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MODERN MATHEMATICAL MODELS OF TIME
AND THEIR APPLICATIONS TO PHYSICS AND COSMOLOGY
Proceedings of the International Conference held in Tucson, Arizona, 11-13 April, 1996
Edited by
W.G. TIFFf
Department ofAstronomy, University ofArizona, Tucson, Arizona, U.S.A.
and
W.J. COCKE
Department ofAstronomy, University ofArizona, Tucson, Arizona, U.S.A.
Reprinted from Astrophysics and Space Science Volume 244, Nos. 1-2, 1996
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-94-010-6372-2

ISBN 978-94-011-5628-8 (eBook)

DOI 10.1007/978-94-011-5628-8

Printed on acid-fru paper
AH rights reserved @1997 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1997
Softcover reprint ofthe hardcover lