redshifts, their paper still had enormous difficulty getting published. Theirs was one of the two "conventional" explanations advanced for the phenomenon. One proposed model had companions expanding away from the central galaxy and our cone of vision intercepting more on the far receding side
than on the near approaching side. The other model had companions falling toward the central galaxy and being hidden by dust on the far, approaching side. Aside
from the disaster for the observed stability of groups, these models were obviously
hopeless from the outset, in the sense that they predicted large numbers of hitherto undiscovered Local and nearby group members. It was indeed ludicrous to consider that any large, low redshift galaxies had remained undiscovered.
Of course, to accept the obvious conclusion from these empirical results meant that the redshift of the companion galaxies was an intrinsic property which overwhelmed the spectral shifts due to true, Doppler velocities. In this case there would be even less than zero evidence for systematic velocities of galaxies in general, and hence no evidence that the universe was expanding. The Big Bang

Fitting Theory to Observation

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Figure 4. Geller-Huchra groups. The blueness of the companion galaxy is shown to be correlated with the amount of its excess redshift in this diagram from Girardi et al. (preprint and 1992).

would be devastated. Clearly this latter the consequence has caused the data to be swept firmly under the rug.
A particularly striking example of how the observational data is misinterpreted is provided by a recent paper by Zaritsky (1992) and particularly a paper by Dennis Zaritsky, Rodney Smith, Carlos Frenk and Simon White (1993). The last author is a researcher on the hypothesis of unseen matter working at the Institute of Astronomy in Cambridge, England. In this latter paper, they survey what they call satellites around isolated spirals of type Sb-Sc and perform dynamical analyses which lead to the conclusion "... that isolated spiral galaxies have massive halos that extend to many optical radii."
Although a total of 16 Figures were presented in their paper, the critical data which showed the differential redshift of the companion galaxy as a function of its relative faintness was not plotted. This figure shown here as Figure 5 was plotted from the data which these authors tabulated. It is immediately apparent that, excluding the obviously distinct set of very faint 4.5 < bomb < 7.2 mag companions, the remaining companions of appreciable mass and luminosity are systematically shifted to higher redshift. This is conspicuous even though they have arbitrarily excluded companions brighter than b.mb < 2.2 mag, a class of companions in which objects like M82, connected to M81 with a hydrogen bridge, has an excess redshift of +288 km s·1• Of course, doing dynamical analyses with redshifts which do not represent velocities does not lead to meaningful results.
The most startling aspect of this study is, however, the fact that the authors do not reference even one of the eighteen independent studies from 1970 onward that

6

HaltonArp

----------•·•-----------eo----oo-<-o -•----------------------

0

ol

Boo

0

I • -a .. • o• 00

... 0 0

0 .o

0.

0

0• °
0

0

. ..oOO

•
• ••

II•

•
0

~

•

•

0 10 '

•

0

0

•

Figure 5. Data on "satellite" galaxies from Zaritsky et al. (1992). Filled circles are low surface
= brightness dwarfs of de Vaucouleurs Type 9-11. Two extreme and undefined objects classified
T 15 are indicated by parenthesis. The authors arbitrarily excluded objects classified companion galaxieS brighter than t.m• < 2.2 mag. One can again clearly confirm, however, that the major companion galaxies are systematically redshifted relative to the dominant galaxy in the group.
established the systematic redshift of companion galaxies. (Most of these references are available, for example, in Girardi et al. 1992). Their new data again confirms the effect but they ignore this confirmation as well as all the previous documentation of the excess red.shift phenomenon in companion galaxies.
What appears to be the actual situation is that younger galaxies are created in or near the centers of older galaxies and are expelled as intrinsically higher redshift galaxies into the near neighborhood of their parent. As the companions emerge, they entrain some pieces of the parent galaxy with them, and these small pieces have the same age and intrinsic redshift as the older galaxy. These are the very low surface brightness dwarfs which are several hundred times less luminous than the parent galaxy. The actual, more recently created major companions (as they are always referred to in my published analyses) are of the order of 10% of the luminosity of the main galaxy and are not all in the class of tiny pieces tom off the original galaxy. Considering the small mass-to-luminosity ratios of these low surface brightness dwarfs, they become even more negligible compared to the mean mass exterior to the parent galaxy which shows such clear cut systematic redshift.

Fitting Theory to Observation

7

Physical Correlations with Excess Redshift
If we ask the natural question, ''What is observationally different about the companions compared to the central, dominant galaxy?" we immediately realize that although they are both made up of the usual stars, gas and dust, many of the companions have a relatively larger percentage of younger, hotter stars. This can be strikingly seen in the extreme excess redshift companions NGC404 and M82. Their spectra are dominated by Hydrogen Balmer lines in absorption, characteristic of stars of evolutionary age 108 to 109 years rather than older stars of 1010 years age. Such stars are hotter and, therefore, bluer. This younger stellar content is confirmed by the effect seen in Figure 4 where the excess companion redshifts increase with blueness.
In fact, the blueness-redshift excess correlation is seen all the way from the smallest to the largest excess redshifts. Compact blue, peculiar and active galaxies show redshifts in the 1,000 to 10,000 km s"1 excess redshift range. In tl:te case of the largest excess redshift quasars, they are so energetic and compact that they must expand quickly from their observed state and, hence, must be dynamically very
young. The consequence of this is very important, namely: empirically the cause of the intrinsic redshift is something related to age.

Quantization of Redshifts
There is another clue to the nature of non-velocity redshifts, viz. the tendency for extragalactic redshifts to occur at certain preferred values. W.G. Tifft in 1972 pointed out the tendency for redshifts to be periodic or quantized. In spite of enormous disbelief and ridicule, every succeeding test has confirmed and strengthened
the result. For example, Figure 3 in the present paper shows a test by H:.Arp and J.
Sulentic in 1985 of a completely different set of galaxies with the tnost accurate redshift measured to that date. The previously predicted peaks at 72 km s"1 intervals stand out conspicuously.
In 1967 G. Burbidge and E.M. Burbidge pointed out the existence of preferred redshifts for quasarS. In 1971 K.G. Karlsson showed they obeyed the mathematical
= formula ~ln{l+z) 0.206. Many investigations confirmed this, but one of the most
recent (Arp et al. 1990) found a confidence level of 99.97% for the existence of the
periodicity. It is instructive to note that a young postdoctoral student, then at the Institute
of Astronomy in Cambridge, England where the director is Martin Rees, rapidly published a paper titled "Against the ~ ln(1 +z):; 0.205 Periodicity in Quasar Redshifts" (Scott 1991). The most complete sample available, the 3CR radio quasars, he claimed, showed no periodicity. Yet both he and the editor of the journal were
shown plots where three of the periodicities, z =.60, .96 and 1.41 were conspicuous.
In this and other samples, he included the faintest apparent magnitude, most uncer-
tain and probably the most distant quasars, the same quasars which Arp et al. had shown did not exhibit the periodicity. Finally, in a new sample of bright X-ray
quasars he again found the periodicity, but ventured the opinion that it would go
away with further measures (i.e. fainter quasars). He ended his paper with the
statement: "The conclusion is, there is no evidence for such a periodic structure."

8

HaltonArp

This is a useful example to cite because it well characterizes how observational evidence which is contrary to the current assumed model is misrepresented.
In the redshift ranges intermediate between the bright galaxies and the quasars, pencil beam surveys in various directions in the sky also reveal dumping of redshifts. (Broadhurst et al. 1990). The investigators, after considerable delay, rather nervously announced this result, but only after turning the redshifts into distances via the assumed redshift-distance relation. They concluded the galaxies were spaced periodically apart by about 128 Mpc. Now, it is a cardinal rule of observational science that one should report the observed quantities which, in this case, were redshifts. To obtain this primary data, however, I had to go to their graphs to read off the measurements, the preferred redshifts. It can be seen in Figure 6 of the present paper that two of the preferred redshifts agree with quasar peaks. The peak at z = 0.3 for galaxies is also conspicuous by casual inspection wherever one looks at galaxy redshifts in the literature. This is as it should be because quasars and galaxies are extragalactic objects which are continuous in their physical properties. What this agreement does, then, is give an independent confirmation of two of the quasar quantization peaks. It also demonstrates that the whole realm of measured redshifts-from the smallest to the largest-is quantized. Redshift is a physical property which comes in discrete, periodic quantities from the highest redshift, large periodicities to the lowest redshift, small periodicities. This property is schematically illustrated in Figure 6.

QUASARS

Alnll•zl =0.205

II I

I

I

I

I

I

.06 .30 .60 .96

Ul

........

I ........

I - ........

1.96

2.64

3.47

..........

I

........
........

l

........ ....... GALAXIES

I

I

.06

.12

" " " ""' L I I I I

72 144 216 288 Km-s-1

I

I

I

.18

.24

.30

GALAXIES IN GROUPS
lz =0.0002n ~

Figure 6. Periodized .l"edshifts: Redshifts from the highest (quasars) to the lowest (differential
redshifts between galaxies in groups) show preferred, i.e. quantized values of redshift.

As for the low redshift, small periodicities, it is very important to note that analysis, first by Tifft and then by Arp showed that the redshifts of the galaxies in the Local Group were quantized in 72 km s-1 steps. In the Arp (1986) analysis of the redshift, the periodicity obtained was 72.4 km s-1 • Now four intervals of this peri-
od would be 4 x 72.4 = 289.6 km s-1• But, astonishingly enough, the galaxy just

Fitting Theory to Observation

9

added to the Local Group, IC342, has the largest excess redshift with respect to M31 and it is observed to be 289 km s·1• In general, hydrogen redshifts are accurate to ±8 km s-1, but since IC342 is so large and nearby, its HI redshift is probably much more accurate, so the agreement with the predicted periodicity is even more impressive.
Finally, the evidence obtained by W. Napier and B. Guthrie on the smallest quantization interval of "'37.5 km s-1 as reported by Napier in these proceedings is the most powerful of all the quantization evidence. In all directions in the sky up to redshifts of 2600 km s·• he finds galaxies quantized in this small interval of redshift with enormous significance. The most important consequence of the observation is that real velocities of galaxies cannot average much more than about 20 km s·1 because, projected at random angles to the radial line of sight, they would wash out the 37 km s·1 quantization.
Again, we have evidence that extragalactic redshifts have negligible connection with velocities, and that we must look for a cause of intrinsic redshift which is physically related to the age of the object and which can be quantized.

Intrinsic Redshifts in Stars
If galaxies in our Local Group have excess, non-velocity redshifts, we should be able to ask whether some parts of these resolved galaxies show more excess redshift than others. In fact, we have predicted that excess redshift is correlated with younger age, so it is appropriate to look at the youngest stars in these nearby galaxies. This is easy to do because the youngest stars are the highest luminosity supergiants. (After a few million years they bum away to become much fainter stars.)

SMC
I
I

No.

150

200

250

LMC
I

.. . No.

I
•t -

.-c .. "'·..

•

••

0

0

250

300

350

400

450

500

IRVI0 kms·l

Figure 7. After correction for velocity of mass loss in each individual star, this best measured sample in the Magellanic clouds shows almost every supergiant has redshift higher than the mean redshift of its galaxy.

10

HaltonArp

In the Large and Small Magellanic Cloud (LMC and SMC) individual supergiants have been well observed by now. Just looking at their redshifts shows that they are indeed systematically higher than the mean of the rest of the material in the galaxy. In fact, the confidence level of just this first order result is at the 99.8% level.
But now we must realize that supergiant stars have tenuous atmospheres in which the radiation pressure from the star propels mass outward in a so called "mass loss wind." This is standard knowledge in astrophysics and this negative velocity coming toward the observer in the absorption lines which overlie· the bright photosphere must be corrected for in order to get the true systemic spectral shift of the star. In practice, the effect has been ignored because it makes the excess redshift of young stars even more excessive.
If we correct the reported spectral shifts (always incorrectly called radial velocities in the literature) for these negative outflow velocities, we find that almost every supergiant star in both Magellanic Clouds has an excess redshift relative to the well determined mean spectral shift of the remaining stars and gas in the galaxy. This is shown here in Figure 7.
Does this result hold for the nearest galaxy of all, our own Milky Way system? Indeed it does, and it has been known since 1911! But the hot, young stars in our own galaxy cannot all be exploding away from us in every direction we look. If this empirical evidence had been heeded, the assumption that redshifts meant only velocity would never have been made, and the conclusion that the universe was expanding would not have been promulgated to the public for more than 60 years.
How good was the contradictory evidence during all these years? After W.W. Campbell announced the "K effect" in 1911 from the first systematic spectroscopic measures of bright stars, the effect has been confirmed over and over again. A few sample determinations are shown in Table 2 here (Table excerpted from Arp 1992b).
Just to illustrate the effect in one case, I show here in Figure 8 the measured spectral shifts for the supergiants in the largest, most conspicuous young star clusters in our own Milky Way Galaxy, h + X Persei. It is clearly evident that the excess

Table 2. Excess Redshift (K-Trumpler effect) in our Galaxy

Stars
B stars OB stars in Gould's Belt 0 stars in Clusters (re B's) B stars in Orion 0 stars in Clusters
Supergiants in h + X Per
Supergiants in Assn's Single 0 stars 0-type binaries 0-type binaries Cluster/assn's O's Field O's Runaway O's
For references, see Arp (1992b).

cllz
+4.7 ± 0.02 +5
+10 ± 1 +11.4 ± .2 +17.6±:5
+15 +15 +0.6 ± 1 +8.5 ± 1 +2.0 +1.8 +6.4 +21.9

Reference
Smart and Green 1936 See Frogel and Stothers 1977 Trumpler (1935; 1956) Findlay-Freundlich 1954
Present paper
Conti eta/. 1977
Gies 1987

Fitting Theory to Observation

11

-20 RAD.VEL. IKM/SECl
l-30
-40

t H
t 0

h•X PERSEI
'!

-50

-8.0

-7.0

-6.0

-5.0

Mvlmag.)

z Figure 8. The points show measured spectral shifts (in km s·1) in the supergiants in h + Per-
sei, the largest, young star clusters in our own Milky Way Galaxy. The figure demonstrates the
increasing redshift as the stars become more luminous (hence evolutionarily younger).

redshift increases with increasing luminosity for stars in the same physical cluster. Of course, the increasing luminosity is quantitatively calculable in terms of the
younger evolutionary age of the stars·. So, again, we have the empirical result that the excess redshift increases as the age of the material decreases.
Roberta Humphries, whose data was plotted in Figure 8, was asked to comment on the excess redshift effect which it showed. She never answered. The detailed, documented analysis of all evidence for systematic redshift in young stars
was submitted to the European Journal, Astronomy and Astrophysics. The editor,
James Leqeux, himself an expert on bright stars in the Magellanic Cloud, forwarded a derogatory referee's report and refused to publish the data. He also did not allow the results to be orally presented at a nearby meeting specifically concemed with the Magellanic Clouds.
After some years' delay, however, the publication of the detailed analysis has
now been entered in the record (Arp 1992b). The detailed data which shows that the
most luminous stars in the three galaxies we know the most about-the Milky Way, Large and Small Magellanic Clouds-have excess intrinsi~ redshifts can now be referred to if anyone so desires. Naturally, we would like now to extend this a little further and ask what is revealed by the next nearest galaxies, where we can still tell

Note on the ages of stars: Evolutionary age means time since the star ignited after, on the conventional view, collapsing from an extended gas cloud. The conventional assumption is that the prestellar material was all created at the same time. But if some material were created more recently, stars made out of the newer material by the usual process would be "younger" than the rest. Stars from the older material would have burned through the supergiant phase, on the average, already, and the brightest stars would, therefore, be preferentially from the younger material and, on our interpretation, of systematically higher redshift.

12

HaltonArp

Table 3. Excess Redshifts of Luminous Stars in Nearby Galaxies

Galaxy
Milky Way LMC SMC NGC 1569
NGC 277 NGC 4399 M31 M33

Kind of Stars
z h + Pers.
supergiants
A B
early integ. spectrum
irreg. blue vars.

K-effect
+(7) km s-1 7
17

Mass loss correction

Total excess redshift cllz

+29 km s-1 +22 +17

(+36) km s-1 +29 ± 6 +34 ± 8 >+36±17 >+35 ± 22 >+21 ± 8 >+25 ± 15
(+100) >+21

something about individual stars. The results of this investigation are given here in Table 3.
It is striking to note that even though we cannot make the corrections for mass loss in these more distant systems, the measured excess redshift is significantly positive and comparable to the amount measured in the three nearest galaxies. A pertinent comment is that stars with chemical compositions which contain fewer metals feel less radiation pressure and, therefore, have lower velocity mass-loss winds. This can be seen empirically in the fact that the SMC has a smaller mass-loss wind correction than the Milky Way and LMC. The four systems immediately following the SMC in Table 3 appear young, thereby, presumably, suffering less metal enrichment, and may tum out to have rather lower mass loss corrections when they are. eventually measured. But they all, as they stand, represent lower limits to the total excess redshifts of the younger stars.
At the end of Table 3 are listed irregular blue variables in M31 and M33. These are very luminous, blue stars which have been known since Hubble's time. The absorption line redshifts (again from Roberta Humphries) are used to derive the excesses in Table 3. It is astonishing that such large redshift discrepancies have gone unremarked for such a long time. The redshifts used in Table 3 are absorption line redshifts and, therefore, have an unknown component of negative mass loss velocity in them. Spectral shifts derived from emission lines, however, should refer to regions outside the line of sight to the photosphere and be much less prone to approaching wind corrections. It is of great interest, then, that Dr. Otmar Stahl, Heidelberg, privately communicated to me his emission line spectral shifts for three of these irregular blue variables.

Table 4. Emission Line Redshifts of Some Irregular Blue Supergiant Variables

star
M31 AE M31 AF
M33 Var C

cz (emission)
-217 km s-1 -282 -117

Az (excess redshifts)
+80 km s-1 +15 +63

Fitting Theory to Observation

13

Again, the star average is surprisingly large compared to their galaxies. (They are not corrected for rotation of the galaxy to which they belong so we can only rely on their average.) In the case of M31, however, we should remember that M31 has an intrinsic blue shift of about -86 km s·1 when viewed from our own galaxy. The~;efore, an M31 star of an age e~ual to the mean age of one of our own stars would have immediately a +86 km s· excess with respect to M31.
When all the measures that should be done on these systems are finally done, one could reasonably expect that, with the exception of M31, the excess redshift of the luminous stars would come out near 37 km s·1 • That is the empirical suggestion of the values so far in Table 3. This is an important number because, as the discussion earlier on quantized redshifts showed, the most significant, empirical peak in redshifts is close to 37 km s·1• The appearance of this quantization value in galaxies reinforces the finding of the same period in stars. If we say that stars are created periodically at intervals of 3 x 106 years, then their redshifts should group 35 km s·1 apart (see later discussion on redshift-age formula).

The Case for Intrinsic Redshift-Age Relation
So far we have investigated the closest galaxies to us and the brightest stars in them. We have found incontrovertible evidence that very little of the galaxy redshift can be due to velocity. We have found that the intrinsic redshift of the galaxy increases as the proportion of young stars it contains increases. Then we have found the youngest, most luminous stars themselves, individually, have intrinsic redshifts which increase generally with the relative youth of the stars. These represent so many independent kinds of determinations on so many independent systems that there would seem to be scarcely any reasonable doubt left that a major cause of extragalactic redshifts is intrinsic and age-related. At this point, before we see whether such observations could be incorporated into the laws of physics as we presently understand them, we should say a few words about tired light.

Tired Light Mechanisms
The plausible arguments that photons on their voyage through space must lose at least some of their energy and suffer a redshift has been made by so many people for so long that I will not attempt to review the subject here. But I will argue the case that the dominant cause of systematic redshift we see in extragalactic objects must be due to some intrinsic property of the material in the object and not to intervening material.
The argument is simply that there are cases of high redshift galaxies and quasars seen interacting with low redshift galaxies (Arp 1987). Because both objects are at the same distance they are seen through the same optical path length and, therefore, their redshift difference must be intrinsic. Even if one postulates a special interacting medium around the high redshift object, one should see gradients of redshifts and occultation effects when different redshift objects intermingle (Arp 1990). Observationally, however, one always sees just discrete sets of redshifts.
In the end, we may eventually be able to observe tired light effects as a higher order effect once the large discordances, which, I believe, are caused by age

14

HaltonArp

differences, are corrected for. The most straightforward way of doing this would be to study the redshift behavior of similar kinds of objects as they are viewed through increasing amounts of galactic material at lower and lower galactic latitudes. Multiparameter analyses of catalogued redshifts, apparent magnitudes and diameters and object types with galactic and supergalactic latitudes should be able to demonstrate effects of tired light or set quantitative upper limits on the mechanism.

A Theoretical Basis for a Redshift-Age Formula

If we consider a homogeneous, Euclidean universe in which the mass of a
subatomic particle, m,, varies as the amount of "gravitons" it can exchange with
particles within its light signal sphere, then:

m Jct

4nr2dr L2

r ex
p

--cx~-

(1)

0

Since the energy of a photon emitted from an atom varies as the mass of the

electron making the orbital jumps, then the wavelength A. varies inversely as the

electron mass:

·

(2)
and the redshift, z, varies as:

t: 1+z1 _ t~
1+z0 -

(3)

where z0 is the redshift of matter created t0 years ago and z1 is the redshift of matter created t1 years ago.
From this· basic formula (3), the redshift of any galaxy or quasar can be calculated from its age since creation (Arp 1991).
The fundamental step in this derivation is the assumption that inertial mass is
induced by interaction with an other visible masses as a 1jr law. Qualitatively this
is Machian physics. But does this satisfy Einsteinian physics? Following Narlikar
(1977) we can write the GR field equations as:

~miRa:-~g~)=-3Tik +m(Dmgik-m;ik)
+{m,;mk -~m·lm,,gik) (4)
Dm+1-Rm=N 6

We see straight away that a solution for these equations in flat space time is given by the Minkowski metric with the mass function:

m=af a=constant

(5)

Fitting Theory to Observation

15

Now, there is a great advantage of this solution over the usual solution. The usual solution is due to A. Friedmann in 1922, who assumed the mass of elemen-
tary particles was constant, i.e. m-:t m(r, t). This assumption was natural in terrestri-
al laboratories and perhaps fine for the local solar system. But did it make any sense cosmologically? If there was only one particle in the universe what would its mass be? In any case the solution in which mass could vary as a function of spacetime coordinates is much more general and, therefore, to be preferred. Scientifically, it is much better to find the general solution first and later make simplifying assumptions if conditions warrant.
The Friedmann solution, of course, led to the expanding universe, as embraced by Einstein, Eddington, Le Maitre et al., where the radius must change as a
function of time. But our solution leads to a nonexpanding universe where, for galaxies born at the same time, the look-back time to distant galaxies reveals them at a time when they were younger than our own galaxy Therefore, they appear to have an intrinsic redshift which is proportional to their distance (Narlikar and Arp 1992). This gives an exact Hubble law-much better than the expanding universe solution in which currently supposed peculiar velocities could and should destroy
the tightness of the observed redshift-distance relation. Therefore, our more general, non-expanding solution gives a better fit to the fundamental Hubble relation which originally gave rise to the conventional Big Bang interpretation.
In another important aspect our more general solution is vastly preferable,
viz. the singular points in spacetime where physics completely breaks down in the
usual m = const. treatment of the field equations. For our moc t2 solution the
particle mass must pass through zero. There the m = 0 hypersurfaces, Kembhavi (1978) showed, are just the old spacetime singularities that embarrass the Fried-
= = mann solution. Moreover m 0 just at t 0, is the natural creation point for the
mass particles. We no longer have an unexplained, ad hoc creation for all matter at
an arbitrary instant as in the Big Bang-instead we have continuous creation possible throughout spacetime. Finally, when passing through m = 0 we pass from m2 < 0 to m2 > 0, that is, from the quantum mechanical realm to the classical physics realm (Khlatnikov 1992). We will comment later on the conclusion from the observatio:p that the quantization in redshifts could only be accounted for by imprinting at the
= m 0, quantum mechanical domain of the creation point.

Quantitative Predictions of the New Theory
From the standpoint of the universe, if we could watch the history of a galaxy run backward in time, we should see the masses of its constituent particles diminish as it approached its origin. Now the rate at which atomic time runs is dependent on the mass of its particles (mp). Since m was smaller in the past in this galaxy, time ran slower. The amount of universal time (t) elapsed in an interval of the galaxy's time (-r) is:

e

' Z "3=t~-

(6)

= = At the origin, t t0 and 'Z" 'Z"0 , giving:

16

HaltonArp

t

1'o = .J!.

(7)

3

Differentiating our redshift·age formula of (3) with respect to At yields:

Ho=~-··2·-

(8)

3-ro

where H is the Hubble constant at z;: 0.
Details of this derivation can be consulted in Arp (1991). But the upshot is that for a flat spacetime, homogeneous universe (the most reasonable starting approximation) we obtain the same expression for the Hubble constant that was obtained
in the conventional solution of the equations of general relativity. That is not
surprising, since our solution with moc t2 is simply a conformal transformation of the usual solution-i.e. it is mathematically the same-only the physical interpreta-
tion is completely different. We can then compute what the Hubble constant, H 0 , must be from the age of
our galaxy (-r0). As customary, the age of the oldest stars is assumed equal to the age of our galaxy. We obtain:

17 >fo >13x 109 yrs. 39 < H0 <51 km s'1 Mpc'1 42 <H0 <56 km s'1 Mpc"1

observed age of galaxy H0 predicted by (8) H0 observed

600
vo
lkm/sec)

4000

2000-

: .. . .
. . . ... · . . '~ ...
. . · . ........ .·:...--
. .. ~ • Jl•_.....-'

.................

.......--···

15

30

45

60

75

drF IMpel

Figure 9. Distances (dTF) from Tully-Fisher estimates of rotational mass, luminosity and apparent magnitude of spiral galaxies are plotted against measured redshift (in km s"1). The redshiftdistance relation for low redshift galaxies is accurately H0 = 50. At higher redshifts younger galaxies are encountered which have intrinsic redshifts and give higher values of H0 •

Fitting Theory to Obseroation

17

The astonishing result is that the application of equation (3), required for galaxies whose intrinsic redshifts are a function of their age, leads to a Hubble constant which is, within the observational uncertainties, numerically equal to that observed. The advantage of our variable mass solution over the expanding universe solution is, however, that our formula predicts the observed Hubble constant with only one observational parameter and has no possibility of adjusting the predicted value, as the Big Bang does, by changing the geometry of the universe or introducing repulsive cosmological constants.

Discordant Values of the Hubble Constant
It is well known that a fierce struggle has been going on for many years
between advocates of the H0 =50 and H0 =80 to 100. The evidence on both sides
is so persuasive that one might suspect that both sides are correct, observationally speaking. How could this be?
Figure 9 shows the best redshift-distance relation available for spiral galaxies. Here the masses are estimated from rotation speeds of the galaxies, luminosities estimated from the masses and the distances estimated from the difference between apparent magnitude and absolute magnitude. These ''Tully-Fisher" distances are, therefore, somewhat independent of the systemic redshifts of the galaxies to which they are being correlated. One sees immediately that nearby (say inside the distance of the Local Super Cluster, at about 15 Mpc from our Local Group of Galaxies), rather accurately, H0 =50. But at greater distances one derives greater H0 's.
In the Big Bang there is supposed to be only one expansion speed over such relatively small regions of the universe. Obviously, Figure 9 shows this is not true. What our redshift-age, equation (3), requires, however, is that all galaxies the same age as our own should give a linear redshift-distance relation with H0 =50 km s·1 Mpc·1• This is true, as the measures in Figure 9 show, out to a distance of about 15 Mpc from our Local Group. Beyond this distance, however, if there are galaxies younger than our own, they will have excess redshifts; and this is exactly what is shown by the higher z spirals.
So we conclude that the faction claiming H0 =80 has more accurate distances
and redshifts to galaxies in a larger volume of space than the side which claims 50 throughout. But both sides refuse to acknowledge that in reality, the value of H0 increases from low redshift samples to samples which include high redshifts. Actually one can get any H0 one wishes by choosing a particular kind of galaxy to measure it with. For example, in our Local Group IC 342 would yield H0 = 161. The only solution to this absurd situation is the one given by our general solution to the Einstein field equations where the universe is not expanding and the redshift reflects the relative age of the galaxy we are viewing.

H0 and the Virgo Cluster
A key object in the determination of the value of the Hubble constant, and, therefore, a bone of contention between both sides, is the mean redshift of the Virgo

18

HaltonArp

Cluster at its correct distance from us. Table 5 below is extracted from Arp (1988), and shows that in all three of the relevant parameters, the two sides have adopted values which either maximize or minimize their resultant H0 •

Table 5. Determination of H0 from the Virgo Cluster

Mean redshift lnfall to Virgo Distance

Author

967 km s·1 1165

220 km s·1 250

21.6 Mpc 15.0*

55 Tammann and Sandage (1985) 94 de Vaucouleurs (1982)

* Distance to S cloud, on de Vaucouleurs precepts the E"cloud" would be closer.

Rigorously, even if one believes redshifts should be interpreted as velocities, the above adopted mean redshifts are both incorrect. That is because the mean
redshift should refer to the redshift of the average mass in the Cluster. The luminos-
ity weighted mean is only 863 krn s'1• (This is still an overestimate because it is derived from the blue luminosity, not the red luminosity). What the conventional procedure does is overweight the galaxies of small or negligible mass in deriving the mean redshift. Naturally, this yields too high a redshift. It is the same result we got in 1970, as reviewed in the beginning of this paper; the companion galaxies have systematically higher redshifts than the dominant galaxies. The size of the effect is even the same, 100 < Lkz <300 krn s·1•

a
2000kms-l o•< DEC <30°

.. . .
. . ••• .lr
1000kms·l

VIRGO CLUSTER

+

+

:

+
t+_, ;.

"+

·~

..···!..,

+

+........ +

··.·"'

+ •
..
. .+' +

...... ·. :· !

. . ....

+ '+-i,·

. ........ '~....

.,. t..,.

.,..,..,.• .,.\.:

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.. . ..... ._.+.,.·....

•
.

•

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+

2000km s-1

Figure lOa. The distribution of redshifts in the Virgo direction in the sky. Data from revised Shapley Ames Catalog (Sandage & Tamman 1981). Size of symbol according to apparent brightness of galaxy.

Fitting Theory to Observation

19

b
No.

-600

0

No.

VIRGO CLUSTER 11h30m< R.A.< 13h3om

-L

0'< DEC< 30'

Vo

!

• 9.3-10.5 mag .

• 10.5-11.5

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+.

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2000kms-1

3000

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VIRGO WEST 10h OOm < R.A. < 11h 30m O'< DEC< 30'

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-600

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1000

2000

3000

4000

5000

Figure lOb. Redshift distribution of galaxies in main Virgo Cluster and Virgo West. The blue luminosity weighted mean redshift is shown by the arrow (from Arp 1988). This demonstrates that fainter galaxies in the "Finger of God" configurations represent galaxies with intrinsic redshifts.

Of course, the situation is even much worse than that. Take any given class of
galaxy in the Virgo Cluster, say the S0 's. One could obtain any mean redshift, from a few hundred km s-1 to almost 2000 km s-1, depending on whether bright or faint Virgo members were selected (see Arp 1988, Figure 2).
An illustration of this chaos in the determination of H0 can be seen in a recent paper by Sandage (1992). In this paper he claims that by using a supposedly very luminous type of spiral galaxy called an Sci, the very low value of H 0 = 43 km s-1 Mpc-1 is derived. (Actually this type of galaxy has been shown to be the least luminous kind of spiral galaxy: Arp 1988b, 1990c, 1991b). But in Sandage's Table 1 he lists
"The Four Largest Virgo Cluster Sci Spirals." One can easily write down the meas-
ured redshifts as taken from Sandage's own Revised Shapley Ames Catalog and derive
a mean redshift of v0 =1747 km s-1• Using Sandage's own infall velocity to Virgo of
220 km s-1 and Sandage's own distance to Virgo of 21.6 Mpc one quickly calculates
= H 0 91 km s-1 for the Sci's which Sandage says are members of the Virgo Cluster!
This is a far cry from H 0 = 43 km s-1, but the higher figure is clearly the more correct one for these younger, intrirlsically redshifted kinds of galaxies.
The only negative redshifts in the sky outside our Local Group are seven in
number, and fall in the center of this populous cluster. Hence they must be members. But they are predominantly big Sa and Sb galaxies, the same kind that domi-

20

HaltonArp

nate more local groups of galaxies and also have relatively negative redshifts. What else could any reasonable judgment of the data be but that these larger galaxies are older and, therefore, have smaller (i.e. relatively negative) spectral shifts? If we take our redshift-age equation (3) and adopt a distance to Virgo of 21.9 Mpc (Sandage and Tamman 1990) the look-back time is 71 x 106 years. Therefore, the age of creation of these Virgo giants is about 95 x 106 yrs, or about a hundred million years earlier than the creation of our own galaxy, which was about 15 billion years ago. As we might expect, older galaxies created relatively close together in time look rather similar. This interpretation of the redshifts in Virgo is quantitatively consistent with an H0 "' 50. The conventional analyses which give both H0 =50 and H0 = 80, however, simply arbitrarily pick the parameters which give their respective "observed" values.

5.4-

4.6

- Figure 11. The redshift-apparent

magnitude diagram for clusters of

j

galaxies as measured by A. Sandage (1975) is shown. Peculiar velocities of clusters are reported :::: 2000 kms·' and should have

3.8 -

dispersed the lower 1/3 of the Hubble diagram as shown by the

dashed lines in the figure.

-

8

12

16

20

CORRECTED APPARENT MAGNITUDE

Another way of illustrating this problem is shown in Figure 10. If we use the redshifts as a measure of distance in the Virgo region of the sky, the galaxies all stretch out in a line just in the direction we are looking. This "Finger of God" stretches as far as we have redshifts (even to negative z's). Figures lOa and bare derived from data in the Revised Shapley Ames Catalog (Sandage and Tamman 1981) which is a complete sample to a limiting magnitude near Bap "'13.0mag. Essentially the same diagram is obtained from deeper surveys (Zucca et al. 1991). As can be seen from both Figures lOa and b, however, the brightest (most massive) galaxies are not at the mean redshift of the Virgo Cluster, as they must be on conventional assumptions! The fainter galaxies, therefore, cannot represent peculiar orbital velocities around the massive galaxies. Instead, as in the nearby groups, the smaller galaxies have excess, intrinsic redshifts of varying amounts.

Fitting Theory to Observation

21

If researchers plotted the wedge diagrams with galaxy symbols proportional to the brightness of the galaxy, as in Figure 10, they would immediately see the velocity interpretation was untenable. Even as they are customarily plotted, without brightness differentiation, one should see a thickening or "knot" at the true redshift of the cluster representing the massive galaxies at the centre, plus orbiting galaxies far out and moving slowly, plus orbits transverse to the line or sight which do not give appreciable radial peculiar velocity. Instead, the diagrams show the galaxies evenly spread out along the "Fingers of God". These "Fingers of God" show up all over the sky whenever there are concentrations of galaxies, and should tell astronomers, at a glance, that velocity differences cannot be responsible for the observed effect.
The Virgo Cluster is just like every other cluster that has been studied in detail in that each type of galaxy within the cluster has its own systematic redshift value. The younger Sc's have the highest. Of course the first discovered, most famous, brightest apparent magnitude quasar, 3C273, also falls in the projected confines of the Virgo Cluster. Recent spectra of 3C273 in the ultraviolet show about 10 times more absorbing clouds than normal between the redshift of 3C273 and the Virgo Cluster. Are absorbing clouds just accidentally piled up in excess just in the line of sight behind the Virgo Cluster? Or should we instead believe the numerous independent studies which show quasars of various redshifts are actually physically associated with the Virgo Cluster (Arp 1992a)?

The Hubble Relation at Larger Redshift
Figure 11 shows an adaptation of the famous redshift-apparent magnitude diagram for clusters of galaxies as reported by A. Sandage (1975). It is often stated that the relation is so tight that it precludes any other explanation than an expanding universe. But, in fact, the relation is much too tight. Various observers have reported peculiar velocities of clusters and groups of galaxies of 2000 km s·1 or more (see Narlikar and Arp 1992). The dashed lines in Figure 11 show how the existence of real velocities of this size would blow up the lower third of the pictured Hubble relation. How can the observational conclusions of these two conventional analyses be reconciled? Only if the dispersion observed in redshifts of clusters is not velocity but age differences and, further, if Sandage has measured only clusters of galaxies which have similar age characteristics.
It is interesting to contrast the claims of the observers who report peculiar velocities of galaxies exceeding 2000 km s·1 with the published results of Yahil, Sandage and Tamman (1980) that the Hubble flow is probably quieter than 50 km s·1• Those claims too can only be reconciled if spectral shifts generally do not indicate velocity differences.

Evolution Away from the Hubble Relation at High z
Spinrad and Djorgovski (1987) report measures of radio galaxies which deviate from the Hubble relation by 5-6 mags at z"" 1.5. This is conventionally attributed to evolution, but it requires these galaxies to be 100-240 times brighter in the past than at present. Naturally this requires "star bursts" of unprecedented scale

22

HaltonArp

X (arc seconds)
Figure 12. High resolution images in redshifted Lyman alpha with the Space Telescope are shown for the system of four quasars surrounding the low redshift spiral galaxy G2237 + 0305. The lower diagram shows that the predictions of gravitational lens theory are exactly opposite to the observations. The observations indicate physical ejection from the galaxy (See Arp and Crane 1992).

Fitting Theory to Observation

23

and would make it necessary to observe hydrogen dominated precursor galaxies which have not been seen. The observational fact that these precursor galaxies are not seen means that apparently young galaxies really are young in the sense that they are more recently created. This observation, by itself, then rules out the Big Bang, where all galaxies are supposed to have been formed in the beginning.
If, however, these active galaxies and the material in them have been created more recently, we would expect by our precepts to have them deviate to higher redshift from the Hubble line. In this respect, the radio galaxies should show a deviation due to intrinsic redshift intermediate between quasars and normal galaxies. This would agree with their generally intermediate physical properties.
More normal E galaxies, however, can be measured out to redshifts z = 1. For observations in the infrared where young stars hardly affect the magnitude, we see deviations of about 2 mag. brightward from an unevolved Hubble line of q0 = 0. It is interesting to note, however, that our predicted value of H 0 pertains only locally,
for z--+ 0. At z =1 we predict H =2.8H0 (see Narlikar and Arp 1992). If this were
interpreted as a deviation from the Hubble relation in an expanding universe, it would require a normal galaxy to be 2.3 mag. more luminous in the past. But, in fact, as we see in the conventional analyses of the evolution of stellar assemblages, this is just about the 2 mag. deviation from the Hubble line which is required for normal E galaxies. The point is that the additional epicycle of systematic evolution which is needed in the Big Bang theory to reconcile theory with observations is not needed in the flat spacetime, continuous creation cosmology discussed here.

High Redshift Quasars Associated with Nearby Galaxies
The evidence that high redshift quasars, which on the Big Bang hypothesis should be out at the edge of the universe, are, in fact, associated with nearby galaxies has been growing since 1966. Reviews of this extensive evidence are available in Arp (1987) and (1992a).
Of course, the quasars nearest in angular separation to the low redshift parent galaxy are the most disturbing to advocates of conventional distance criteria. One famous example is the bright apparent magnitude quasar Markarian 205 which is only 40" south of the extremely disturbed, radio ejecting galaxy NGC4319. In a study with the Hubble space telescope, Bahcall et al. (1992) found that the quasar had much less absorption in front of it than would be expected due to the intervening galaxy NGC4319 (about 10% of what was expected). They then concluded that this was "consistent with the cosmological interpretation." Of course, a more accurate statement would have been, "this is most consistent with the quasar being 90% in front of the galaxy."
X-ray extensions from the quasar to the nucleus of this active galaxy were uncovered in the Einstein satellite archives (Arp 1990b). After much resistance, the object has finally been assigned observation time with the German X-ray satellite, ROSAT.
But one of the associations that conventionalists could not ascribe to chance was the so-called "Einstein Cross", which consisted of four quasar images of

24

HaltonArp

z =1.7 all within one arc sec of the nucleus of a galaxy of redshift z =0.039. It was
explained by gravitational lensing and splitting of a fainter, accidentally aligned background quasar. By consulting the space telescope archives, however, Arp and Crane (1992) were able to add and image process all the best resolution images of the configuration. Figure 12 here shows that the predictions of the gravitational lens imaging are completely and orthogonally violated.
Instead there are luminous, ffiamentary connections back to the nucleus in just the fashion expected if the quasars arose from an ejection episode in the nucleus of the galaxy. It seems difficult to conceive of any more direct observational evidence against the gravitational lens model and for the ejection model.
Of course, this observational evidence from the world's most expensive telescope was refused publication in the journals which routinely publish space telescope data. We can comment here that gravitational lensing, which is used regularly as a deus ex machina to explain a host of discordant observations, depends on very massive galaxies to create the needed effects. We have seen earlier that galaxy masses have been customarily overestimated by one to two orders of magnitude. For realistic galaxy masses, gravitational lens effects may some day show up, but on a much smaller scale than currently claimed.
Gravitational lens interpretations which are rapidly published, however, claim the data confirms the standard theories. One example of such a paper is Rix, Schneider and Bahcall (1992). They compute that lensing in the Einstein Cross requires a mass of 1.1 x 1010 M0 inside the very small radius of 0.29 where the quasar images are located. This computation is essentially no different from Howard Yee's (1988) analysis which derived a mass of 1.2 x 1010 M0 • As Yee stated, this leads to a massto-light ratio of MjL ~ 13, which "...is near the high end of that of large spiral galaxies... but is entirely acceptable." Well not quite, if you consult the measured MjL ratios for galaxies (Kormendy 1988) you see that this M/L is completely above bulges of spiral galaxies, even above that for ellipticals and that is for a lower limit on the required MjL. In fact, if you compute the luminosity required for an ellipti-
cal to have this M/L ratio it comes out Mp = -25 mag! How bright is Mp = -25 mag? Well, quasars are defined as starting at Mp = -23 mag. So this is a galaxy 2 magnitudes brighter than a quasar! And this is just a lower limit!!
This so-called confirmation of the lens theory by the observations rests on assumptions that the redshift dispersions in galaxy interiors represent both velocities and velocities in equilibrium, which, as we have seen, the observations show is incorrect on both counts and generally overestimates the masses in galaxies. Furthermore, the mass needed for the lensing is underestimated by assuming it is all concentrated at a point in the center of the galaxy-hence the lower limit. In addition, a disk galaxy is called an elliptical, and mass-to-light ratio comparisons are shuffled between blue, visual and red. Even after all this, the result is that one requires an extraordinary and unprecedented galaxy to satisfy the lens require-
ments. This is called a rigorous and exact confirmation of the lens predictions, and it
is there for all to read in the professional journals. Direct images of the object with the best resolution telescope available directly contradict the predictions of lens theory, but are refused publication in these same journals. It would seem that if the theory had not failed, there would be no need to censor the contradictory data.

Fitting Theory to Observation

25

Cosmic Background Radiation
In April 1992, enormous publicity was given to the announcement that a satellite observing in the microwave region of the energy spectrum had detected irregularities in the sky. These were interpreted as "fingerprints of primordial galaxy formation" and said to have (once again) proved the correctness of the Big Bang theory.
The claim of "proof" of Big Bang was later severely criticized by rival establishment astronomers. Nevertheless, there was never any discussion of how the evidence actually is very difficult to reconcile with a Big Bang model. The point is that in a universe expanding faster at each further distance observed, the 2.7· K black body energy curve would be smeared out unrecognizably by Doppler recession velocities. Therefore, one must only observe a single, thin shell. In the Big Bang model, it is assumed this is the shell at which radiation decoupled from matter in the beginning. But the irregularities which were forming galaxies should be seen! The really astonishing fact of the background observations is that they are smooth to about one part in a hundred thousand-not that they are irregular (on too large an angular scale) to about one part in a million.
In the nonexpanding universe, however, the intergalactic medium can be observed from here to the edge of the visible universe with no velocity smearing. The integration through this maximum distance is most capable of smoothing out all fluctuations in background radiation received from all depths in the universe. In the nonexpanding universe an obvious, and much simpler, explanation of the observation is that we are simply seeing the temperature of the underlying extragalactic medium.
It is customarily stated that the Big Bang predicted the correct temperature of the cosmic background. But, as A. Assis discusses in this volume, G. Gamow (1961)
predicted T =so· K. It was static, tired-light models which predicted values around
2.8· K. As early as 1926, A. S. Eddington calculated the temperature of interstellar space as -3· K. Many investigators have since pointed out that if one takes the ambient starlight and thermalizes it to lower energy photons, one gets closely the observed microwave background temperature. F. Hoyle and C. Wickramasinghe have suggested that iron whiskers blown out of supernova explosions could effect this thermalization (see Arp et al. 1990). Narlikar and Arp (unpublished) have considered whether m= 0 electrons, which are extremely efficient thermalizers, could be the agents responsible. Creation events, in the variable mass theory, could supply abundant low mass particles, either from active galaxies or in smaller events spread throughout the intergalactic medium. Recently, Burbidge, Hoyle and Narlikar (in press) have summarized the evidence from recent gamma ray observations which can be interpreted as direct detection of creation events.
Mass Creation and Quantum Mechanics
One of the great searches in modem physics has been to connect the realm of the submicroscopic quantum mechanics to the macroscopic world of classical mechanics. There are, however, some classical formulae which work in the quantum domain if m2 < 0 (see for eqs. I. Khalatnikov 1992). It is very provocative, therefore,

26

HaltonArp

when we obtain a general solution for the classical equations of general relativity, equation (5) here, which gives m ~ 0 when t ~ 0. In other words our creation events go exactly through the juncture between quantum and classical mechanics. It is, therefore, possible to conceive of new-born matter having been previously in a state where its constituent wave packets were unbounded and spread throughout the universe. The materialization of this matter at a certain point in space at t "' 0 would then represent not matter from "outside" the universe but merely the rearranging of mass/energy within the universe. In this case conservation laws could hold in general, while at the same time opening vastly greater possibilities for morphological change within the universe.
Are there any observations which can give clues in the macroscopic domain to the nature of their connection to the quantum domain? There is one kind of observation which apparently does just that. That observation is the quantization of redshifts. As Figure 6 showed earlier, the whole of the measured redshift phenomenon is split into periodicities: large periodicities for the large redshifts and small periodicities for the small redshifts. It has been commented that the

,,0.:::~:.::.:0 '"'"'' / /

LO AL SUPERCLUSTER

/

OLD
GALAXIES
QUASARS • I
-·.,o·-vouNG • • "' GALAXIES

/

~ ~·~LOCA(MILLKWGARYO)UP

/

COSMIC BACKGROUND RADIATION FROM STATIC INTERGALACTIC SPACE

~j:////

Figure 13. Schematic model of our nonexpanding universe is shown. The region inside an indefinitely large universe with which we communicate is the speed of light times the age of our galaxy, r = c-r0 • Background radiation can be smooth and pervasive or very slightly non-homogeneous in direction of Local Supercluster.

Fitting Theory to Observation

27

presence of any appreciable peculiar velocities of these extragalactic objects is ruled out by this quantization. If the age is responsible for the spectral shift, however, the age of the extragalactic objects could be quantized. Since the material
comes through the quantum domain of m= 0, periodicities of M could well be
impressed at that stage which would remain imprinted, albeit growing relatively smaller as the material gained age and mass.
This cannot be the whole story, of course, because as more distant objects of our own age are considered, the look back time determines their apparent redshift. This should be continuous, but instead is implied to be some sort of cellular structure. Possibly coherence and interference effects will have to be considered.
However, whereas the pervasive quantization observed in redshifts seems possibly compatible with age and quantum effects, the current interpretation of redshifts as velocities offers no hope of either glimpsing the correct model of the universe, or gaining physical understanding of the physical laws which relate the macroscopic and microscopic scales. The discouraging situation is, of course, that so long as the validity of the observations is denied on the grounds they do not fit the current theory-just that long will it be impossible to correct the theory.

The Best Current Model of the Universe
Finally, considering all the observations, the model of the universe which can
fit is shown in Figure 13. It is a universe which is not expanding and in which we, from our Milky Way Galaxy, see out to a radius of the speed of light times the age since our creation. Of course, galaxies could have existed before that, and if they were enormously brighter than galaxies we have any knowledge of, we could see out even further than this r = c-r0 = 15 billion light years. Therefore, we must always be open to the possibility of surprises as time passes and as signals from new events just penetrate to us or as our horizon expands to embrace older events.
The Local Supercluster is the largest aggregate of material about which we have certain knowledge. We are near the edge, at about 15-20 Mpc from the center.
= When we get through remapping all the young, high redshift objects like quasars
and active galaxies to their correct distances rather than their redshift velocity distances, then the Local Group and Local Supercluster will become much more populated relative to the more distant regions than is presently believed. In fact, it may be relatively quite empty beyond the confines of the Local Supercluster. In that case, a cap may be set upon the exchange of gravitons with distant matter and, with it an upper limit upon the blue spectral shift of the oldest galaxies which we can see.
The cosmic background radiation could also be fairly concentrated in the vicinity of the Local Supercluster, because there is no velocity restriction on the Black Body peak wavelength. Asymmetries and irregularities could be indicative of local features, whereas the utterly smooth part could represent integrations through more distant regions.
In summary, a true scientific process of inferring a theory which fits all the observations, instead of the usual inverse procedure yields a consistent, physically plausible picture which opens the possibility of understanding much more about the universe in which we live. We have not dared to invent "new physics"; only carefully, empirically, earned our way to more correct physics.

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HaltonArp

References
Arp, H., 1986, Astron.Astrophys. 156:207. Arp, H., 1987, Quasars, Redshifts and Controversies, Interstellar Media. Berkeley. Arp, H., 1988, Astron.Astrophys. 202:70. Arp, H., 1988b, in: New Ideas in Astronomy, Cambridge Univ. Press, eds. F. Bertola, J.W.
Sulentic, B.F. Madore, p.161. Arp, H., 1990a, IEEE Trans. on Plasma Sci. 18:77. Arp, H., 1990b, Phys.Lett.A. 146:172. Arp, H., 1990c, Astrophys. Space Sci. 167:183. Arp, H., 1991, Apeiron 9-10:18. Arp, H., 1991b, Sky and Telescope 81:373. Arp, H., 1992a, Observational Problems in Extragalactic Astronomy, in: IAU Highlights of
Astronomy, Vol. 9:43. Arp, H., 1992b, Mon. Not. Roy. Astr. Soc. 239:800. Arp, H., Burbidge, G.R., Hoyle, F., Narlikar, J.V. and Wickramasinghe, 1990, Nature 346:807. Arp, H. and Crane, P., 1992, Phys. Lett.A 168:6. Arp, H. and Sulentic, J.W. 1985, Ap. J. 291:88. Arp, H., Bi, H.G., Chu, Y. and Zhu, X., 1990, Astron.Astrophys. 239:33. Bahcall, J.N., Junuzzi, B.T., Schneider, D.P., Hartig, G.F. and Jenkins, E.B. 1992, Ap. f. submit-
ted. Bottinelli, L. and Gougenheim, L., 1973, Astron. Astrophys. 26:85. Broadhurst, T.J., Ellis, R.S., Koo, D.C. and Szalay, A.S., 1990, Nature 343:726. Collin-Souffrin, S., Peeker, J.-C. and Tovmassian, H.M., 1974, Astron. Astrophys. 30:351. Field, G.B., Arp, H. and Bahcall, J.N., 1973, The Redshift Controversy, W.A. Benjamin Inc.,
Reading, Mass. Jaakkola, T., 1973, Astron. Astrophys. 27:449.
Girardi, M., Mazzeti, M., Giurcin, G. and Mardirossian, F., 1992, Ap. J. 394:442. Khalatnikov, I., 1992, Phys. Lett. A. 169:308. Kembhavi, A.K., 1978, Mon. Not. Royal Astr. Soc. 185:807. Kormendy, J., 1988, Ap. J. 325:128. Madore, B.F., and Freedman, W.L., 1992, P.A.S.P. 104:362. McCall, M.L., 1989, A.f. 97:1341. Narlikar, J.V., 1977, Ann. ofPhys. 107:325. Narlikar, J.V. and Arp, H., 1992, Ap. f. in press (20 Feb 93). Rix, H.-W., Schneider, D.P. and Bahcall, J.N. 1992, A.J. 104:959. Sandage, A and Tamman, G., 1981, Revised Shapley Ames Catalog of Bright Galaxies, Carnegie
Institution of Washington.
Sandage, A. 1992, H0 = 43± 11 km s·' Mpc·' Based on Angular Diameters of High Luminosity
Field Spiral Galaxies. Preprint, The Observatories of the Carnegie Institution of Wash-
ington.
Sandage, A., 1975, Ap. J. 202:563. Scott, D. 1991, Astron. Astrophys. 242:1. Spinrad, H. and Djorgovski, S., 1987, IAU Symposium No. 124:29 (Dordrecht: Reidel). Vader, J.P. and Chaboyer, B., 1992, P.A.S.P. 104:57. Yee, H.K.C., 1988, A.f. 95:1331. Zaritsky, D., 1992, Ap. f. 400:74. Zaritsky, D., Smith, R., Frenk, C. and White, S.D.M., 1993, Ap. f. 10 March issue. Zucca, E., 1991, Mon. Not. Roy. Astr. Soc. 253:401.

Redshift Periodicity in the local Supercluster
W.M. Napier and B.N.G. Guthrie
Royal Observatory, Blackford Hill Edinburgh EH9 3HJ, Scotland, U.K.
Persistent claims have been made over the last -15 years that extragalactic redshifts, when corrected for the Sun's motion around the Galactic centre, occur in multiples of -24, -36 or -72 km s·1 • A recent investigation by us of spiral galaxies out to 1,000 km s·1 gave evidence of a periodicity -37.2 km s-1• Here we extend our enquiry out to the edge of the Local Supercluster (-2600 km s"1). We confirm that, when corrected for the Sun's galactocentric motion, the redshifts are strongly periodic (P- 37.5 km s"1). The periodicity is coherent over the entire Supercluster. The formal confidence level of the result is very high, and the phenomenon apparently cannot be ascribed to observational artefact or group membership. Various types of 'oscillating physics' are considered, such as variations in the fundamental constants, or the coupling of light to a universal, coherently oscillating scalar field. These run up against geological constraints or other difficulties. The possibility that massive galaxies comprise a conformally expanding lattice is discussed.
1. Introduction
The term 'quantized redshifts' encompasses a set of claims which are surely amongst the most bizarre to have been made in modern astrophysics. The first claims under this category were made by Tifft, who in 1976 stated that the redshifts of galaxies in the Coma cluster were preferentially offset from each other in multiples of 72.46 km s-1 . These redshifts were determined optically, and were of relatively low accuracy. However, within a few years, more accurate extragalactic redshift determinations were becoming available from 21 em determinations: the HI line profile of a spiral galaxy may be several hundred km s-1 wide, but if it is fairly symmetric, the systemic redshift of the galaxy may be consistently determined to within a few km s-1. Making use of these more accurate redshift data, it was claimed that binary galaxies were similarly offset (Tifft 1980), and that this redshift periodicity (-72 km s-1) occurred also within groups and associations of galaxies (Arp and Sulentic 1985).
In 1984, Tifft and Cocke (1984: TC hereinafter) claimed that the redshifts of galaxies occurring anywhere on the sky are periodic when a suitable correction for the solar motion is made. That is, there exists a global periodicity, and not one

Progress in New Cosmologies: Beyond the Big Bang

Edited by H.C. Arp eta/., Plenum Press, New York, 1993

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W.M. Napier and B.N.G. Guthrie

confined to the differential redshifts of adjacent galaxies. 1his global periodicity, however, was not 72.46 km s·1 but one half (36.3 km s"1) if the galaxies were broadlined, and one third (24.2 km s·1) if they were narrow-lined. These periodicities emerged when the same solar motion was subtracted from each of the redshift sets.
The phenomenon, if real, is unrelated to known physics and inexplicable in terms of current cosmological paradigms. Further, the entities for which the periodicities are claimed are not exotic objects which might conceivably be the sites of unfamiliar physics, but ordinary galaxies. It is perhaps not surprising that few astronomers have taken these claims seriously. On the other hand, there is abundant historical precedent for the discovery of phenomena which were regarded as bizarre and inexplicable at the time. Implicit in our examination of the question, then, is a rejection of the philosophy that physics and cosmology are at the stage where unexpected new phenomena can be confidently excluded; we have adopted instead the view that the existence or otherwise of redshift 'quantization' is a matter for empirical enquiry. In recent years there has been a large increase in the numbers of redshift determinations using 21 em line profiles; because of this greatly enhanced dataset, it should now be possible to settle the question through rigorous statistical analysis.
A previous analysis by us (Guthrie and Napier 1991) of field galaxies seemed to support the claims of redshift periodicity amongst spiral galaxies out to 1000
km s·1• In that study, we found no periodicity when the redshifts were corrected for a solar vector with respect to the Local Group or the microwave background, or when it was allowed to vary with distance as described by de Vaucouleurs and Peters (1984). Although the mean solar apex may vary by -30° over the distance range investigated (-15 Mpc), the periodicity emerged only when a local solar vector (i.e. one close to the Sun's motion around the Galactic centre) was subtracted from the heliocentric redshifts. It appears that the redshifts have to be corrected for a unique, local solar vector irrespective of the dimensions of the region being explored. 1his result, while unexpected, implies that a periodicity of -24 or -36 km s"1 in galactocentric redshifts might exist and be detectable to much greater distances, and so prompted us to investigate the question out to a much larger volume of space, namely the whole of the Local Supercluster (LSC). Galaxies belonging to the LSC have corrected redshifts ranging up to -2600 km s·1 (Flin and Godlowski 1989). The outcome of this enquiry is described in the present paper: our earlier conclusions are confirmed and strengthened.

2. The Methodology
In testing a statistical hypothesis, the following recipe is generally followed:
(i) The hypothesis is set up, derived from a theory, an early set of data or whatever.
(ii) From this initial hypothesis, a specific prediction is made concerning the behaviour of new, independent data. The prediction should ideally contain no unspecified parameters, but if it does, the freedoms they introduce must be accounted for in the reckoning, for example by estimating the effective number of independent trials that they represent.
(iii) The prediction having been made, it is then tested on a new dataset. 1his new

Redshift Periodicity

31

set must be (a) independent of the initial one from which the hypothesis was formulated, and (b) unbiased. The latter condition requires, inter alia, that any culling of the data from a larger set should be done once and for all, prior to the analysis, in a way which will not alter the outcome of the testing. In evaluating the outcome of a test, other questions may reasonably be asked of the investigators, such as: did they play around with other datasets, other selections and values of parameters? Was there a 'termination bias', the tendency to stop when a 'success' has been attained? (iv) It will often be found that, as new or better data accumulate, some modification of the original hypothesis gives a better fit: probably all statistical hypotheses are destined to fail in their original form (they are only models). Such modifications may carry with them the suspicion that the investigator is 'shifting the goalposts'; but equally, one expects the original perception of a phenomenon to be sharpened up as the data available expand or improve in quality. The test of whether a given 'improvement' of the original result is genuine is to apply the improved hypothesis to a new, independent dataset. Thus, exploratory and confirmatory phases intermingle until a precisely formulated hypothesis is reached or one runs out of data. (v) Multiple hypothesis testing is important: periodicity might fit a redshift dataset better than the null (random) distribution; but clustering might fit better still.

3. The Technique

The technique most commonly applied in testing for periodicity is power spectrum analysis, in which a given set {V;} of N numbers is circularly transformed with respect to a trial period P, and a statistic I ;:: 2R2jN is calculated. Here R represents the magnitude of the vector sum of the unit vectors

_ . (2nv;) e; -exsm -p +eycoJ'\z-npv;)

(1)

Essentially a string, along which the signals {V;} are marked, is wrapped around a drum of circumference 2nP, and the corresponding unit vectors in the plane are added. Thus in Figure 1, R;:::: OP is the distance moved from the origin by the legendary drunk man performing a random walk of N unit steps.

p

Figure 1. The connection between PSA and the drunkard's walk. Linear data are converted to circular by wrapping them around a drum of circumference 2nP.

32

W.M. Napier and B.N.G. Guthrie

In such a random walk Roc JN, and the statistic I represents a normalized
distance whose behaviour is understood from the theory of the random walk in two
dimensions. A power spectrum or periodogram is a plot of I(v), where v =ljP. A
periodicity in the data may be observed as a peak at the relevant frequency; the
higher the peak, the straighter the walk and hence the greater the probability of a real periodicity in the data. For large N, for random, uniform and independent data, and neglecting edge effects (non-integral wraps around the drum), the probability p of obtaining a value I :<:: Imax by chance in a single trial is

(2)
and the mean value I= 2.
3.1 Against PSA
Although power spectrum analysis in some form goes back to the 19th century, it was first rigorously discussed by Bartlett (1955), who found substantial problems with the method and quickly abandoned it. The apparent limitations of PSA have recently been discussed by Newman et al. (1992).
First, the statistic I is a biased estimator. A departure from non-uniformity in
the redshift distribution will in general yield I -:F- 2 and also a departure from the
exponential distribution (2). Only in the limit of high frequencies are these formulae applicable. Bias is also created if, as is always the case, the dataset N is finite.
Second, I is inconsistent, a fact which manifests itself in the 'grassy' or noisy appearance of a periodogram, the relative variance (J(I)ji remaining of order unity even as N -? oo. Should a large number of trials be involved, even random data may
yield surprisingly high values for I: for nr independent trials, the expectation value of Imax is E(Imax) -1.2 +2ln nr. The inconsistency can be greatly reduced by the use
of smoothing techniques (there is a large literature on 'window carpentry'), but at the cost of increasing the bias and introducing further degrees of freedom.
Finally, even when bias is not a problem (say for high frequencies), Newman et al. (1992) find on empirical grounds that, as N increases, convergence towards the form (2) is slow for high I. But of course, it is precisely the high peaks which are of interest in testing for periodicity. Newman et al. conclude that PSA is 'limited and possibly dangerous in that quantitative assessments in the sense of hypothesis testing are not meaningful'.
3.2 In Defence of PSA
In spite of these disadvantages, some of which are more widely known than others, PSA remains the most widely used period-hunting tool in the physical sciences (for discussions of the technique in an astrophysical context, see Scargle 1982, Home and Ballunas 1986, Stothers 1991). Its usefulness lies in the increase of signal strength with N, and in its simple limiting statistical behaviour as described by (2). It is also a sensitive technique, signals too weak to be seen by eye often being detectable by it.
The bias due to the finiteness of N is, for a truncated series of data, of order ln N/ N and so tends to zero as N -? oo • It is not important, in probability terms, for

Redshift Periodicity

33

the present problem. In the datasets analyzed so far (Guthrie and Napier 1990, 1991), the redshift distributions were fairly uniform, and the distribution of peaks
in the power spectra, other than those under test, showed no significant departures
from the expected I= 2 and exponential decline. In any case, the periodicities under
test are of high frequency in relation to those of trends and range of the dataset and so bias due to these factors is not expected.
The convergence of I towards the exponential formula has been examined by Buccheri and de Jager (1989) through numerical experiments. For samples of random data with N -100, of the order discussed in this problem, the cumulative probability distribution of I closely follows the form (2) down to probabilities p - 10-6, corresponding to I - 28.
Finally, the inconsistency of the statistic I (the variance equals the mean) does
not prevent the estimation of the significance of a high peak if n.r can be assessed or
comparison is made with suitable synthetic data (Guthrie and Napier 1991b). In the present paper, the significance of the power I(v) in the actual redshifts
is assessed by a ranking procedure, simply comparing I(real) with I(synthetic) derived from artificially generated redshifts constructed so as to closely simulate the actual redshifts (including any non-uniformities in distribution). This procedure is robust, and questions of bias, consistency and convergence are simply bypassed: indeed almost any measure of periodicity would do! Analyses of the same data using absolute rather than ranked values of I, and using a linear rather than circular analytic technique (Stothers 1991), have yielded essentially the same results (Guthrie and Napier, unpublished).

4. The Database
4.1 The Galaxy Sample
In our previous study, mentioned above, we used the database for 6439 galaxies compiled by Bottinelli et al. (1990). Galaxies with the most accurately determined HI redshifts (i.e. those with database errors a cz $ 4 km s-1) were taken from the list. From these were eliminated possible members of the Virgo cluster, nonspirals and galaxies previously used by TC in their study. Of the remaining spirals, 89 had redshifts < 1000 km s-1 after correction for the Sun's motion around the Galactic centre (taken as V0 :::: 252 km s-1, 10 ::::100°, b0 :::: 0°, although the precise solar vector is not critical here). These constituted an independent dataset of the nearby field spirals, culled once and for all in an objective, reproducible manner from the catalogue. The data were then divided into 40 'more accurate' (a$ 3 km s-1) and 49 'less accurate' galaxies (the remainder) and analyzed, separately and together.
For the present analysis, the culling was carried out in similar fashion, with the exception that the corrected redshift limit was extended from 1000 ·km s-1 to 2600 km s-1, the recognized limit of the LSC. Thus, the expanded database incorporates our earlier one and so conclusions drawn from it are not to be read independently of our earlier ones. The present study may rather be regarded as a simpler statistical treatment of an extended redshift sample. With the extension to 2600 km s-1, and after eliminating Virgo members and galaxies previously used by TC (34 of them), the dataset expands to 247 galaxies, of which 97 are 'more accurate'

34

W.M. Napier and B.N.G. Guthrie

(a::::; 3 krn s-1 and redshift calibrators adopted by Baiesi-Pillastrini and Palumbo 1986); this compares with 89 galaxy redshifts in our earlier sample, of which 40 were 'more accurate' (a::::; 3 km s-1). Two large clusters (UMa and Fornax with 61 and 49 members respectively) are now encompassed; whether these should for consistency have been excluded from the sample as were the probable Virgo spirals is perhaps arguable. However because of the large computational effort involved in the study (-108 PSAs!) we generally operated only on the 97 very accurately measured redshifts, exploiting the full sample only when its behaviour as a function of accuracy was under consideration.

4.2 The Solar Vector
The circular velocity of the solar neighbourhood has been determined from HI
data (Gunn et al. 1979), yielding E> = 220 ± 10 km s-1, and from an examination of
the solar motion relative to the nearest members of the Local Group (Einasto 1979, Haud et al. 1985), yielding 221±5 krn s-1 and 218±5 km s-1 . Taking account only of the solar peculiar motion relative to the local standard of rest (Delhaye 1965), a
resultant galactocentric solar vector \!;:.) = 232 krn s-1, l<·) = 88°, b<·) = 2° is found.
However, the presence and orientation of a strong bar in the central regions of the Galaxy (Blitz and Spergel1991) are consistent with a local expansion velocity in the range 20-40 krn s-1 (Combes and Gerin 1985 and Napier, unpublished), while evidence has been presented (Clube and Waddington 1989) that the local standard of rest has an outward motion of -40 krn s-1. Additionally, the Galactic disc may possess a warp, introducing some uncertainty (which can only be guessed at) in the local perpendicular velocity relative to the mass plane of the Galaxy. Allowing for
these factors, the galactocentric solar vector may be taken roughly as "V;::J = 233 ± 7
km s-1, 10 = 93 ± 10°, b0 = 2±10° where the uncertainties are largely in the modeling. This is very close to the V<·) for which TC claim the periodicities emerge (233.6 km s-1, 98.6°, 0.2°), and justifies the formulation that: the periodicities emerge when the heliocentric redshifts are corrected for the galactocentric solar motion. The alleged periodicities are therefore nucleus to nucleus between galaxies. Thus, we are testing whether extragalactic redshifts tend to occur in multiples of -24, -36 or -72 km s-1, when corrected for the Sun's galactocentric motion V0 , against the null hypothesis that there is no periodicity.

5. Is the Hypothesis Reasonable?
A hunt for a signal within the range of uncertainty of V<·) is in effect an exercise in optimization of the statistic I, equivalent to carrying out a number of independent trials. The 'correction' for v(.) thus introduces three additional degrees of freedom, which might cause an otherwise insignificant signal to be artificially boosted.
This additional freedom can readily be allowed for by 'optimizing' artificial redshift data in identical fashion to the real data. However a potentially more serious consequence of having V<·) as a free parameter is that TC might at the outset have been guided to search for periodicity only in the local neighbourhood of an astrophysically significant solar vector and around a previously suspected period (or a simple fraction thereof). But one can imagine that, if one were to vary the solar

Redshift Periodicity

35

vector over the entire celestial sphere and search for periodicity over a wide range, peaks would arise in all sorts of directions and for all sorts of 'periodicities'. In that
case the (Vc-J,P) derived would measure nothing more than the bias of the original investigators, and its proximity to a solar vector of consequence would have no significance.
To investigate this possibility, the solar vector Ve-l was varied in direction over the whole sky and in speed over the wide range 140 to 300 km s·1 (in steps of 2° in bc·l' 2 or 3° in lev and 5 km s·1 in Vc.J)- For each solar vector a set of 97 corrected redshifts was derived and a periodogram constructed in 490 equal frequency steps over the period range 20-200 km s·1; thus in all, for two interlaced grids, about a million periodograms were constructed, for each of which the maximum power I was recorded.
Figure 2 reveals the outcome of the exercise, in which the (Vel' lw bel) box has been collapsed on to (10 , b0 ) and the ten highest peaks have been plotted.
The presence of multiple peaks illustrates the importance of Ve-l in this problem. One might have supposed that, for a real periodicity, only a single peak would have emerged, but (for reasons to be discussed) this is not the case. Five of the ten peaks correspond to periods 24±3 km s·1 and seem to lie roughly on a band just south of the galactic equator. The other five have essentially the same period (37.5±0.2 km s·1), and three of them lie close to the current best estimates of the galactocentric
solar motion, within its uncertainties. Keeping in mind that the dataset is completely independent of that employed by TC, this analysis indicates that the hypothesis (a redshift periodicity ~36.3 km s·1 after subtraction of the galactocentric V0 ) is a reasonable one to test, in the sense that the whole sky is not filled with high peaks at all sorts of frequencies. Indeed, only the TC solution stands out.
The absolute deviations from periodicity of the corrected redshifts were evaluated for the ten peaks, and the inter-peak Spearman rank correlation coefficients were obtained. The three peaks marked (206, 217, 223) were found to be strongly correlated, as were (258, 292). There was also cross-correlation between the members of these two sets, although at a weaker level. The five peaks at ~37.5 km s·1 therefore appear to be caused by a single underlying phenomenon. As to why there should exist multiple peaks as well as signals at -24 km s·1 in other directions of the
sky, some more or less speculative comments are made later.

b0
oo f--

• •

'I- 292
• 258
@ 223 206 217
•

I

I

240°

10

120°

Figure 2. Ten highest peaks (out of -106 ) in a whole-sky search (140 :s; V0 :s; 360 krn s·1), over 20 :s; P :s; 200 krn s·1 . • = 24±3 km s·1, *= 37.5±2 krn s·1• The formal error box of the solar galactocentric motion is shown.

36

W.M. Napier and B.N.G. Guthrie

6. The Significance of the Signal
The next step in the analysis was to assess the significance of this redshift structure, in the sense of asking whether a random redshift distribution might yield
it. TC claimed a periodicity of 36.3 km s-1 for a solar vector (Vw 10 , b<·)) = (233.6
km s-1, 98.6°, 0.2°) on the basis of 40 galaxies with broad HI lines. The proximity of three out of the ten highest peaks to this solution has probability ::::; 1004 , smaller if comparison is instead made with the best estimate of the Sun's galactocentric vector; however this calculation does not yet take account of the absolute heights of the peaks (I- 38).
First, the power structure in the neighbourhood of the region under investigation was examined: a coarse-grid exploration was carried out over the region shown in Table 1.

Table 1. Search range for the 97 spirals. P was searched in equal frequency steps. (V~),P) in km s-1, (l<·)' b0 ) in degrees.

parameter
v0 /0 b0 p

min max
203 263 78 108 -13 +17 34 39

step nos.
6 15 15 8

-2 log p
-4
-6

' '

_________.__________ -a~---------~----------._

~--------~

0

10

15

20

25

n2o

Figure 3. Probability that a set of randomized redshifts, constructed and analyzed as described in the text, would yield more than n20 spectral peaks.

Redshift Periodicity

37

Thus a generous allowance was made for uncertainties in the galactocentric solar vector and the predicted period, and 10,800 !-values were obtained. Of these, 12 were> 25,25 were> 20 and 76 were> 15, i.e. n25 =12, n20 = 25 and n15 = 76. These high I values are not in general independent.
These numbers were then compared with the corresponding values obtained by constructing synthetic datasets and analyzing them in identical fashion to the real data. The positions of the galaxies on the celestial sphere were preserved, and each real redshift was randomized by adding to it the difference of two random numbers in the range (0, 50) km s-1 (S.E. 20 km s-1), large enough to smear out the periodicities under test but small enough to preserve the overall redshift distribution. The real and synthetic datasets were, therefore, identical in all respects except for the deletion of this fine structure, and so any significant difference between the real and synthetic data could only be ascribed to the presence of redshift structure coherent on a scale :::; 50 km s-1 say.
Ten thousand sets of 97 randomized redshifts were so constructed, and grid searches were carried out on each set. No values of n25 ~ 12, n20 ~ 25 or n15 ~ 76
were found (the highest values obtained were nzs = 5, nz0 = 13 and n15 =52). The
cumulative distributions of n20 and n15 were used to give the single-trial probability
nzo p of exceeding any prescribed value of or ~5 : in Figure 3, logp is plotted against
n20 ; an extrapolation yields the 1a range for the probability of obtaining n20 > 25 in a single trial as 5 x 10-s :::; p(n20):::; 2 x 10-6; for n15 ~ 76, 2 x 10-6 :5 p(n15):::; 1.5 x 10-s. Note that comparison is being made with a part of the 'whole-sky' box which is of significance in its own astrophysical right and not simply because it contains strong peaks. We see, therefore, that when the observed LSC redshifts are referred to the nucleus of the Galaxy, strong redshift structure, centred on ~37.5 km s-1, emerges. We can make this statement at a confidence level of, say, a million to one. At this stage of the argument, we are not describing the structure as a periodicity. However already we see that there is a suggestion of something 'bizarre': why should strong redshift structure emerge with respect to the Sun's galactocentric motion, which can have little relevance to the redshift behaviour of galaxies scattered throughout the LSC?

7. Statistical Behaviour
Good statistical behaviour is expected of a real phenomenon: if the strength of the signal failed to increase with increasing quality of the data, or with increasing sample size, or if the derived parameters were unstable, the 'best' values hunting around without convergence as the dataset increased, then one would suspect that some gremlin lurked in the analysis.
In the present case, the signal strength appears to concentrate in the best data. In our initial analysis of galaxies out to 1000 km s-1, we randomly extracted 40 galaxies from the 89 in the set, and computed the signal strengths; we found that the peak derived from the 40 'accurate' galaxies was exceeded by chance only with probability ~0.03 (the figure is ~0.002 for the 97 out of 247 LSC galaxies, but there may be a complication, as discussed below). The signal strength also increases with sample size: taking the 'best' galaxies in each case, I~ 29 for the 40 nearby galaxies and I ~ 38 for the 97 LSC galaxies. Finally, the derived parameters are remarkably stable: as shown in Table 2, the signal holds steady at ~37.5 km s-1, for a solar vector

38

W.M. Napier and B.N.G. Guthrie

varying by only 3 km s-1 in speed and -2° in direction, as the sample is extended from the best 40 to the best 103 redshifts (Section 8.3).

Table 2. Optimized solar vector for the most accurate available data, as a function
of increasing sample size. Note (a) the stability of the peak, and (b) the progres-
sive increase of signal strength. N =40 refers to the original sample; N =97 to the
set described herein; and N = 103 to the 'best' dataset, constructed as described in
the text.

N

40 29 37.5 215 94 -12

97 38 37.5 217 95 -12

103

52 37.5 218 96 -12

8. Gremlins
8.1 False Peaks
The various analyses carried out by Tifft and colleagues have involved small samples, often (in the earlier papers) of relatively low accuracy, while the solar vector was varied over a very limited range. However our analysis reveals that in finding and assessing any periodicity, Vc~ cannot be treated as a 'fudge factor'. It is in fact an optimizing parameter which, uncontrolled, could mislead the investigator into deducing the existence of spurious periodicities.
A number of trials were carried out in which synthetic periodic data (say 100) were split into small groups (say 10) of adjacent redshifts, a random redshift was added to each group, and PSA was then carried out on the whole jumbled dataset.
Quite frequently, the dominant peak was found at some simple fraction (J5., Xor %
say) of the basic periodicity, depending on how the random runes were cast. This result leads us to conjecture that the -24 km s-1 peaks which turned up
far from the galactocentric vector in our whole-sky study (Figure 2) may result from an analogous effect: essentially a solar motion correction far from the true one may stretch and distort the real redshift periodicity, resulting in a 'best fit' on to some fractional one. We also consider that the similar periodicity which TC claimed to have found for the narrow-line galaxies, which we cannot find, may be an artefact due to the smallness of their sample and their binning technique, which can settle on a fraction of any basic period. However, we emphasize that, at the time of writing, these comments are conjectural.
8.2 Radio Telescopes
Several investigations have been undertaken on internal errors within telescopes, and consistency of measurement between them (Rood 1982, Tifft and Cocke 1988, Tifft 1990, Tifft and Huchtmeier 1990). For the best data a consistency of $ 3 km s-1 is routinely obtained in the determination of systemic velocities, both with

Redshift Periodicity

39

different profile reduction techniques and between telescopes. Each galaxy in the list of 97 has several line profile determinations, obtained from different telescopes, and a separate assessment of 0' from each individual group of radio astronomers. It seems unlikely that an artefact, communal to all radio telescopes and capable of generating a false periodicity after subtraction of the solar galactocentric motion, could have gone unnoticed for ~30 years.

8.3 Foreground Contamination
Exarnirtation of the deviations of the redshifts of individual galaxies from the periodicity showed no obvious relation to sky position or morphological type. However, a few of the HI line profiles revealed evidence of asymmetry, as might arise from foreground contamination by our own Galaxy. An exploratory list of 115 redshifts was therefore compiled, comprising the 97 above enhanced by the 18 most accurate redshifts used by TC, and an{ galaxy whose profile (at the 20 percent level) was within 100 km s-1 of 0 km s- was rejected. This reduced the list to 103. The signal for this uncontaminated sample was very strong: Imax = 52 (see Figure 4)
for P = 37.45 km s-1 and a solar vector (218.6 km s-1, 95.8°, -11.5°). A histogram of
the corrected redshift differences taken in pairs is shown in Figure 5 for these 103 redshifts. The periodicity-for Figure 5 clearly reveals it to be such-is coherent over the entire LSC (~63 cycles). Note that this is not a 'statistical result': when the most accurately observed redshifts of the LSC are corrected for the prescribed solar vector, the resultant {cz;} distribution is observed to be highly periodic, independently of any statistical analysis.

200

37.5

P(km/s)

20

v0 ; 218.3km s-1 (0; 95.8" b0; -11.5"

0.005

Frequency

0.05

Figure 4. Power spectrum of the 103 most accurate, uncontaminated redshifts corrected for the optimum solar vector (218.6 km s-1, 95.8°, -11.5°).

40

W.M. Napier and B.N.G. Guthrie

9. Group Membership
These results show that there is consistency with the hypothesis of a strong redshift periodicity between the nuclei of spiral galaxies in the LSC. The hypothesis that the redshift distribution is random gives an extremely poor fit by comparison and cannot be sustained. However we do not know, for example, that the solar vector has the precise parameters yielding the strong peak in Figure 4. It therefore remains to be seen whether some phenomenon other than periodicity might, with the search procedure used, be made to mimic a periodicity: after all, the procedure involves varying parameters to make the data appear as strongly periodic as possible!
Many of the 'field' galaxies in the sample in fact belong to loose groups and
associations (catalogued by Fouque et al. 1992} containing a few bright galaxies.
Since the Monte Carlo simulations smear out redshift correlations::; 20 km s-1 in the real data, it is conceivable that the difference between the real and the synthetic data is due, not to a periodicity, but rather to clustering, assuming the latter has redshift coherence on this scale.
9.1 Redshift Accuracy and Group Membership
As a prelude to this question, we examined the behaviour of the signal as a function of redshift accuracy and group membership. A sample of 261 spirals was
taken, comprising those galaxies in the Bottinelli et al. {1990) catalogue with cz <2600 km s·1 relative to the Galactic centre, with ucz ::;; 4 km s·1, and excluding members of
the three large groups (Virgo, UMa and Fornax clusters). This sample includes a few galaxies previously used by TC but this may be methodologically justified as this part of our investigation is exploratory.
Power spectra were constructed over the ranges of period and solar vector shown in Table 3.

Table 3. Search range for the 261 spirals. P was searched in 24 equal frequency steps.

parameter
v0 /0 b0 p

min max
200 260 60 120 -30 +30 37 39

step size
2 kms -1 1" 1"

Two high peaks were found for this sample, namely:
I= 38 for P = 37.8 km s-1 when (~>' l~>' b~>) = {209.0, 94.5, -7.3); and
I= 33 for P = 37.1 km s·1 when (\'c.), 10 , b0 ) = (219.9, 99.3, -4.1).
(These peaks are somewhat displaced from those previously derived, as expected since the overall accuracy of the sample is reduced.) The absolute deviations le-;1 of the corrected redshifts from these two solutions are significantly correlated (Spearman's rank correlation coefficient r8 - 0.33). Thus the peaks are related, and

Redshift Periodicity

41

the dependence of the mean absolute deviations i"E;I on redshift accuracy and group membership was studied.
The 261 redshifts were classed as 'accurate' (acz < 4 km s·1 or calibrator: Baie-
si-Pillastrini and Palumbo 1986) or 'less accurate' (O"cz =4 km s·1 and non-calibra-
II;I tor), and they were also designated as 'group' or 'non-group' according to the
Fouque et al. catalogue of groups. The values of are on average smaller for the 111 'accurate' redshifts than for the 150 'less accurate' ones, the chance probability of this being p - 0.014. However the more accurately measured galaxies tend to
belong to groups, a chi-squared test revealing that this correlation has chance prob-
ability p - 0.002 (Table 4).

Table 4. Correlation between accuracy of redshift measurements and group membership.

group
accurate 72 less accurate 66
total 138

non-group

39

111

84

150

123 261

500

Figure 5. Two-point correlation function

-..0
'-
-e
::1

corresponding to the redshifts and optimum solar vector employed in the previous figure. Vertical dashed lines represent the best-fit periodicity, which seems to

:z

hold over the whole of the Local Super-

cluster.

42

W.M. Napier and B.N.G. Guthrie

a

b

0

310

,:)cJ7.5 km;s
Figure 6. Histograms of differential redshifts dV for the 53 galaxies linked by group membership: (a) heliocentric redshifts, (b) redshifts corrected for V0 =(216 km s·1, 93°, -13°). Bin-width is 10 km s·1• Vertical arrows mark a periodicity of 37.6 km s·1 and zero phase.

Similar statistical exercises on the 261 galaxies revealed that there was a strong tendency for 'linked' galaxies (two or more measured in a group) to have more accurate redshifts than isolated galaxies or single representatives of groups (p- 0.001), and a further tendency (p - 0.012) for such linked, accurately measured galaxies to possess a stronger signal (grid searches yielding Imax -37 for the 111'linked' galaxies and -22 for the 'unlinked' ones).
To determine whether the J?;/are directly correlated with accuracy (rather than group membership), we examined the sets of 138 group and 123 non-group galaxies separately, before combining the probabilities. (The probabilities are derived using the one-sided Mann-Whitney test and are combined using the Fisher formula.) The upshot is that the signal does indeed seem to be stronger in the more accurately measured data (p - 0.043), consistent with a real signal, however caused.
These analyses confirm the tendency for the signal strength to reside in the best data; but they also reveal a complication, in that the best data tend to belong to small groups and associations. This illustrates the increasing difficulty of periodicity-testing as the search range extends beyond -1000 km s·1 where only a small

JO

37.6

I

200

20

Figure 7. Power spectrum of differential redshifts in Figure 6b.

Redshift Periodicity

43

proportion of galaxies have accurately measured redshifts, and the factors involved in selecting galaxies for accurate measurement are largely unknown.
9.2 Local Redshift Periodicity
The 53 linked galaxies in the accurate sample of 97 comprise 9 doubles, 6 triplets, 3 quadruplets and 1 quintuplet. Subtracting each heliocentric redshift from every other, within each group, yields 55 local differential redshifts (of which 34 are
independent). The sample is smaller and less accurate (the errors now being .fi
times the previous ones), and the number of cycles within each group is small. Thus any periodicity will appear with less accuracy and reduced significance.
The uncorrected differential redshifts are plotted in Figure 6a. Although not readily evident to the eye, PSA of this sample yields a weak periodicity at - 38 km s·1• Under the hypothesis that the corrected redshifts are periodic, it is not surprising that the raw redshifts should reveal one also, since the differential correction for the galactocentric solar vector, across a group of angularly close galaxies, is relatively small.
However, even this relatively small correction must be allowed for in the assessment of periodicity within a group. In Figure 6b are plotted the differential
redshifts after subtraction of Vc0 =(216 km s·l, 93°, -13°). Since the solar correction
is now second order, the precise choice within the accepted galactocentric range is not critical. A periodicity can now clearly be seen, and the corresponding power spectrum (Figure 7) peaks at 37.6 km s·1, with Imax - 25.4. The significance of this peak value can be gauged by comparison with the I"""' distribution obtained from synthetic data, equal to the real data except for the addition of random redshifts in the range ±50 km s·1 (S.E. 20 km s·1). In these trials, signals anywhere in the range 20-200 km s·1 were recorded. The result of 1000 such trials is plotted in Figure 8.
One peak of similar magnitude occurred, but at P =20.5 km s·1 and tfJ- 66°, far
from the ranges (24, 36 or 72 km s·1) and zero phase being tested. Allowing for these latter factors, the periodicity seen in Figure 6b is found to have a chance probability p -10-4, to within a factor of a few.
Figure 6 reveals a difficulty with any hypothesis in which local redshift periodicity is ascribed to observational selection effects: any such factors would operate on the observed redshifts, whereas the periodicity emerges strongly only with respect to the corrected ones.
9.3 Local to Global
These results seem to indicate that there is indeed a periodicity within groups and associations of galaxies. It remains to be seen whether the fundamental process is this local periodicity, or whether galaxies in clusters are more or less test particles detecting a global one; the question reduces to whether these local periodicities are coherent in phase, from one cluster to the next. A grid search applied to the heliocentric (not differential) redshifts of the 53 group-linked galaxies reveals the presence of a sharp peak (Imax- 41) at a periodicity -37.8 km s·1 and phase 27.SO, a remarkably strong signal for the size of the sample (Figure 9).
Its significance was assessed by shifting the groups randomly (within ±100 km s·1) while preserving their internal relative heliocentric redshifts. This is equivalent to shifting the groups by 1-2 Mpc radially with respect to the Sun, destroying

44

W.M. Napier and B.N.G. Guthrie

lmax

30

Figure 8. Distribution of Imax from PSAs of synthetic data simulating dV (real).

any global periodicity but preserving the internal ones. For each LSC so construct-
ed, a grid search was carried out over a 20 x 20° area, from 200 to 260 km s·1 in 'fc.),
for periodicities between 34 and 39 km s·1. The maximum peak found after 100 such
trials was -29.5 (Figure 10). The significance of the I - 41 peak is hard to assess precisely from such a
limited number of trials, but an exponential fit (theoretically expected) on to the
high tail yields a probability p-10-'4 that the real groups, by chance, would be so
placed as to give the illusion of a strong global phenomenon. Thus, the evidence of these simulations is that (a) clustering cannot generate the observed signal; and (b) the periodicity is global in nature.

10. Summary
We have demonstrated the following:
(i) The data are consistent with the existence of a strong, coherent redshift periodicity of -37.5 km s·1 extending over at least the Local Supercluster.
(ii) At a high confidence level, the observed peaks in the power spectra cannot be reproduced by a random redshift distribution.
(iii) Likewise, membership of groups and associations does not yield the observed signal.
(iv) The phenomenon is global, extending over at least the dimensions of the Local Supercluster.
The presence of an obscure observational artefact can never be absolutely excluded, but there is no independent evidence for its existence. The periodicity emerges only after correction for the galactocentric motion, and the phase coherence over the sky cannot readily be produced by, say, proximity effects. Thus, neither random nor clustered extragalactic redshifts, nor observational artefacts, seem capable of yielding the strong peaks observed, and we conclude that the periodicity is, in all likelihood, real.

Redshift Periodicity

45

37.6

30

200

20

P kms- 1

Figure 9. Power spectrum of the 53 linked galaxies, with V0 correction.

11. Possible Physics
Until the phenomenon has been fully explored observationally, any discussion of the physics is likely to be premature. We may nevertheless consider a few hypotheses, with all due caution. In principle, redshift periodicity might arise from regularity in the structure of the LSC, or from oscillating physics, acting either on the atoms in the galaxies or on the photons along their flight paths.
If the redshifts were simply taken at face value, (i.e. as velocities) then we would have to suppose that the galaxies are arranged in a regular structure, have little or no peculiar motions, and that the whole rigid framework partakes conformally in the universal expansion. This simple notion has the advantage that it predicts the correct quantization interval Q to within a factor of two or three: it is given by Q= H0 d, where H0 represents the local Hubble constant and d is the
projected scale length of the lattice. For H0 =75 km s·1 Mpc-1 and d =0.5 Mpc (if the
mean distance between quantized galaxies in a group represents the lattice scale
length), then Q =37.5 km s·1. A cubic lattice of side 37.5 km s-1 has r.m.s. disper-
sion, corner to corner, of -10 km s·1• Numerical trials are under way to determine whether the observations can, in fact, be reproduced by a lattice structure.
Assuming that a lattice exists and is not due to a multiply connected Universe (Fang 1990), how could it be maintained dynamically? A network of cosmic strings (Luo and Schramm 1992) is unlikely to have the required regularity. A gravitational pulse A. -1 M£c may be associated with the anisotropic collapse or explosion of a mass M- c2Aj2G -1019 M0 , but would be too transient to generate periodic structure. If the nuclei of massive galaxies were formed, dissipatively, at the nodes of a system of standing waves, then the phenomenon might in principle be explained. The need for coherence of the periodicity over the LSC (at least) might imply inflation, and hence that such regularities existed within a microscopic horizon and were maintained during the inflationary expansion (cf Buitrago 1988).
The hypothesis is outlandish, but only because the phenomenon is equally so. However, it is not clear that the hypothesis of lattice structure, whether imposed by 'quantum imprint' or otherwise, could account for the observed streaming motions;

46

W.M. Napier and B.N.G. Guthrie

and because of random projection, it cannot account for the -72 km s-1 periodicity supposed to occur in binaries (Tifft loc. cit.).
Periodic oscillations in the fine structure constant a and the mass of the electron m. (quantum electrodynamics connects the two) could in principle lead to redshift periodicity. However such variations are strongly constrained by geology: the Oklo natural reactor in west equatorial Africa, which went 'critical' -2 Gyr ago,
has been used to put a variation of :::ao-17 yr·1 on the proportional change in a, with
a variation of similar order on m. (Hill et al. 1990; Shlyakhter 1976). The periodicity, on the other hand, would require variations -10-10 yr-1•
Such oscillating physics models share the common difficulty that peculiar systemic motions would probably wash out any periodicity imposed through temporal variations in the atomic constants (or in the metric, or in Hubble's constant: Morikawa 1990). While the virial masses derived for galaxy groups may have little meaning, due to the superposition of redshift periodicity, the expected velocity dispersions based solely on the luminosity masses of galaxies are ~20 km s·1 for a typical group, well in excess of the dispersion - 8 km s·1 observed for the 'best' solar vector. However, at the time of writing we have still to test the possibility that u - 20 km s-1 (say), with a non-optimum vector, and is artificially reduced by the optimizing process.
Inflation, whether of the garden variety or of that originally envisaged by Hoyle and Narlikar (1966) in their C-field theory, might enter the story through the presence of a weak scalar field ~, oscillating in a harmonic potential due to its own mass m2~2 and interacting weakly with some other field or particle involved with light propagation (Hill et al. 1990, Crittenden and Steinhardt 1992) such fields are expected in some inflation-based cosmologies (Linde 1990). A rapidly oscillating vacuum energy and a finite photon rest mass (S10-43 g) may be implicit in such a photon/soft boson interaction. Finite photon mass can be made compatible with both Lorentz invariance and QED (Vigier 1990). The absence of peculiar motions is still problematic in such a scheme.
These highly speculative comments neglect the other redshift anomaly claims made by Arp and colleagues over the years. However, given the existence of one type of redshift anomaly, it becomes unsafe to ignore the others, and the true explanation may tum out to bear no relation to any of the above.

n(Imax)

Figure 10. IDW< distribution from 100 box searches on data simulating the 53 linked redshifts.

Redshift Periodicity

47

12. Conclusion
The falling of stones from the sky is physically impossible. Paris Academy of Sciences (Memorandum, 1772).
Redshift anomalies have a long and contentious history in astrophysics. Our analysis of new data was intended to confirm or refute the existence of perhaps the most bizarre of such claims, namely redshift quantization. In the event, the phenomenon has been confirmed at a high confidence level.
An 'anomaly' in science, as defined by Lightman and Gingerich (1991), is an observed fact that is difficult to explain in terms of existing paradigms. Their historical analysis of past anomalies indicates that these are generally ignored until given compelling explanations within a new conceptual framework. Whether any of the currently fashionable concepts and models of cosmology can absorb this mysterious phenomenon remains to be seen. If not, the periodicity may indeed have to await the development of new perceptions before it can be assimilated into the mainstream of scientific thought.

References
Arp, H.C. and Sulentic, J.W., 1985, Astrophys. J. 291:88. Baiesi-Pillastrini, G.C. and Palumbo G.G.C., 1986, Astron. Astrophys. 163:1. Bartlett, M.S., 1955, An Introduction to Stochastic Processes, Cambridge University Press. Blitz, L. and Spergel, D.N., 1991, Astrophys. J. 379:631. Bottinelli, L., Gouguenheim, L., Fouque, P. and Paturel, G., 1990, Astron. Astrophys. Suppl.
82:391. Buccheri, R. and De Jager, O.C., 1989, in: Timing Neutron Stars, eds. H. Ogelman and E.P.J.
van den Heuvel, p.95, Kluwer Academic. Buitrago, J., 1988, Astron. Lett. 27:1. Clube, S.V.M. and Waddington, W.G., 1989, Mon. Not. R. astr. Soc. 237:7P. Combes, F. and Gerin, M., 1985, Astron. Astrophys. 150:327.
Crittenden, R.G. and Steinhardt, P.J., 1992, Astrophys. J. 395:360. de Vaucouleurs, G. and Peters, W.L., 1984, Astrophys. J. 287:1. Delhaye, J., 1965, in: Galactic Structure, Stars and Stellar Systems, eds. A. Blaauw and M.
Schmidt, 5:61, University of Chicago Press.
Einasto, ]., 1979, in The Large-Scale Characteristics of the Galaxy, IAU Symp. No. 84, ed. W.B. Burton, p.451, Reidel.
Fang, L., 1990, Astron. Astrophys. 239:24. Flin, P. and Godlewski, W., 1989, Sov. Astr. Lett. 15:374. Fouque, P., Gourgoulhon, E., Charmaraux, P. and Paturel, G., 1992, Astron. Astrophys. Suppl.
93:211.
Gunn, J.E., Knapp, G.R. and Tremaine, S.D., 1979, Astr. J. 84:1181. Guthrie, B.N.G. and Napier, W.M., 1990, Mon. Not. R. Astr. Soc. 243:431. Guthrie, B.N.G. and Napier, W.M., 1991, Mon. Not. R. Astr. Soc. 253:533. Haud, U., Joeveer, M. and Einasto, J., 1985, in: The Milky Way Galaxy, IAU Symp. No. 106,
eds. H. van Woerden, R.J. Allen and W.B. Burton, p.85, Reidel. Hill, C.T., Steinhardt, P.J. and Turner, M.S., 1990, Phys. Lett. B 252:343.
Horne, J.H. and Baliunas, S.L., 1986, Astrophys. J. 302:757. Hoyle, F. and Narlikar, J.V., 1966, Proc. Roy. Soc. A290:162. Lightman, A. and Shapiro, 0., 1991, Science 255:690. Linde, A.D., 1990, Inflation and Quantum Cosmology, Academic Press. Luo, X. and Schramm, D.N., 1992, Astrophys. J. 394:12. Morikawa, M., 1990, Astrophys. J. 362:137.

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Rood, H.J., 1982, Astrophys. f. Suppl. 49:111. Scargle, J.D., 1982, Astrophys. f. 263:835.
Shlyakhter, A.I., 1976, Nature 264:340. Stothers, R.B., 1991, Astrophys. J. 375:423. Tifft, W.G., 1976, Astrophys. J. 206:38.
Tifft, W.G., 1980, Astrophys. f. 236:70. Tifft, W.G., 1990, Astrophys. f. Suppl. 73:603. Tifft, W.G and Cocke, W.J., 1984, Astrophys. f. 287:492. Tifft, W.G. and Cocke, W.J., 1988, Astrophys. f. Suppl. 67:1.
Tifft, W.G. and Huchtmeier, W.K., 1990, Astron. Astrophys. Suppl. 84:47.
Vigier, J.-P., 1990, IEEE Trans. Plasma Science 18:64.

Compact Groups of Galaxies
Jack W. Sulentic
Department of Physics and Astronomy University of Alabama, Tuscaloosa 35487 USA
We discuss the history and current status of the paradoxes associated with compact groups of galaxies. Dynamical theory requires that compact groups merge rapidly. Currently observed groups must, therefore, continually collapse out of the looser group environment. The observations do not support these model predictions nor do the models explain how the groups resist the onset of merger while in the process of formation. The observations are more consistent with the notion that the compact groups are long-lived or even primordial. At the same time, conventional theory completely ignores the large number of compact groups with at least one discordant redshift member. There are approximately nine times more such configurations than are expected by chance (37 vs. 4). Recognition of this fact may represent the greatest challenge to conventional ideas about this remarkable form of clustering.
Compact Groups and Clustering
Compact groups of galaxies (hereafter CGs) are a constant source of challenges to our ideas about galaxy evolution as well as the nature of the redshift. It can be said that the redshift controversy originated in the late 1950's with observations of the famous group called "Stephan's Quintet." Often apparent anomalies or perceived problems with a scientific paradigm do not stand the test of time. These false clues become weaker as more data is accumulated or some new theoretical idea shows them to not be the problem first imagined. Yet CGs have stood the test of time and remain a paradox. As additional data have accumulated, the problems posed by CGs have grown. This review the history of observations and ideas about compact groups will show that they pose some of the toughest questions for conventional ideas about galaxies. This is true whether or not the discordant redshift components are considered. Perhaps a resolution of the first problem lies with an understanding of the second.
It is now well established that we live in a universe characterized by clustering. Galaxies, the fundamental building blocks of the universe, are clustered on many scales from loose groups (i.e. the Local Group) to rich clusters. It is now realized that these groups and clusters exist in larger assemblages called superclusters. The concept of a more diffuse "field" population of galaxies has gradually

Progress in New Cosmologies: Beyond the Big Bang

Edited by H.C. Arp et al., Plenum Press, New York, 1993

49

50

Jack W. Sulentic

Figure 1. The environs of Seyfert's Sextet (Palomar Sm image). It is the most compact and one of the more isolated compact groups. There are no galaxies of comparable brightness within 45 arcmin.
faded over the past twenty years. This was perhaps most forcefully demonstrated
by the discovery of large voids between the superclusters (see e.g. Sulentic 1980 for
one of the first hints). Compact groups have emerged during the past decade as an "unexpected" form of galaxy clustering. CGs involve aggregates of from 4-10 galaxies with projected separations often on the order of the component diameters. Compact groups show surface density enhancements over their local environment on the order of 102 to 103 which imply space densities as high as 104 Mpc-3. Accepted as physical aggregates, they are as dense as the cores of rich galaxy clusters. A most surprising aspect is that these dense cores are found in lower density regions of extragalactic space.
The reason that the compact groups have recently, in effect, thrust themselves upon us is historical. Some of the most famous ones were recorded in the peculiar galaxy catalogs of Vorontsov-Velyaminov (1959, 1977) and Arp (1966). The most famous of them, Stephan's Quintet, was discovered in the 19th century (Stephan 1877), and studied spectroscopically in the late 1950's. CGs were regarded by most astronomers as rare curiosities or even accidental projections of unrelated galaxies. Almost all of the papers about CGs published before 1985 focused on the three famous discordant redshift groups: Stephan's Quintet (SQ), Seyfert's Sextet (SS) and W172 (W). Early impressions and the focus of effort changed with the publication of a reasonably complete survey of these objects (Hickson 1982; hereafter HCG). The HCG contains a compilation of 100 compact groups found during a visual search of the Palomar Sky Survey. This survey indicates that approximately one percent of the nonclustered galaxies are members of compact groups or, alternatively, that one CG exists for every 50 loose groups (Mendes de Oliviera and

Compact Groups ofGalaxies

51

Figure 2. Computer processed image of Seyfert's Sextet. This Sm image was enhanced to show the luminous envelope surrounding the galaxies.
Hickson 1991). The realizations: a) that the compact groups are relatively common, and b) that they are difficult to explain and have generated considerable recent observational and theoretical interest.
Selection Criteria: The Uniqueness of Compact Groups
The selection criteria used in assembling the HCG are a reflection of the characteristics that had previously been noted about objects like SQ, SS and W. They are compact aggregates of four or more galaxies located outside of clusters. Figure 1 shows an image of SS that was chosen to illustrate the relative isolation that is characteristic of most compact groups. There are no galaxies of comparable brightness within 48 group diameters {0.8 and 3.5 Mpc at the low and high redshift distances; H0 = 75). Figure 2 is a computer processed image of the same group that emphasizes the compactness and the signs of interaction between the galaxies (see Sulentic and Lorre 1983). The HCG selection criteria, consequently, involved richness, compactness and isolation.
Richness: The HCG consists of groups of four or more galaxies with a spread in apparent magnitude mF -m8 ~ 3.0, where m 8 and mF are the magnitudes of the brightest and faintest components.
Compactness: Groups were required to have a mean surface brightness J1 ~ 26.0 mag. arcsec-2 .

52

Jack W. Sulentic

Isolation: The distance to the nearest non group neighbor was required to be greater than three times the group radius (RN ;;:: 3 RG where RN is the distance to the nearest neighbor with apparent magnitude in the range of the group and Rc is the group radius). The final catalog contains 463 galaxies in 100 groups.
A very difficult question is the degree to which these selection criteria bias the HCG sample of compact groups. Certainly they insure that the HCG contains most of the compact groups with surface brightness as high as SQ, SS and W (Jl = 22, 20 and 24 respectively). The HCG is estimated to be nearly complete for compact groups with Jl ~ 24.0 (Hickson 1982). A V/Vm calculation (Sulentic and Raba~a 1993) shows that the HCG becomes seriously incomplete for groups with a com-
bined magnitude below me =13.0. Where are these missing CGs and what are their
properties? Will they change our basic description of compact groups and their relationship to other forms of clustering?
Possible evidence for the uniqueness of compact groups as a class of clustering (and, therefore, a negative answer to the latter question) comes from recent work towards a southern hemisphere catalog. Prandoni et al. (1992) are attempting an automated search of the southern sky for compact groups satisfying the HCG selection criteria. In the process of incorporating the selection criteria into their algorithm, they have graphically represented the selection domain of the HCG. It is possible to show the boundaries of the HCG selection domain in a plot of group radius versus magnitude of the brightest group member. Figure 3 shows a schematic representation of the compact group domain in relation to richness, isolation, and compactness. It is clear that compactness and richness are the defining criteria for most compact groups. The isolation criterion is redundant for groups with the brightest member above 16th magnitude. In other words, groups of four or more galaxies that have a combined surface brightness above 26.0 always satisfy the isolation criterion. Similar groups in or near clusters might not pass an isolation criterion. One candidate group was found near the Virgo cluster (Mamon 1989);

&RDUPS

10

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.... ....."' :.. ••·~ 55 . . . .

• ••

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10

12

14

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brightest member magnitude m8

Figure 3. A graphical representation of the selection domain for the HCG (adapted from Iovino et al. 1993). Approximate boundaries of the richness, isolation and compactness criteria are indicated. The three famous quintets SQ, SS and VV are indicated.

Compact Groups ofGalaxies

53

but objects like SQ, SS and VV are not often seen near clusters. The HCG sample is plotted within the domain represented in Figure 3. If compact groups were an extension of the more general population of loose groups, we would expect the HCG points to cluster near the upper boundary of the domain. Looser groups would have larger size and lower surface brightness than compact groups like SS. Note that HCGs concentrate near the center of the selection domain. The most compact CGs fall near the lower richness boundary. The HCG was assembled with a visual search which will be most sensitive to the most obvious compact groups. Will the many CGs missed in the HCG survey fill in the upper part of the selection domain of Figure 3?
Recently Iovino et al. (1993) have published a list of the first 55 compact groups detected in the automated survey. Differences between brightest and faintest group member magnitudes were evenly scattered between 0 and 2.5 in the HCG while the new sample is strongly peaked between 2.5 and 3.0. Thus the new sample contains more low surface brightness groups, as expected from the VfVm results. Despite the difference, however, the new groups do not concentrate at the upper boundary of the selection domain. They generally fall higher than HCG objects, but they do not appear to bridge the loose group domain. This suggests that compact groups may well represent a unique form of galaxy clustering. Images like Figures 1 and 2 certainly reinforce this impression.

Conventional Ideas About Compact Groups and Problems
Are compact groups physically dense systems and, if so, what are the implications of this? It may seem difficult to imagine that anyone would question the physical nature of groups like SQ and SS. The fact that this question has been raised, and for reasons beyond the issue of discordant redshift components, is a reflection of the difficulties that CGs pose for conventional ideas. Let us assume for the moment that most compact groups are real. Following the current fashion, we will ignore the discordant redshift components. Note that SQ, SS and VV are still compact quartets in this case. Components in the groups show very small projected separations, implying very high space densities. The velocity dispersion is usually quite small (SQ at 400 km s-1 is twice the mean for the HCG). Attempts to simulate the evolution of a compact group always lead to the same result: they merge very quickly into presumably elliptical-like remnants (Carnevali et al. 1981; Ishizawa et al. 1983; Mamon 1986; Barnes 1985, 1989). The exact time scale varies depending upon the exact recipe: e.g. distribution and amount of dark matter, velocity dispersion and group crossing time. The main result is that in timescales on the order of a few crossing times (typically a few times 108 years) the groups will have become triplets, binaries or single remnants. The final coallescence may take more than a Gyr, but the groups will disappear from a catalog like the HCG in much less time. This result implies that the compact groups now observed are all "young" systems. They are found in lower density regions of space, which implies that they continually form out of their looser group environment. Otherwise we should observe no compact groups at all. Note that attempts to prolong the lifetime of a CG (e.g. Governato et al. 1991) invoke special conditions that are not obviously applicable to most objects.

54

Jack W. Sulentic

As is often the case, the observations appear to contradict the theoretical predictions. Let us count the ways: 1) The foremost difficulty is how to bring four or more galaxies very close together, allowing them time to dynamically evolve, before the onset of the first merger. 2) The ratio of early to late type galaxies in compact groups is different from their local environment. They show a distinct
excess of E and SO galaxies (Hickson et al. 1989, Mendes de Oliviera and Hickson
1991, Rabac;a and Sulentic 1993). It seems unlikely that secular evolutionary effects would have time to account for these changes if most present groups are recently collapsed from the field. 3} The observations reveal little evidence for mergers in progress. 3a} The ellipticals in the HCG show no evidence of color anomalies expected if they are the first stage in the coallescence of currently observed groups (Zepf and Whitmore 1991). 3b) The ellipticals in compact groups have also been shown to be not sufficiently "first ranked" compared to the predictions of models that view them as partial mergers (Mendes de Oliviera and Hickson 1991). 3c) There is a surprisingly low level of optical, FIR and radio enhancement in compact groups considering that widely cited merger remnants like Arp 220 are so active at these wavelengths (Sulentic and Rabac;a 1993, Sulentic and de Mello Rabac;a 1993). In fact, long wavelength enhancements are generally interpreted as evidence for merger-induced starburst activity. 4) Searches for merger remnants in the environment where the compact groups are found reveal few candidates (Sulentic and Rabac;a 1993). The models have suggested quite high densities of such remnants implied by the rapid coallescence timescales (e.g. 10-4 Mpc-3, Barnes 1989}. The few elliptical galaxies found in loose groups tend to be significantly lower in luminosity than would be expected for the remnants of compact groups. Claims to the contrary (e.g. Zepf and Whitmore 1991) involve comparison samples rich in luminous cluster (e.g. Centaurus A and Fomax A) elliptical galaxies (see Rabac;a and Sulentic 1993).
It is the above impressive array of observational and theoretical contradictions that has motivated some to argue that compact groups cannot be real. The implications are otherwise too disturbing, for they suggest that the groups are long-lived, maybe even primordial configurations. We cannot rule out the possibility that the HCG represent the dynamically "lucky" part of a much larger primordial population of compact groups. Argument 4 above remains the strongest argument against this view since any existing remnant population is quite small. The published article that described the most sophisticated compact group simulation so far (Barnes 1989) was accompanied by an invited (or contributed) editorial. This accompanying piece, after summarizing the model predictions, contains the comment: "A quick check of recent observations shows no contradictions with the scheme!" It is left to the reader to decide whether the above discussion indicates a contradiction or not.

Compact Groups: Real or Imagined?
The strongest advocate of the chance projection hypothesis argues that 70% or more of the HCG represent various types of chance alignments or false groups (Mamon 1986, 1993). The strongest argument against the chance projection idea is the low surface density of galaxies found near the compact groups. Three independent estimates of the actual surface densities have been made (Sulentic 1987, Rood and Williams 1989, Kindl 1990). Each used slightly different procedures, but the studies all yield the same essential result. Figure 4 illustrates the results from

Compact Groups ofGalaxies

55

• DENSE GROUPS IN LOOSE GROUPS

Ill: 11.1 ID
:1
z::I
Figure 4. Distribution of galaxy surface densities for the HCG (adapted from Sulentic 1987).Values are given for a one half degree search radius in units of galaxies deg-z.
Sulentic (1987) where the very isolated, loose group and clustered regimes are indicated. They suggest that compact groups are found in low surface density "loose-group" type environments. Is this a reasonable estimate? The Sulentic (1987) estimates were based upon galaxy counts out to a radius of one degree around each CG. A fixed search radius was chosen in order to avoid any dependence on the
redshift. Following the conventional procedure, one degree at V0 =104 km s-1 (and
H0 = 75) corresponds to 2.3 Mpc which is a typical loose group diameter. This suggests that our procedure is also reasonable from the standard redshift-distance relation point of view. Estimates of the number of chance projections by accordant redshift interlopers using the above results yield very small numbers. The surface densities are simply too low to produce many false groups with accordant redshifts. Note that the fraction of compact groups decreases as the surface density increases in Figure 4. This emphasizes the point that CGs are typically found in nonclustered regions. If the opposite were true, then the number should increase with surface density until the effect of the isolation criterion becomes strong. Stated another way, if all isolated CGs are due to chance alignments, then we should see large numbers of CG-like configurations in clustered fields (even if they do not satisfy the HCG isolation criterion). My own observational experience suggests that this multitude of nonisolated false groups does not exist.
The other arguments against the chance projection hypothesis are multifold. They involve the observational evidence that the groups are physical systems. It is worthwhile to summarize here the principal elements: A) Compact groups tend to be deficient in neutral hydrogen by roughly a factor of two (Williams and Rood 1987). This probably indicates that the gas has been stripped in close encounters and collisions between the groups members. B) More than half of the spiral components that have been studied kinematically show rotation curve peculiarities (Rubin et al. 1991). C) Some of the groups are surrounded by a common luminous envelope (e.g. SQ, SS and W172) (Sulentic 1987) or show bridges, tails and other deformations suggestive of interaction. D) Admittedly limited data show three out of five observed compact groups as X-ray sources, two of which are diffuse sources

56

Jack W. Sulentic

(Bahcall et al. 1984). The detection of a considerable number of additional diffuse X-ray sources associated with compact groups would provide the most ironclad proof that they are physical systems. Hickson and Rood (1988) presented a more detailed summary of the evidence that compact groups are real.
The bulk of the evidence at the present time leads us to conclude that compact groups are real. Their properties are sufficiently unusual that we must consider them as a unique form of galaxy clustering: aggregates of galaxies with implied densities like the cores of rich clusters but located outside of clusters; systems tlult appear to be much more long lived tluln theory predicts. At the very least, CGs will teach us something fundamental and new about the dynamics of dense galaxy systems. At the outside, they may teach us new things about the entire galaxy formation process. We raise the possibility that the final understanding of compact groups may also involve the discordant redshift components. There are far too many discordant members of compact groups for any reasonable interloper hypothesis. This conclusion is not obvious from perusal of the literature. In order to emphasize the problem and provide the information upon which an opinion should be based, we review the history of discordant redshifts in compact groups. The history begins, appropriately enough, with a discussion of Stephan's Quintet.

,,> ... , .. .. ...... . •

Figure 5. Image of the Stephan's Quintet region including NGC 7331 at the upper left (Palomar 1.2 m image). The galaxy images are overexposed to emphasize faint structure.

Compact Groups ofGalaxies

57

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Figure 6. Schematic representation of Stephan's Quintet. High redshift HI and radio continuum (20 em) contours are superimposed. Redshifts are indicated under each galaxy.

Discordant Redshifts: Direct Evidence
Figure 5 shows an image of Stephan's Quintet and its neighborhood. The quintet consists of four galaxies, NGC 7317, 18, 18B and 19, with redshifts near 6000 km s·1 and one galaxy NGC 7320, with a redshift near 800 km s·1• The discovery of the "discordant" redshift for NGC 7320 was announced by Burbidge and Burbidge (1961) well before the discovery of quasars. There are two possible interpretations for this puzzling result. NGC 7320 is either a member of the group or is a foreground projection. If the former is true then either the redshift of NGC 7320, or those of its companions, do not obey the standard redshift-distance relation. There are three approaches for deciding between the possible interpretations. 1) One can look for evidence that NGC 7320 is interacting with the other galaxies in the Quintet. 2) One can try to derive redshift independent distances for the galaxies in SQ or 3) One can estimate the probability that NGC 7320 is accidentally projected on the accordant redshift quartet.
Work before 1982 tended to focus on the two former approaches because compact groups were known to be so rare that any estimate of the latter kind provided a disturbing answer. The probability calculation also had the disadvantage of being a posteriori, since at first only one (the Burbidges' estimated lQ-3 probability of chance projection for SQ), and then three examples (SQ, SS and VV) were known. Any such calculation will almost always yield a very small probability because it depends upon the (very small) surface area of the group. The Burbidges discussed the size and luminosity of the discordant galaxy implied both by

58

Jack W. Sulentic

its redshift and the mean redshift for the remainder of the group. They had earlier noted (before the redshift of NGC 7320 was measured: Burbidge and Burbid?e 1959) that the velocity dispersion for this group was quite high (about 400 km s· ). Using virial theorem arguments popular at that time, they concluded that SQ was unbound (in an early reference to a now very popular concept, they argued against the existence of sufficient "dark matter" to bind the system).
The two decades following the discovery of the discordant redshift in SQ saw a large number of arguments and counter-arguments about the relationship between the high and low redshift galaxies. This group has probably been observed with more telescopes and at more wavelengths than any other galaxy aggregate. The results are a lesson in how subjective the interpretation of data can be and how difficult it can be to estimate a redshift independent distance. They also reveal, unfortunately, how the credibility of an observation or interpretation depends less on its quality than upon its implications for the standard paradigm. We summarize many, but not all, of the arguments raised. Figure 6 presents a schematic of SQ which can be used as a reference to the cited work along with Figure 5. Redshifts are indicated under each of the galaxies in Figure 6. NGC 7320C, which may be related to SQ, is also shown. The bright Sb spiral NGC 7331 (with redshift similar to NGC 7320) is located one half degree to the upper left (NE).
1) Kalloglyan and Kalloglyan (1967) pointed out that "The only-though fairly strong-argument against NGC 7320 being a member of the quintet is its radial velocity." They presented three color photometric data which showed that NGC 7320 was brighter in the U band on the side towards the high redshift galaxies. They argued that the data was more consistent if NGC 7320 was at the higher redshift distance.
2) In a paper titled "Stephan's Quartet?" Allen (1970) presented the first neutral hydrogen measures for NGC 7320. As the title suggests, he found the HI measures consistent with the redshift distance of the galaxy.
3) Arp (1971) suggested that the four higher redshift members of the quintet might be at the same distance as NGC 7320. He proposed that the group was ejected from NGC 7331, located 30 arcmin distant.
4) Arp (1972) argued that there was an excess of strong radio sources in the region between SQ and NGC 7331. He suggested that they were related to SQ and the proposed ejection event.
5) Lynds (1972) published redshifts for a number of galaxies in the region of NGC 7331 and SQ. He argued that the results were consistent with two unrelated sheets of galaxies at distances consistent with the two redshift systems in SQ.
6) Allen and Hartsuiker (1972) published a high resolution radio continuum map for SQ. They found a source coincident with NGC 7319 and a peculiar "arc" of emission between NGC 7319 and 7318B. It was noted that the arc extended south to the interface with NGC 7320.
7) Vander Kruit (1973) employed new Westerbork observations to argue that there was "definitely" no excess of radio sources in the region.
8) Arp (1973) presented images and spectra of the HIT regions in the high and low redshift members of SQ. He showed that the HIT regions in NGC 7320 were concentrated on the side towards the higher redshift quintet members. Arp argued that the largest HIT regions in NGC 7320 and higher redshift NGC 7318 showed similar apparent size. He argued that this was most consistent with the

Compact Groups of Galaxies

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known properties of the largest HTI regions in galaxies if both were located at the redshift implied distance of NGC 7320. Observations of a supernova in NGC 7319 were found to be inconsistent with either redshift distance, but more seriously with the lower value.
Finally, Arp presented new images that revealed a curved filament extending from the SE end of NGC 7320 opposite the center of SQ. He argued that the width and resolution of this feature suggested that it was an appendage of NGC 7320. He argued that this feature was strong evidence for interaction between NGC 7320 and the rest of SQ. 9) Balkowski et al. (1973) published HI observations for NGC 7319 and concluded that this high redshift member was most likely at a distance near NGC 7320. 10) Shostak (1974ab) published HI observations for NGC 7319 and concluded that this high redshift member was most likely at its higher redshift distance. The principal difference between 9 and 10 was the calibration sample used. 11) Kaftan-Kassim and Sulentic (1974) published new low frequency radio continuum observations of the SQ and NGC 7331 region. They found evidence both for a diffuse radio connection between these two objects and for an excess of (steep spectrum) radio sources in the field. 12) Kaftan-Kassim et al. {1975) published a high resolution radio continuum map of SQ. They resolved the radio "arc" discovered previously. The southern component of the "arc" falls near the interface between NGC 7318ab and 7320 (see X in Figure 6).
Stridency alert: The establishment papers begin to take on a much more strident tone at this point. The frequency of words like "normal", "not unusual" and "typical" show a dramatic increase.
13) Gillespie (1977) published deep radio continuum survey data for the NGC 7331/SQ area. He concluded that the region was "normal in all its radio properties except for the distribution of the brightest sources." He concluded that these were unrelated to SQ or NGC 7331.
14) von Kap-herr et al. {1977) published radio continuum maps of the NGC 7331/ SQ region. They concluded that no extended emission is present between the objects. They confirmed an excess of steep spectrum sources in the area.
15) Gordon and Gordon (1979) report on a search for HI emission in the velocity range between the two redshift systems in SQ. They detect no emission and conclude that "the data are consistent with the standard cosmological interpretation of redshifts."
16) Allen and Sullivan (1980), Peterson and Shostak (1980) and Shostak et al. (1984) reported new high resolution HI measures at both the high and low redshifts associated with SQ. They found the high redshift HI was not coincident with the optical galaxies but, instead, is displaced in several large clouds (Figure 6). This result invalidated all previous attempts to assign distances to the galaxies using HI properties. They found that low redshift HI associated with NGC 7320 showed "no peculiarities which cannot reasonably be related to known instrumental deficiencies." The latter authors found HI derived distances for galaxies near the quintet (with redshifts similar to the higher system). Those HI properties were found to be consistent with the redshift implied distance.

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17) Kent (1981) used velocity dispersion measures for the high redshift members of SQ and the HI profile width for NGC 7320 to conclude that "All objects are found to be at distances consistent with their redshifts."
18) Vander Hulst and Rots (1981) published VLA radio continuum maps of SQ. They confirmed the previous resolution of the radio "arc" into two sources. The lower source peaks at the interface between the high and low redshift systems (NGC 7318B and 7320).
19) Sulentic and Arp (1983) reported new HI measures for NGC 7320. They argued for the presence of low redshift HI significantly displaced from NGC 7320. They showed that NGC 7320 is strongly HI deficient for its type. They argued that these results indicate that NGC 7320 is interacting with its higher redshift neighbors.
20) Bahcall et al. (1984) reported the X-ray detection of SQ. A diffuse source was found essentially coincident with the radio continuum emission at the interface between the high and low redshift systems (X in Figure 6). At this point we enter the "rejection phase" where it is considered inappropri-
ate for respectable scientists to carry out further observations of discordant redshift systems. We find both sides of the controversy convinced that their interpretation is the correct one. What have the data told us? The optical observations are extremely difficult to interpret. Comparisons between control samples and the high redshift SQ members are unlikely to prove anything. These galaxies are unambiguously involved in a strongly interacting system. Thus any discussion of abnormality in their properties cannot prove anything except that they are perturbed by interaction. NGC 7320, from this point of view, is favored for study and it does show some peculiarities. The most striking optical peculiarities include the luminous tail as well as the U band and HII region asymmetry. Does this evidence point towards interaction with the high redshift galaxies in SQ or a long past encounter with NGC 7331? Are the same peculiarities sometimes observed in isolated galaxies?
HI data for the high redshift galaxies reinforces the previous point about the uselessness of inferences concerning strongly interacting galaxies. The peculiar state of the HI is consistent with the general HI deficit in compact groups. The HI is not missing in this case, but merely displaced. It certainly establishes the physical nature of this compact quartet (or, at least, triplet). There is general disagreement over the level of peculiarity in the HI properties for NGC 7320. The claimed deficiency in HI is surprising and is a general property of galaxies in compact groups. If NGC 7320 is peculiar, who is responsible?
The radio continuum and X-ray data provide perhaps the most striking puzzle. The presence of diffuse X-ray emission supports the idea of SQ as a physically dense (and dynamically evolved) system and provides a further source for some of the missing HI. The centroid of the X-ray emission and one of the radio sources (X in Figure 6) falls near the SQ-NGC 7320 interface. It is not clear why this should be if NGC 7320 is a foreground projection. The lack of a clearcut answer from any of the above observations leads us to look for a statistical resolution of the problem.

Discordant Redshifts: Statistical Arguments
Much of the work on SQ was stimulated by the discovery of discordant redshift galaxies in two more of the most famous compact groups: Seyfert's Sextet

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(SS) and VV172 (VV) (Sargent 1968, 1970; Burbidge and Sargent 1970). Seyfert's Sextet is the most compact (highest surface brightness) and one of the most isolated compact groups. The probability of a chance interloper in this case is vanishingly small. The problem with all of the individual calculations of interloper liklihood is that they are a posteriori. Further it is difficult to frame the appropriate question in the first place, since one can obtain any desired value for the probability of chance occurence by phrasing the question suitably. For example, the probability that a bright background Sc spiral falls along the same line of sight as a bright galaxy quartet is very small. In spite of this, the existence of three such discordant associations by the early 70's was a general source of uneasiness. Anyone familiar at the time with galaxy statistics and distributional properties appreciated the general rarity of compact groups and the consequent improbability of so many chance alignments.
The return to a statistical analysis of the problem was motivated by these three compact groups. A definitive statistical result, in the minds of many, was published in 1977 (Rose 1977). First it was noted that SQ, SS and VV are all quintets with a single discordant component. This reduces the problem to estimating how many real quartets of galaxies should have an unrelated galaxy superimposed. In principle, the simpler and better defined the question, the more credible and tractable the answer. One can simply estimate the interloper fraction by counting
the number of quartets on the sky. It then follows that N 5 =N 4 R, where R = A a
(N4 and N 5 are the number of quartets and false quintets, A is the average group
surface area and a is the surface density of field galaxies). Rose (1977) reported the
results of a search for galaxy quartets on the Palomar Sky Survey. He reported 26 definite and seven probable quartets on 69 (6" x 6.) Sky Survey fields. He extrapolated from this result an estimate of 433-550 compact quartets on the sky. This value, coupled with an estimate for the field galaxy density, yielded an expectation of 1.5-2.0 discordant redshift compact groups-in "remarkable agreement" with observation. This result was widely cited as the definitive resolution of the
redshift controversy. I can remember the uncritical and unreserved relief with which the above
study was greeted. I can also remember how clear it was that the result was incorrect. There are nothing like 400-500 compact quartets on the sky with properties remotely similar to SQ, SS and VV. This fact became obvious with the publication of the HCG (Hickson 1982). Contemporaneously, I carried out my own reanalysis of the Rose survey (Sulentic 1983). The reanalysis was carried out by myself and, independently, by two of my undergraduate students. The idea was to compare an experienced and potentially biased result (my own) with the results of two completely naive catalogers. They were given a set of finding charts with SQ, SS and VV depicted at the same scale as the Palomar Sky Survey. They were told to catalog all systems of four or more galaxies with similar brightness and isolation. Results were compared and a final list of compact groups was assembled and compared with the list of Rose (1977).
The results of the reanalysis revealed that Rose (1977) had overestimated the number of galaxy quartets by a factor of between 2 and 10. Some of the objects were not even quartets. Many of the quartets were much fainter in apparent magnitude and lower in surface brightness than SQ, SS and VV. We found 2-3 times fewer objects in the same fields using soft selection criteria. We found ten times fewer objects when we required group properties to be similar to the famous three quin-

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tets (hard criteria}. Note that this is true even if we neglect the contribution of the discordant components. At the same time, Hickson (1982) catalogued 100 compact groups down to declination -33°. He found 60 quartets which agreed well with our results. The HCG selection criteria accepted many compact groups with properties much less striking than SQ, SS and W. Perhaps the most remarkable result of the Rose analysis was that no more than 10-12 of the 400-500 claimed compact groups had measured redshifts in 1977. Yet all of the expected discordant quintets had been discovered! It was immediately clear that this was extremely unlikely. This was pointed out in our reanalysis, which was accepted for publication in the Astrophysical Journal. Sadly, the referee commented that while acceptable for publication, our results were "unlikely to have any effect on thought."

The Latest Statistics on Discordant Redshifts
As stated earlier, the HCG has opened a new chapter in the study of compact groups. The existence of a reasonably complete sample has stimulated much study and underscored the difficulties summarized in earlier sections of this paper. Recently a redshift survey was completed for the HCG. The data have been kindly made available by Paul Hickson. The result is that approximately 37 out of 100 compact groups have at least one discordant redshift component (a galaxy with velocity differing from the mean of the accordant members by more than 2000 km s"1). With complete redshift information we are in a position to obtain a reliable statistical expectation for interloper contamination in compact groups. We proceed by asking the simplest possible question. How many interlopers are expected in the HCG given the local surface densities. The HCG provides measured diameters for all HCG groups. Three independent sets of galaxy surface densities have been measured in the HCG fields (Sulentic 1987, Rood and William 1989, Kindl1990}. My survey counted galaxies in two zones of radius 0.5 and 1.0 degree. Two zones were used because not all neighboring galaxies are expected to have discordant redshift. In a superclustered universe, one expects many galaxies near any CG to have redshifts similar to the CG members. This is especially true if these neighbors have apparent size and magnitude similar to the CG components. Our inner count was intended to estimate this accordant redshift contribution. The outer annulus from 0.5 to 1.0° was regarded as the best estimate of the discordant redshift field. One can argue about the details of the procedure, but most of the numbers are small no matter how you do it. We used the local surface density and compact group diameter to estimate the number of discordant interlopers expected in each case. We then summed the expectations for the entire catalog and found values of 6, 0.2 and 0.02 for the number of single, binary and triplet interlopers. About one third of these objects are estimated to show accordant redshift with their respective compact groups. This leaves an expectation of four discordant compact groups in the HCG. The HCG redshift survey shows 26 single, 3 binary and 2 triple galaxy discordant interlopers. In addition we find five groups where all of the galaxies are discordant. In summary, we find about nine times more discordant cases than expected.
There is another viewpoint. Hickson et al. (1988) published an independent estimate of the interloper fraction. They concluded that the observed large number of discordant compact groups agrees well with statistical expectation. How could there be such a disagreement over such a straightforward calculation? We derived

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63

MAXIMUM DIAMETER FOR 1 - - - POSSIBLE INTERLOPERS
~- HCG DIAMETER

Figure 7. A comparison of the group diameters used in Sulentic (1987) and Hickson et al. (1988) for estimating the discordant redshift interloper fraction in Seyfert's Sextet.
an estimate for all of the compact groups using their local surface densities and observed diameters. Hickson et al. (1988) returned to the question of the number of discordant quintets expected. This difference is irrelevant. The two estimates use similar galaxy surface densities but they use very different estimates for the area subtended by the groups. This difference will dominate any estimate, be it for one or one hundred groups. Sulentic (1987) used the actual group diameters as tabulated in the HCG. Since the group diameters include the discordant components, this seems a reasonable approach. The other advantage was that the definition of group diameter was independent of the test. Our approach becomes a simple question of how many interlopers are expected in a 0.5 deg 2 patch of sky (the combined area of the HCG groups).
Hickson et al. (1988), on the other hand, argued that the correct group diameter should represent the maximum group size where an interloper would still pass the HCG selection criteria. Figure 7 illustrates this point for SS. This group has an HCG defined diameter of approximately one arcmin. However, if an appropriately bright interloper had fallen up to approximately 8 arcmin from SS it would have passed the selection criteria. This argument leads to an increase in the surface area of "hypothetical SS" by more than 250 times. Using this approach Hic;kson et al. (1988) concluded that the large interloper population was expected. They argued that the Sulentic (1987) approach was valid only for internal discordant members. We find 10 HCG with internally discordant components (15 if one includes the 5 groups that are totally discordant) which is still a large excess over expectation.

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We disagree with the conclusions of Hickson et al. (1988) and argue that their approach does not allow for the physical uniqueness and rarity of compact groups. This refers us back to Figure 3 which shows that compactness, and not isolation, is the determining factor for most compact groups. It seems unreasonable to base a calculation upon what groups might have been, when we have a well defined
catalog of real groups to work with. It still might be argued that the discordant component excess is an effect of
the incompleteness of the HCG. The lower surface brightness compact groups are expected to have a much higher fraction of interlopers, as shown by Prandoni et al. (1992). Perhaps the discordant components pushed many lower surface brightness groups above the selection threshold. This seems unlikely to remove the excess for
two reasons: 1) Only four groups fall in the surface brightness range f1 = 25.0-26.0
(the HCG cutoff). In most cases the addition of a discordant galaxy will not produce
a large enough enhancement to elevate a group from below f1 = 26.0 to above f1 =
25.0, and 2) There is also a large excess of discordant groups among the subsample
thought to be most complete (surface brightness above f1 = 24.0). It is not obvious
how a selection effect can explain the excess of discordant redshift groups. It has become unpopular (if it ever was popular) to discuss discordant red-
shifts, and especially to argue that there are too many of them. The bottom line, however, is whether we evaluate results based upon their scientific correctness or
by the degree with which they fit into our preconceived ideas. There are far too many compact groups with discordant redshift components. The reason for this is not yet clear. As suggested earlier (and in Sulentic 1987), this excess may be a part of
the solution to the more conventional challenges raised by the groups.

References
Allen, R.J. 1970, Astr. Astrophys. 7:330. Allen, R.J. and Hartsuiker, J. 1972, Nature 239:324. Allen, R.J. and Sullivan, W.T. 1980, Astr. Astrophys. 84:181. Arp, H. 1966, Astrophys.]. Suppl. 14, No. 123. Arp, H. 1971, Science 174:1189. Arp, H. 1972, Astrophys. J. 174:L111. Arp, H. 1973, Astrophys. J. 183:411. Bahcall, N., Harris, D. and Rood, H. 1984, Astrophys. J. 284:129. Balkowski, C., Bottinelli, L., Chamaraux, P., Gouguenheim, L. and Heidemann, J., 1973, Astr.
Astrophys. 25:319. Barnes, J.E. 1985, Mont. Not. R. Astr. Soc. 215:517. Barnes, J.E. 1989, Nature 338:123. Burbidge, G.R. and Burbidge, E.M. 1959, Astrophys. J. 130:15. Burbidge, E.M. and Burbidge, G.R. 1961, Astrophys. J. 134:244. Burbidge, E.M. and Sargent, W.L. 1970, in: Nuclei of Galaxies, ed. D. J. K. O'Connell, (Amster-
dam: North Holland), p. 351.
Carnevali, P., Cavaliere, A. and Santangelo, P. 1981, Astrophys. J. 249:449. Gillespie, A.R. 1977, Mont. Not. R. Astr. Soc. 181:149. Gordon, K.J. and Gordon, C.P. 1979, Astrophys. Lett. 20:9. Governato, F., Bhatia, R. and Chincarini, G. 1991, Astrophys. J. 371:Ll5. Hickson, P. 1982, Astrophys. J. 255:382. Hickson, P., Kindl, E. and Auman, J. 1989, Astrophys. J. Suppl. 70:687. Hickson, P., Kindl, E. and Huchra, J. 1988, Astrophys. J. Lett. 329:165. Hickson, P. and Rood, H. 1988, Astrophys. J. Lett. 331:169.

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Iovino, A., Prandoni, I., MacGillivray, H., Hickson, P. and Palumbo, G., 1993, in: Proceedings of Observational Cosmology, in press.
Ishizawa, T. et al. 1983, Pub. Astr. Soc. ]pn. 35:61. Kaftan-Kassim, M.A. and Sulentic, J.W. 1974, Astr. Astrophys. 33:343. Kaftan-Kassim, M.A., Sulentic, J. and Sistla, G., 1975, Nature 253:1. Kent, S. 1981, Pub. Astr. Soc. Pac. 93:554. Kalloglyan, A.T. and Kalloglyan, N.L. 1967, Astrophysics 3:99.
Kindl, E. 1990, Ph.D. Thesis, Univ. of British Columbia. Lynds, C.R. 1972, in: External Galaxies and Quasi-Stellar Objects, eds. D. S. Evans, (Reidel:
Dordrecht), p. 376. Mamon, G.A. 1986, Astrophys. ]. 307:426. Mamon, G.A. 1989, Astr. Astrophys. 219:98.
Mamon, G.A. 1993, in: Proceedings of HST Workshop on Groups ofGalaxies, in press. Mendes de Oliviera, C. and Hickson, P. 1991, Astrophys. ]. 380:30. Peterson, S.D. and Shostak, G.S. 1980, Astrophys. ]. 241:11.
Prandoni, 1., Iovino, A., Bhatia, R., MacGillivray, H., Hickson, P. and Palumbo, G., 1992, in:
Digitized Optical Sky Surveys, eds. H. T. MacGillivray and E. B. Thompson, (Kluwer
Academic Publishers), p. 361. Raba~a, C. and Sulentic, J.W. 1993, Astr. Astrophys., submitted. Rood, H. and Williams, B. 1989, Astrophys.]. 339:772. Rose, J. 1977, Astrophys. ]. 211:311. Rubin, V.C. et al. 1991, Astrophys. ]. Suppl. 76:153. Sargent, W.L. 1968, Astrophys. ]. 153:1135. Sargent, W.L. 1970, Astrophys.]. 160:405. Shostak, G.S. 1974a, Astrophys.]. 187:19.
Shostak, G.S. 1974b, Astrophys. J. 189:11. Shostak, G.S., Sullivan, W.T., III, and Allen, R., 1984, Astr. Astrophys. 139:15.
Stephan, M. 1877, Mont. Not. R. Astr. Soc. 37:334. Sulentic, J.W. 1980, Astrophys. J. 241:67. Sulentic, J.W. 1983, Astrophys. J. 270:417. Sulentic, J.W. 1987, Astrophys. ]. 322:605. Sulentic, J.W. and Arp, H. 1983, Astron. ]. 88:267. Sulentic, J.W. and de Mello Raba~a, D. 1993, Astrophys.]. June 20.
Sulentic, J.W. and Lorre, J.J. 1983, Astr. Astrophys. 120:36.
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press.
van der Hulst, J.M. and Rots, A.H. 1981, Astron. J. 86: 1775. van der Kruit, P.C. 1973, Astr. Astrophys. 29:249.
von Kap-herr, A., Haslam, C.G. and Wielebinski, R., 1977, Astr. Astrophys. 57:337. Vorontsov-Velyaminov, B. 1959, Atlas and Catalog ofInteracting Galaxies, (Moscow). Vorontsov-Velyaminov, B. 1977, Astr. Astrophys. 28:1. Williams B. and Rood, H. 1987, Astrophys.]. Suppl. 63:265.
Zepf, S.E. and Whitmore, B.C. 1991, Astrophys. J. 383:542.

Is there Matter in Voids ?

Bogdan Wszolek
Jagiellonian University Astronomical Observatory ul. Orla 171, 30-244 Krakow, Poland Fax: (12) 37-80-53 E-mail: bogdan@oa.uj.edu.pl (internet)
The results of studies of the South Coma void are compared with searches for intergalactic dust in the same region. The presence of dust in voids is suggested.
Key words: intergalactic matter, voids, redshifts
1. Introduction
Measurements of redshifts of galaxies allow us to speculate about the 3-dimensional distribution of these objects in the Universe. The most widely accepted interpretation of the observed redshifts is a Doppler shift. If this is the case, measured redshifts combined with the Hubble-law give direct information about the distance to objects. Observations of the 3-dimensional distribution of galaxies reveal a bubble-like structure of the Universe. Groups and clusters of galaxies occupy about .Koth of the available space. The remaining volume is taken up by voids, which contain almost no luminous matter. The spatial scale of these voids is (1040)h-1 Mpc, where his the Hubble constant in units of 100 km s"1 Mpc.
On the other hand, there also exists non-luminous intergalactic matter, which theoretically may occupy galaxy clusters as well as large volumes within voids. The interactions of intergalactic matter with galaxies, and with radiation produced by them, may affect the interpretation of the extragalactic observations. Unfortunately, our present knowledge of the content and the distribution of intergalactic matter is very limited.
Intergalactic clouds are believed to be common in the remote Universe (absorption features in quasar spectra), but nearby examples are exceedingly rare. Good examples of large intergalactic clouds that are sufficiently close for there to have been extensive multifrequency studies are in the M96 group of galaxies at a distance of about 10 Mpc (Schneider et al. 1983) and in the vicinity of NGC300 at a distance of about 3 Mpc (Mathewson et al. 1975). These clouds were originally discovered by means of their radio emission at 21 em wavelength from atomic hydrogen (HI). A multifrequency survey of the cloud in M96 group (Schneider et al.

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Bogdan Wszolek

1989) indicates that intergalactic gas in this cloud is nearly devoid of stars. For this reason, other objects of this type will be difficult to find, even though they may constitute an important population in the Universe. A few other nearby intergalactic cloud candidates have also been discovered by means of the their resulting extinction (Hoffmeister 1962, Okroy 1965, Rudnicki & Baranowska 1966).
The first systematic search for non-luminous matter in cosmic voids was made by Krumm and Brosch (1984). The authors tried to detect isolated HI clouds in two nearby voids in the direction of the constellations of Perseus-Pisces and Hercules. They concluded that there are no signs of the existence of proto-galactic-size HI clouds in these voids.
Yet there are good arguments for the existence of intergalactic matter within voids. In the Bootes void, several faint emission-line galaxies have been detected
(Moody et al. 1987; Weistrop 1989). Gondhalekar & Brosch (1986) have observed
Lya, SiiV and CIV absorption lines in background quasars in the direction of the Bootes and Perseus-Pisces voids, and they have argued that these lines are produced within voids.
In the present paper the possible presence of dust in voids is suggested.

2. Observations in South Coma Void Region
In 1965, long before hearing about voids in the distribution of galaxies, Okroy noticed a large area (about 150 square degrees) with a visible lack of galaxies in the direction of the Coma/Virgo constellations. Murawski (1983) suggested that this deficit was due to an obscuring cloud of intergalactic nature rather than to a variation in the distribution of galaxies. He showed that the N(m)-curve of galaxies in the direction of the cloud is shifted towards fainter stellar magnitudes (Wolf-diagram) as compared to a control region. He also noticed that the galaxy colors in the cloud area are redder than in the surrounding parts.
The presence of a large void in redshift space in the region of the Okroy cloud (The South Coma void) has been proposed by Tifft and Gregory (1988). They showed that a region of about 110 square degrees at velocities between 5000 and 6000 km s-1 is quite empty of galaxies with mS15.7.
It should be mentioned that the break in the Wolf diagram and the redder average colors can, in principle, be well explained by the missing galaxy population at intermediate z-values, as occurs in the presence of a void. It simply indicates that the more distant and on the average redder galaxies contribute relatively more to the total sample. The numerical results due to the two effects (obscuration and true void) may be quite different, and are strongly dependent on the distance and size of the void. In the most general case, the two effects occur together.
Wszolek et al. (1989) have carried out an analysis of the Okroy cloud using
infrared data (IRAS). We have found infrared emission from the cold dust from the central part of this cloud.

3. Discussion
For the South Coma void there is a very good coincidence with the Okroy cloud (see also Wszolek 1992). The 100JJ.m radiation has a clear maximum near the

Is there Matter in Voids?

69

center of the void and could extend to the outer parts, where the presently available infrared signals are too weak to be differentiated from noise. The other known intergalactic clouds also seem to coincide with voids, but the overlap is not as clear as for the Okroy cloud. For these clouds no infrared emission was found in IRAS data.
While dust absorption as the sole cause for the absence of galaxies in the region of the Okroy cloud can be ruled out, the presence of dust in the direction of a well established void may be of great importance. The existence of non-luminous matter in voids would be very significant for cosmological theories because such theories consider mainly gravitational masses. The matter distributed on the line of sight to the observed voids interacts with electromagnetic radiation coming from galaxies to the observer. If scattering processes are not purely elastic, this matter can produce additional redshifts, independent of any Doppler shift. However, no physical process has so far been accepted to explain the origin of such additional redshifts. Unfortunately, to show that voids are occupied by a reasonable amount of matter, or that any hypothetical process produces redshifts, and perhaps voids, more data are needed.

References
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Schneider, S.E., Helou, G., Salpeter, E.E. and Terzian, Y.,1983, Ap. f. 273:Ll.
Schneider, S.E., Skrutskie, M.F., Hacking, P.B., Young, J.S., Dickman, R.L., Clausen, M.J.,
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97:666.
Tifft, W.G., Gregory, S.A., 1988, Astron. f. 95:651. Weistrop, D., 1989, Astron. J. 97:357.
Wszolek, B., Rudnicki, K., Masi, S., deBernardis, P. and Salvi, A., 1989, Astroph. Sp. Sci. 152:29. Wszolek, B., 1992, Apeiron 13:1.

Redshifts and Arp-like Configurations in the Local Group

M. Zabierowski
Wroclaw Technical University Wyb. Wyspianskiego 27 50370 Wroclaw, Poland
It is shown that each of the geometrically defined "lines" (subgroups) of galaxies in the Local Group of galaxies (considered by Iwanowska) contains members of various redshifts. In each line, however, we can distinguish members of quasi-discrete "quantized" redshift states. The so-called "possible" members of LG are real members of LG, according to the criterion developed in present paper. The redshift
state of our Galaxy is represented by k =-1.

I. Velocity Dispersion sn-t in the Local Group

1. All Galaxies in lwanowska Lines

We consider all galaxies classified by Iwanowska (1989) as members of Arplike lines contained in the Local Group (LG). The mean residual velocity of all galaxies listed by Iwanowska is

v=60±84{sn_1), n=37, (s~v)

(1)

It is evident that the dispersion sLG,n-1 (all velocities are given in km s-1) is higher than the mean velocity itself. Here, n is the total number of galaxies forming all the lwanowska's line configurations (resembling Arp configurations).
Let the velocity dispersion sn_1 be denoted simply as s. The Local Group dispersions is comparable with the dispersion of the Virgo ellipticals (E+SO) investigated, among others, by Sulentic (1977), although the Local Group and Virgo Cluster are not comparable with respect to number of members. Hence the following question arises: Is the high value of dispersion sLG a subclustering effect (caused by the existence of galaxy subgroups)? Furthermore, will it be possible to reduce this high value of sLG by dividing it into subgroups?
For this purpose, we consider a division of the Local Group into its two most natural parts: the M31 galaxy system and the system our Galaxy. Afterwards, we will also investigate the subgroups distinguished by Iwanowska. To ensure the

Progress in New Cosmologies: Beyond the Big Bang

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M. Zabierowski

uniformity of our material and to avoid the objection that we may have selected the material expressly for our purpose, we will use only Iwanowska's data. She distinguished the Arp lines of galaxies associated only with the Andromeda Galaxy (M31) and with our Galaxy.

2. The M31 Group

The mean residual velocity in the case of the M31 system of galaxies is

v=71±86, n=15, (s~v)

(2)

the dispersion value 86 km s-1 and all values of dispersion being hereafter denoted simply as s (standing for sn_1). In the present case of the M31 Group, the value of dispersion sM31 is roughly equal to sLG· With this division, the large value of s cannot be reduced.

3. Our Galaxy Group: the Next lwanowska Class

The Milky Way system of Iwanowska lines yields

v=53±83, n=22, s~v

(3)

Again the dispersion of values is higher that the mean value itself. All the numbers given in (1), (2) and (3) are of the same order of value. Again, the division of LG into subgroups causes neither any reduction of redshift dispersion nor any substantial change of the mean redshift. Thus, the following question appears: can we improve the situation by dividing the groups considered above into Iwanowska lines.

4. Five Subgroups in the Local Group: All lwanowska Lines

The next possible partition of the Local Group follows from the lwanowska's interpretation of the spatial distribution of galaxies in LG. She obtained five, physically related, straight galaxy lines (called by Iwanowska "bipolar jets").
The three bipolar jets connected with Andromeda Galaxy are denoted by lwanowska as A, B and C. For these three jets we have obtained respectively:

v = 5±71, n = 6, (jet C)

(4a),

v=72±120, n=4, (jet B)

(4b)

v = 88±83, n = 7, (jet A)

(4c)

again the value of s is close to the value of sLG· For the bipolar structure associated with our Galaxy, denoted by Iwanowska
as "a" and "b", we have obtained respectively

v = 44±102, n = 8, (jet a)

(Sa)

v = 51±78, n = 15, (jet b)

(Sb)

Configurations in the Local Group

73

and again, the dispersion values of single jets are similar to the values of sGa1, sM31 and sLG.
We come to a highly illuminating conclusion: it is impossible to reduce the velocity dispersion by dividing galaxies into separate geometrical groups. The same, very large s is preserved for all five subgroups (lines of galaxies); the value of s actually increases instead of decreasing. This means that the high value of the velocity dispersion is a basic regularity.

5. Some General Remarks

In this work, we have not used any a posteriori partitioning of the Local Group. We have used only the partition proposed by Iwanowska. We can see that the two kinds of space partition do not lead-in the case of the Local Group-to any substantial reduction of the velocity dispersion. For all galaxies in the Local Group, the dispersions is about 80 (1). For smaller, geometrically distinguished narrow groups, we obtained values of the same order-(4a), (4c) and (Sb}-or even as high as 100 km s-1 and more-(4b) and (Sa). It would be quite unnatural for galaxies to form some peculiar configurations (several geometrically recognizable lines) in physical 3-space; nevertheless, the velocity dispersion s cannot be reduced by space subdivisions.
Although each bipolar line can be divided into two segments, no velocity improvement (reducing s) has been reached in this way. Our conclusion is that the redshift states were well mixed even in quite isolated segments of Iwanowska's geometrical3-dimensionallines in the Local Group. Thus, taking into consideration present results, it becomes even more difficult to argue that stability of the chainlike configurations of galaxies when we try to retain the Doppler interpretation of redshifts.

6. Towards an Explanation

Instead of the spatial partition, we can examine the velocity (redshift) partition. Surprisingly, all the galaxies considered above may be grouped into five distinct redshift groups:

1: Galaxy, Ora, M31, IC 10, 1613

(6a)

sn-1 =8, sn =7, n=S

2: LMC, SMC, Agr, For, Leo A, Scl, Sgr, UMi, NGC 6822, IC 5152, WLM (6b)

Sn-1 =17, Sn =16, n=ll

3: Peg, M32, M33, NGC 147, 185,205, 1569,6456, A92

(6c}

Sn-1 = 16, Sn = 15, n = 9

4: Sex A, Sex B, NGC 1560, 3109, 4236, DOO 187, GR 8, Maffei 1, 2

(6d)

Sn_1 =20, Sn =19, n=9

5: Car, NGC 404, DOO 47

(6e)

sn-1 :::;24, sn =20, n=3

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M. Zabierowski

This grouping of galaxies minimizes s, which varies by about 10. The values of
sn are presented for comparison. The values of s are stable. The expected value of s
(random distribution of redshifts) is 22. The value obtained is slightly larger only in one group (6e). The values of s increase systematically from class 1 to 5.
In the calculated mean velocities v for the respective groups we also find a permanent regularity resembling Tifft's redshift states among residual velocities v = 72 k km s-1, k = 0,±1,.... Comparison of observational data with expected Tifft-
values yields the following:

Group 1: v =-58 (vT = -72, k = -1}

(7a)

Group 2: v = 1 (vT = 0, k = 0)

(7b)

Group3:v=65(vT=72, k=1}

(7c)

Group 4: v = 141 (vT = 144, k = 2)

(7d)

Group 5: v = 219 (vT =216, k =3)

(7e)

It is worthwhile to point out that not only is the observed periodicity consistent with the Tifft's 72 km s-1 periodicity, but also one of distinguished mean velocities coincides almost exactly with the expected k = 0 value, i.e. no phase shift was revealed. This fact cannot be explained easily in terms of Doppler effect.
The important question arises: How does the grouping of redshifts repeat in the case of the individual lines; or how are individual groups occupied?

II. Distribution of Redshifts in lwanowska's Richest Line, the Milky Way "b"-Chain
1. k = 0 State
The zero velocity group is made up of the following Milky Way companions: Aqr, For, Leo A, Scl, Sgr, NGC 6822, IC 5152, WLM. The mean residual velocity is close to zero. Moreover, the values of all the residual velocities are close to zero, thus v = 0 for the whole group and V0 is nearly equal to zero jv0 j < 27; the index "o" stands for an individual velocity. The exact value is
(8}
Indexes 1,2,3,... denote cases (1),(2),(3},... respectively. It is evident that s8 « 5:! and the value of v8 is quite different from v1, v2 and v3 (Equation 3). The outstanding value of v (here v8) confirms the hypothesis that it is a separate" state" of redshifts.
2. k = -1 State
The Companions of Our Galaxy. If one adds, to the galaxies mentioned above, all the other companions (excluding the Galaxy itself), then s rapidly increas-

Configurations in the Local Group

75

es from s =14 to s =74. This fact justifies the isolation of the zero-velocity group. For
all the companions we have:

v=59±74, n=14, (5g~s8 )

(9)

The Companions Plus Our Galaxy. Our Galaxy itself seems to form a separate z-state. The "apex" velocity of our Galaxy determined in a classical way from
"radial velocities" of Local Group galaxies is accepted here as the "redshift" of our Galaxy. In this case, we have a highly negative state, i.e. V0 = -60 (here V0 means the individual velocity of our Galaxy). This negative state does not fit the general
* tendency given by v =59 (Equation 9). When our Galaxy is included, the value ~
increases, but Sg also increases because the outstanding value of V0 v9 is not compensated by increasing n. For the whole "b"-jet (companions plus the Milky
Way) we have

v= 50±78, n = 15, (Sto > Sg ~ s8)

(10)

The value obtained for Sto supports the hypothesis advanced in section 1.6 that there
is a negative state (k =-1) of z such that its vis close to V0 =-60. If this hypothesis
is correct, we should expect a low dispersion around 10 for the k = -1 state. This
claim can be easily verified empirically in the future. Some arguments in favor of it will be given below.

3. High Velocity State: k = 2

There are two arguments that the five N-companions (the North galaxies of the "b"-jet), i.e. Sex A, B, NGC 3109, GR 8, and DDO 187, form a separate redshift class:
a. All these galaxies constitute the substantial part of the northern half of the b-jet ("substantial", i.e. without Leo A and DDO 47-these two galaxies fit a new redshift state). They form the distinguished, i.e. nonrandom concentration of galaxies in the "b"-jet and, moreover, there is no standard-explanation of such a high concentration of the same redshifts in a single position of the LG-space.
b. Comparison of v and s with the values given by Equations (8) and (9) is decisive, namely:

v=128±8, n= 5, (v11 ~v9 ~v8 )

(11)

This result for v and s (large v-excess ~1 - v8) indicates that it is not the zero-velocity group; nor is it the all companions group (9), because vis too large (~1 -v9, v11 -v10) and sis small (Sg ~ 5t1 and Sto ~ St1); evidently 5t1 has a value similar to s8.
Hence, the above-mentioned group of five galaxies does not belong to the
zero-velocity group (8), to the all companions group (9), to the galaxies of the "b"-jet
[the jet includes our Galaxy, (10)], or to our Galaxy state, called the k =-1 state. The
pair of values of v and s compared with the previous results (other groups in the
"b"-chain) reveals that the (11)-group has to be treated as separate.
The pairs of v and s values obtained above show that the separate redshift
states appear also in a single Iwanowska line. The next questions are: Do there exist

76

M. Zabierowski

unoccupied states? Can the so-called "possible" members of the Local Group fit the
proposed redshift grouping scheme? Is there any small redshift dispersion §roup of
the LG-galaxies not fitting the empirical"quantization" law v = 72 k km s- ?

4. DDO 47: An Observational Outsider and Possible k = 3 State

This companion probably forms a separate redshift state with a proposed vk=3 near the individual velocity V0 characterizing DDO 47

vk = V0 = 191, s = 10, (n = 1)

(12)

If the companion DDO 47 is classified as belonging to the k = 2 state, then the
addition of this one single member makes the dispersion increase from s = 8 to s =
27. Thus, this high velocity outsider ("possible" companion) belongs instead to the higher state k = 3.

5. The Five Different States in the Case of the "b"-Chain

We have obtained the five different states:
k =-1, our Galaxy, n = 1, s = 10? (hypothetical estimate)
k = 0, the zero velocity group, v =-1, s =14, n =8
k = 1, the unoccupied state (and there are no galaxies in
the "b"-chain between V0 = 33 and V0 = 118; moreover
the dispersions s of the neighborhood states are very
low and reliable due to large n)
k = 2, the high-velocity group, v = 128, s =8, n = 5
k = 3, DDO 47, v = V0 = 191, s =25? (estimate from the difference 216-191 = 25)

{13a) (13b) (13c)
(13d) (13e)

The empirical status of s in (13a) and (13c} is different because the redshift of DDO 47 is established directly, and the redshift of our Galaxy is established from statistical investigation, as noted in section II.2.b.

Ill. The Milky Way: "a"-Straight Chain

The recognized companions of the "a"-line (the companions directly included in Iwanowska's diagram (Figure 6 in the referenced work by Iwanowska) yield

k = 0, v =6, s =26, LMC, SMC, UMi, n =3

{14a)

(tides are often considered as influencing their velocities)

k = 1 unoccupied

(14b)

k = 2 unoccupied
k =3, v =234, s =18? Car, n =1,
(estimated from the difference 234-216 = 18)

(14c) {14d)

Configurations in the Local Group

77

and there is one negative state in the case of this lwanowska line, represented by two members-Ora and Milky Way:

k = -1, v =-59, s = 1, Ora, Milky Way, n = 2.

(14e)

Iwanowska has found the geometry of the "a"-bipolar line of the companions of our Galaxy. Nevertheless, two galaxies, i.e. NGC 6456 and 4236, have been treated in two ways in her work, since, on the one hand, the unusual 3-space geometry forces us to include these companions in one bipolar jet, while on the other hand, some authors consider them only as "possible" (the term "possible" stands for the whole astronomical tradition; we can recognize the meaning of this word from the context of the astronomical works) member of the Local Group. Thus Iwanowska also treats them as uncertain because there was no extra criterion for their membership. Now, using the regularity discovered in the present paper, we are forced to fit them into the empty states presented in (14b) and {15c):

k = 1, V0 = 73, NGC 6456, s = -10,74-73 = 1, n = 1

(14b')

k = 2, V0 = 142, NGC 4236, s =-10, 144-142 = 2, n =1

(14c')

There is no question whether the two mentioned galaxies considered as "uncertain" belong to the former or the latter state. Of course, they fit the regularity of
z obtained just from "certain" members. I follow lwanowska's terminology, which
is part of the whole internal problem (history and logic) situation in astronomy.

IV. The M31 Configuration of Galaxy Lines

1. All M31 Jets

The full set of M31 jets yields the following redshift states:

k = -1, v =-57, s = 11, IC10, 1613, M 31, n =3,

(15a)

k = 0, unoccupied (expected redshift state),

(15b)

k = 1, v = 68, s = 16, NGC 147,205,1569, M32,33, Peg, A92 n = 7, (15c)

k = 2, v = 156, s = 16, NGC 1560, Maffei 2, n = 2.

(15d)

We ignore here NGC 185, which is considered by lwanowska as a "certain" member of the M31lines. Its velocity is V0 = 41; thus, it could be classified as a k =
1 state. However, no included galaxy has such great difference l72c·Jk-v0 1, which is
31 in the case of NGC 185. If one includes NGC 185 as a member of the most abundant state (k = 1 , n = 7) then the result for v and s remains almost unchanged. Nevertheless, we must point out this individual case.
In the astronomical literature, there are often questions as to whether NGC
404 is a member of the Local Group or not. lwanowska's approach creates a new
criterion, and we can argue that NGC 404 is a member of the M 31line system. The approach presented here (similar to Tifft's) creates a second criterion: again NGC

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M. Zabierowski

404 is a LG member. The velocity of NGC 404 is V0 = 232. Thus it fits the k = 3(!)
state. As a result, we have the following redshift state

k =3, v =205, s =38, NGC 404, Maffei 1, n =2.

(15e)

2. The Three Bipolar Jets
There are three bipolar jets in M31 system selected by Iwanowska. However, all three jets are poor in galaxies with measured z. We can observe that the general regularity discovered for the Local Group, the Milky Way and the entire M31 system is repeated in each individual case of these three chains. This explains why
the sub-partition of the Local Group does not show the decreasing s. It is expected
that in the individual cases, a Tifft-like picture of the galaxy redshifts could be only slightly influenced by the tides. The connection between the hypothesis of the bipolar jets, Arp's hypothesis, and the role of tides can be considered an open problem (cf. Grabinska and Zabierowski 1979).
3. Some Peculiarities of the M31 Jets
Assuming that there exist no Tifft (intrinsic) redshift states, i.e. that redshifts
are explained in terms of velocities and these velocities V0 are dynamical, caused by gravitational attraction, we are unable to explain the observed highly unbalanced distribution of positive and negative values of V0 •
Iwanowska (1989) has noted that galaxies located on both ends of the A line of the M31 system show a negative V0 • M31 has itself the same negative value. However, the A-line galaxies located between the main galaxy and the end companions all have positive V0 • In the Doppler approach, this phenomenon is very strange. It appears exactly as if the intermediate galaxies of this line are not bound physically to the mother-galaxy, and do not participate in the common group movement. Nevertheless, they are located on the same geometrical line. In the Tifft approach, this phenomenon is at least completely possible and perhaps even points toward a new regularity.

Discussion
In the investigations presented here, all galaxies considered by Iwanowska were used. Only one galaxy (NGC 185) did not fit the "quantization" scheme very well, but even this one would not spoil the general picture in a statistical sense (the s criterion is fulfilled: see section IV.l). It is impossible to identify any group of redshifts outside Tifft's scheme. Thus, it is hard find any convincing argument that single galaxies or groups of them move one another.
The LG-velocity dispersions was compared with the velocity dispersion of the
ellipticals of the cluster in Virgo, which is s£ = 70-80 km s-1 (Sulentic 1977). The
peculiar form of Iwanowska's configurations contradicts the high value of sLG. Iwanowska (1989) doubted that bipolar galaxy lines considered by her were
formed by capture during collapse (isotropic or anisotropic, cf. Rudnicki et al. 1989).
Arp' s hypothesis is particularly relevant for the problem. But why did lines of galaxies survive? Iwanowska's application of Arp's hypothesis to the galaxy lines in

Configurations in the Local Group

79

the LG is valid if we assume that basic components of redshifts are due to quantization of an unknown physical nature and small relative motions of galaxies produce only low Doppler deviations from these main "quantum" states, causing the observed dispersions s.
Another result of our analysis is that the redshift state assigned to our Galaxy
is not k =0 but k =-1.

References
Grabinska, T. and Zabierowski, M., 1979, Astrophys. Sp. Sci. 66:503. Iwanowska, W., 1989, in: From Stars to Quasars, S. Grudzinska and B. Krygier (eds.), Mikolaj
Kopernik University, 159. Rudnicki, K., Grabinska, T. and Zabierowski M., 1989, in: From Stars to Quasars, S.
Grudzinska and B. Krygier (eds.), Mikolaj Kopernik University, 119, 125, and 137.
Sulentic, J., 1977, Astrophys. J. 211:L59.
Tifft, W., 1975, Discrete States of Redshift and Galaxy Dynamics, Steward Observatory Preprint No44.

Are the Galaxies Really Receding?
Fred L. Walker
3881 S. Via del Trogon Green Valley, Arizona 85614
·Sixty years of competing speculation and theory have failed to establish conclusively whether the Big Bang expansion concept is valid. Three methods to resolve the continuing impasse are discussed. First, it can be shown that two initial assumptions of the theory directly contradict each other, producing inconsistent and unacceptable results. Secondly, based on well established facts and assumptions, an organized, disciplined proof shows that observed conditions in a hypothetical expansion would be contrary to those which are now actually observed. Finally, a new method is presented to directly determine whether galaxies are receding or not based on rotation velocity and independent of the redshift. If no recession is found, there can be no universal expansion.
Introduction
Although serious questions about the validity of the Big Bang expansion concept have been raised by recent astronomical evidence, most scientists still support the concept. Various alternative concepts have been presented by some scientists, but these have received little notice. Thus, the growing diversity of ideas continues, with no conclusive results in sight.
The chief difficulty with proving or disproving the universal expansion theory is that all arguments on both sides of the question are, to some extent, speculative and are, therefore, subject to misinterpretation and some degree of uncertainty.
Such uncertainty is unavoidable in many areas under investigation, but in the case of expansion theory, a body of empirical evidence has accumulated during the sixty years since the idea was launched, such that it may now be possible to resolve this issue on a less speculative and more factual basis. Two possible methods for doing this are discussed here: that of formal proof and that of direct empirical measurement.

Progress in New Cosmologies: Beyond the Big Bang

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81

82

Fred L. Walker

The Formal Proof
One method to formally disprove a theory, on a purely logical basis, is to show that the initial argument behind the theory is inconsistent with the rules of logic. For example, the expansion theory derives from a number of assumptions, and it can be shown that two of these assumptions directly contradict each other, resulting in mathematical inconsistencies (Walker 1989). Thus, the expansion theory assumes that the present time recession velocity of galaxies in an expansion is proportional to the distance light has traveled from each galaxy to the observer and also to the actual present time distance of each galaxy.1 Yet, it can be demonstrated that these two distances are different, that this fractional difference varies with galactic distance, so that both assumptions cannot be true.
Another method to formally disprove a theory such as the Big Bang would be to show that an observer's view of such a theoretically expanding universe would be contrary to what astronomers actually observe in the real universe. To do this, there must first be available sufficient empirical evidence or well established assumptions to determine clearly how the universe does appear to astronomers and how it would appear in a hypothetical expansion.
On this basis, using presently established facts and generally agreed upon assumptions, it can be logically demonstrated that the observed density of galaxies along any line of sight would increase systematically with distance in an expanding universe. This means that galactic densities at 1010 light years would be at least several times greater than the density nearby. This is contrary to the actual observed results from recent galaxy mapping projects, and the logical conclusion is that the universe is not expanding (Walker 1991).
Although physicists are skeptical about this type of approach based primarily on logic, the method may offer considerable advantage in specific problem areas where direct conclusions cannot otherwise be reached.

Direct Measurement
Another more direct method might be to directly measure the recession or non-recession of the galaxies independently of the cosmological redshift. Such a measurement, if successful, would provide conclusive and final evidence that space is or is not expanding.
Edwin Hubble and Richard Tolman attempted such a direct measurement approach in 1935, based on decreased surface brightness as a function of redshift. Their test, together with recent applications, was described by Jaakkola (1988) as a powerful indication that the galaxies are not receding.
However, neither this test nor other proposed tests of the expansion hypothesis have been generally accepted as conclusive.

1 Ed. Note: The measured spectral shift is believed by most astronomers to refer to the time at which the light left the galaxy, and thus the spectral shift should be proportional to the distance of the galaxy. At the present time, both are greater, and hence there is no contradiction with a theory of an expanding universe. See discussion in Apeiron No. 6, 1990. H.C.A.

Are the Galaxies Really Receding?

83

At the same time, it is well known that a number of scientists have proposed
non-Doppler mechanisms to explain the redshift without any withdrawal of the
galaxies Gaakkola 1978, Vigier 1990, Arp 1991, LaViolette 1986, Marmet 1991). Consequently, the redshift itself is not finally conclusive as an indication of expansion.
For a fully conclusive test, it would be necessary to observe some regularly periodic event (a Cepheid variable, for example) which is intrinsic to all galaxies. In an expanding universe, the rate of any regular periodicity should appear to slow down as galactic distances and recession velocities increase.
The fact that such a slow-down does occur as any recurring event moves away from an observer was confirmed by observations made in 1676 by Swedish astronomer Olaf Roemer, who discovered that the regular orbital rate (eclipse rate) of Jupiter's moons appears slower when the distance between the earth and Jupiter is increasing and faster when the distance is decreasing (Singer 1990).
The reason why such regularly periodic events appear to slow down when
they are receding is easily seen in Figure 1, which gives a simple illustration of the mechanics. A rapidly rotating disc is at a distanced from an observer. If the disc rotates at regular time intervals, each equal to ll.t, an observed point P on the rim at a time t will be seen to return to that same location after each time interval .!lt if the disc remains at the same distance d from 0. Thus, if the observed starting location of Pat time tis at the end of a radius, CP, which is perpendicular to the line of sight
OC, P will complete one revolution and return to that location at time (t +ll.t).
However, if the disc is receding from the observer at velocity, v;., while it
completes one revolution, the disc will have moved away by a distance V,.!lt during that time, and its center C will have arrived at 0'. The observed point P would now be located at P' at time (t +L\t).
Now, the light from P' must travel the additional distance V,..!lt to reach the
observer, so that its arrival at 0 will be delayed by an additional time interval
V,..!ltIc, where c is the speed of light.
Consequently, when the disc is withdrawing, the observed time for the disc to
complete one revolution is ll.t(1 +V,. Ic), and its period of rotation has increased by a
fraction V,.lc. Since the observed time required for a point on the periphery to
complete one revolution is greater, its observed orbital velocity V0 is lower.
Here, however, it is important to note that, although the observed orbital velocity V0 , relative to 0, is slower, the actual orbital velocity V relative to the center of the disc remains always the same. V0 is observed to be slower only

{:~=C:-:~::.l---- 0...-C-... - - - - - - - - - - - - __ .JQ!?I!!.r'!!0.
\ ..... ~I,/I

B

A

1-- VrAI

d --------1

Figure 1. Rotation period of a receding disc. A. Stationary disc completes one observed rotation during each time period t::.t B. Receding disc completes one observed rotation during a longer time period t.t+(V,Mfc)

84

Fred L. Walker

because of the increasing time lag required for light from point P to reach 0 as the
disc recedes. With this in mind, the relation between the actual rotation velocity V of point
P and its observed rotation velocity V0 is readily seen. Since P travels the same
orbital distance V..1t in an observed time period which has increased to M +(V, /c)M, the observed orbital velocity of a point on the rim is now:

(1)

Because of this relationship, Roemer was able to compute, with remarkable accuracy for that time, the speed of light which was indicated by the slower eclipse rate (and reduced rotational velocity) of Jupiter's moons when the planet was receding, and vice versa.
Similarly, it can be shown that the observed time period for any regularly periodic event will increase as it recedes from an observer.
Periodicity of Galactic Rotations
The only regularly periodic event other than the frequency of light which is now observable in a distant galaxy is its orbital period, which is a function of its orbital velocity.
Rotational velocity can be determined either at radio wavelengths, by measuring the global HI profile width (Tully and Fisher 1976), or optically from a spectral profile of redshifts along a galactic diameter perpendicular to the line of sight (Rubin 1983). In the latter case of a spectral profile, after deducting the central, cosmological redshift, the remaining "Proper motion" redshifts indicate tangential velocities of visible material in the galaxy at each radial distance from the galactic center.
In this way, an astronomer can directly measure the observed orbital velocity of the material objects (gas and dust clouds, stars, etc.) which exist at any point along a galactic radius. The entire assemblage of such materials at the observed point corresponds, on a far vaster scale, to the dot, P, on the disc in Figure 1, as previously discussed.
A most interesting fact which results from such spectral examinations is that spiral galaxies of the same morphological type (Sa, Sb, Sc) and absolute magnitude have the same rotation velocities independently of their distance from the observer.
First indications of this were reported by Tully and Fisher (1975) who proposed that there is "a good correlation between the global neutral hydrogen line profile width, a distance-independent observable, and absolute magnitude". Here, the profile width also gives maximum rotation velocity.
This Tully-Fisher relation clearly establishes that, within distances of about 375 million light years (115 Mps), all observed galaxies of the same absolute magnitude have approximately the same maximum rotation velocity (Vmax), independent

Are the Galaxies Really Receding?

85

of distance. Yet, these same galaxies are thought to be receding from the Milky Way at velocities which vary from less than 110 krn s-1 for the closest galaxies, at about 2.5 million light years (.75 Mps), to more than 6,000 krn s-1 for the farthest galaxies at about 375 million light years (115 Mps).
Accordingly, as previously discussed, these observed galactic rotation rates should not be the same in an expansion. Instead, the observed rotation rate should decrease as galactic distance and recession velocities increase. Since, according to the TF relation, they do not decrease, this would indicate that the galaxies are not receding.

Optical Measurements of Rotation
These radio observations are confirmed by an optical survey of galactic rotations made by scientists at the Carnegie Institution (Rubin et al. 1980 and 1982). Their analysis confirms that, for galaxies of the same S type (Sa, Sb, or Sc), there is a good correlation between rotation velocity (Vmax) at the isophotal radius and absolute blue magnitude. Their farthest reading, for galaxy U12810, was at a distance of 165 Mps with magnitude -22.6, and a redshift recession velocity of 8124
km s-1. (Using an H value of 50 krn s-1 Mps-1, and z = 0.02708).
Accordingly, if U12810 is, in fact, receding, its observed rotation velocity V0 should be less than its normal rotation velocity, as previously discussed.
Since the observed orbital velocity V0 is 235 krn s-1, the relation given in equation (1) may be used to determine what the actual orbital velocity V would be if the
redshift, z = 0.02708, represents a velocity of recession. At this relatively short
cosmological distance, z =V,jc, so that V = 241.36 krn s-1 .
The actual rotation velocity should be greater than the observed rotation velocity by 6.36 krn s-1 or 2.6%-if the galaxy is receding.
A consistent variation of this magnitude between normal and observed rotation rates could probably be detected if there were sufficient observational evidence.

Testing the Galactic Recession Hypothesis
Now, considering all the factors discussed so far, the procedures necessary to determine whether the galaxies are actually receding becomes apparent.
First, we would need to determine the rotational rate for nearby galaxies of a particular spiral type and magnitude at distances within several Mps. Here, distances and magnitudes are well established from the distance scale. Observed information on a number of galaxies could be averaged to obtain their most accurate rotational velocity. At this short distance, (small z), this observed rotation velocity should be approximately equal to the normal rotation velocity, V, for galaxies of that type and magnitude.
Unfortunately, the nearby galaxy samples used by Tully and Fisher were of various types and magnitudes which are not suitable for our present purpose.
Next, rotational information should be obtained, at the farthest observable distances (largest redshifts), for a reasonable number of galaxies of the same spiral

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Fred L. Walker

type and magnitude used for the nearby galaxy sample. From this, the observed rotation velocity at that distance would be approximated.
Here again, the most distant observations made by Rubin et al., are not suitable for our purpose (Table 1). Instead it would be desireable to have a larger galaxy sample with less variation in luminosity reaching to a greater and distance.
However, if suitable data were obtained, the nearby (normal) rotation velocity of a particular galaxy sample could be compared with its observed rotation velocity at a distance in order to discover any difference.
Obviously, such a comparison cannot be made from existing data. Extensive additional research would be required for meaningful results.

Table 1. Optical samples for distant galaxies. Data is for the 5 most distant Sb galaxies discussed by Rubin et al. in their examination of 23 Sb galaxies for optically observed rotation properties. V, is galactic recession velocity in km s·1 indicated by the redshift, V0 is observed rotation velocity (Vmax) in km s·1 • (Source: Rubin et al., 1982)

NGC

Mo Distance v,

v.

z

(Mps)

U1Hl10 2590 1417 1085
U12810 Total
Average Values

-21.2 -21.9 -22.3 -22.4 -22.6 -110.4
-22.08

98.3 95.8 81.5 136.0 165.0 576.6

4709 4985 4114 6784 8124 28716

115.3 5743

197 256 330 310 235 1328
265.6

.0157 .0166 .0137 .0226 .0271 .0957
.0191

Conclusion
Even so, the stakes are high, and the results should be worth the extensive time and resources needed. Such a direct measure of the withdrawal or non-withdrawal of the galaxies could finally resolve any questions about the validity of the expansion idea and Big Bang once and for all.
If the galaxies are receding in a general expansion of universal space, their observed rotation rates must decrease with distance. However, if the universe is not expanding, no ~ch decrease would be found.2
If an adequate research effort confirms that there is no such decrease, then the unavoidable conclusion would be that the Big Bang never happened.
In that case, a new cosmological concept would be needed to replace the Big Bang. It would have to provide some plausible alternative mechanism for the creation of matter ranging in scale from the subatomic size of the smallest particles to the vast magnitude of the largest galaxies. Since a continuous creation of matter

2 Ed. Note: If clocks run slower on younger galaxies, rrtore distant galaxies, because of look-back time, would show slower rotation in a non-expanding universe. H.C.A.

Are the Galaxies Really Receding?

87

could not be accommodated indefinitely in a static space, provisions would be needed for a balanced cycle of events in which the creation of matter in parts of the cycle would be balanced by the conversion of matter back into energy in other parts.
One possible concept might incorporate a static universal space, occupied by a dynamic ether in which both electromagnetic wave (photon) energy and atomic particles (rotational energy) such as electrons and protons would exist. Energy radiation from stars and galaxies would power the synthesis of basic particles (rotational energy) in interstellar regions of the ether while large scale currents and eddies in the ether would then impel these particles inertially into the centers of stars and galaxies to provide fuel for the fusion (and other) processes going on there. Such a universe would be quasi-static, stable, infinite, and would remain always in a state of equilibrium. Such a concept is no more speculative than the Big Bang, but, as I have shown elsewhere (Walker 1992), it might explain a number of mysteries which are now unresolved.

References
Arp, H., 1991, How non-velocity redshifts in galaxies depend on epoch of creation, Apeiron 9-10:18.
Encyclopedia Britannica, 15th Edition, Vol. 10, p. 164. Jaakkola, T., 1988, Four applications of the surface brightness test of the cosmological expan-
sion hypothesis, in: Proceedings, 6th Soviet-Finnish Astronomical Meeting, eds. V. Hanni and J. Tuominen. Jaakkola, T., 1978, The redshift phenomenon in systems of different scales, Acta Cosmologica 7:17. LaViolette, P., 1986, Is the Universe really expanding? Ap.J. 301:544. Marmet, P., 1991, A new mechanism to explain observations incompatible with the Big Bang, Apeiron 9-10:45. Rubin, V.C., Burstein, D. and Thonnard N., 1980, A new relation for estimating the intrinsic luminosities of spiral galaxies, Ap.J. 242:L149. Rubin, V.C., Ford W.K. Jr. and Thonnard, N., 1982, Rotational properties of 23 Sb galaxies, Ap.J. 261:439. Rubin, V.C., 1983, Dark matter in spiral galaxies, Scientific American 248:6:96. Singer, C., 1990, A History of Scientific Ide11s, Dorset Press. Tully, R.B. and Fisher, J.R., 1976, A new method of determining distances to galaxies, Astron. Astrophys. 54:661. Vigi~r, J.P., 1990, Evidence for nonzero mass photons, IEEE Transactions on Plasma Science 9:1. Walker, F., 1989, A contradiction in the theory of universal expansion, Apeiron 5:1. Walker, F., 1991, The stationary universe theorem, Unpublished. Walker, F., 1992, Where is the cosmological alternative?, Physics Essays 5:3:340.

The Case Against the Big Bang

Eric J. Lerner
Lawrenceville Plasma Physics 20 Pine Knoll Drive Lawrenceville, New Jersey 08648
Despite its widespread acceptance, the Big Bang theory is presently without any observational support. All of its quantitative predictions are contradicted by observation, and none are supported by the data. Its predictions of light element abundances are inconsistent with the latest data. It is impossible to produce a Big Bang "age of the universe" which is old enough to allow the development of the observed large scale structures, or even the evolution of the Milky Way galaxy. The theory does not predict an isotropic cosmic microwave background without several additional ad hoc assumptions which are themselves clearly contradicted by observation. By contrast, plasma cosmology theories have provided explanations of the light element abundances, the origin of large scale structure and the cosmic microwave background that accord with observation. It is time to abandon the Big Bang and seek other explanations of the Hubble relationship.
I. Introduction
While the Big Bang is widely accepted as a scientific explanation of the Hubble relation, it rests on very few quantitative predictions. The most definite such quantitative predictions are the abundances of the light nuclides He4, D, and LF. Wellknown results, (Wagner, Fowler and Hoyle 1966) based on nuclear physics and the assumptions of the Big Bang, show that the pre-galactic abundances of these three nuclides are a function only of the photon-proton ratio, which, by the Big Bang theory, is an invariant in the universe. Since the number of photons, (which is dominated by the number of photons in the cosmic background radiation) is known accurately, this ratio is in effect a function of the baryon density in the present day universe. In practice, this density is not known very accurately, and it has been treated as a free variable. The Big Bang predictions, therefore, reduce to a prediction of the abundances of two of the light nuclides, given the abundance of one. This one abundance is used to derive the "true" photon-baryon ratio and thus the other two abundances. The apparent validity of this prediction, based on data available in the late 1960's, was one of the main reasons for the general acceptance of the Big Bang.
The second and less specific prediction is that no object in the universe is older than the Hubble age, the age of the universe estimated from the inverse of the

Progress in New Cosmologies: Beyond the Big Bang

Edited by H.C. Arp et al., Plenum Press, New YOik, 1993

89

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Eric J. Lerner

Hubble ratio relating the redshifts and distances of galaxies. While this is qualitatively a very firm prediction of the theory, it is quantitatively vague for two reasons. One, the Hubble constant itself is not accurately determined, and second, the deceleration parameter, which indicates how rapidly the assumed expansion of the universe proceeded in the past, is also not known, and is dependent on the actual density of all matter in the universe. However, the range of these values compatible with observations does, as we shall see, set very real limits on the age of objects in the universe, if the theory is valid.
The third and final quantitative prediction of the theory, in its current form, is the existence of an isotropic Planckian background cosmic radiation. The temperature of this radiation is not predicted by theory, but, in the inflationary form currently popular, its isotropy and blackbody spectrum are. As we shall note below, these are not valid predictions of the Big Bang in its most general form.
These three predictions and their claimed correspondence with observation are the entirety of the evidence cited in favor of the hypothesis that the universe originated in an instant in an intensely hot, extremely dense state. What is striking is that at the present time, not one of these predictions can be validly cited as evidence for the Big Bang, which, therefore, is entirely unsupported by observations. The first two predictions are flatly contradicted by observation, while the third does not actually constitute evidence as to the primordial state of matter, and involves additional predictions which are themselves contradicted by observation.

II. Light Element Abundances
The key problem for Big Bang nucleosynthesis (BBN) predictions of the light element abundances lies in the discrepancy between the predictions for deuterium and He4• The predicted abundance of He4 decreases with decreasing baryon-photon ratio, 7J, while the predicted abundance of D decreases with increasing 7J. Since the observed upper limits on the pre-galactic abundances of both elements have been declining, we now have a situation where there is no value of the density parameter which yields predictions agreeing simultaneously with both observed He4 and D ablilldances.
We begin with deuterium: Hubble Space Telescope observations by Linsky fix the current abundance of D at 1.65±0.1 x 10-5 by number relative to H (Linsky 1992). Thus the 3 sigma upper limit is 2 x 10-5. Of course, much of the pre-galactic deuterium could have been destroyed in stars. However, many authors have placed strict limits on how much of the primordial D could have been destroyed. Yang et al. (1984), for example, show that while D is easily burned to He3, He3 is destroyed only where temperatures are high enough to burn H to He4• Considerations of the amount of He3 produced in the galaxy, combined with calculations as to the production of He3 in stars, leads to the conclusion that the current sum of abundances of D and He3 is at least half the pre-galactic value. This leads to an upper estimate of the pregalactic D abundances of about 8 x 10-5 • Delbourg-Salvador et al. (1987)
conclude that a destruction of more than %of the pre-galactic D by astration would
lead to great variations in current D, depending on the exact history of a given region. Since such variations are not observed, they calculate that primordial D abundance is less than 3 times present, or, based on the Linsky observations, less than 6 x 10-5.

The Case Against the Big Bang

91

Physically, both of these arguments are related to the fact that if the whole of the galactic material is processed on average once through stars, about e-1 of the deuterium will not have been so processed. Deuterium destruction much greater than this requires two such processings. But this rate of nuclear processing would produce about twice as much energy, He4 and heavier elements, such as CNO, as are observed.
By the BBN formula, upper limits on D abundance set lower limits on the density parameter 1J . D abundance of 6 x 10-S imtfi'lies 1J > 3.4 x 10-10 while D abundance of 8 x 10-5 implies a limit of 3.0 x 10- . These limits in turn imply lower limits on the predicted primordial abundance of He4 of 23.9% by weight and 23.6% respectively. These estimates are based on an assumed neutron lifetime of 882 sec, the current two sigma lower limit. A "best" value of 888 sec would increase these limits to about 24.1% and 23.8% respectively.
The abundance of He4 is therefore a crucial test of BBN. Since He4 is produced by stars, observers have long sought to focus on those galaxies with the least stellar production, which in tum is indicated by the abundance of heavier elements, C, N and 0. It is assumed, based on theories of stellar evolution, that He4 abundance should increase as a function of heavy element abundance, so that the pre-galactic

2.4x1o·'

Helium

1.0x10_.
1.0x10.s 1.0x10.g
1

Figure 1. Abundances of elements predicted by Big Bang nucleosynthesis vs. observed abundances (horizontal lines). Predictions from Olive (1990) observed values from Olive (1990) and Fuller (1991). There is no value of 1J (ratio of protons to photons x 1010 ) that gives accurate abundances for all elements.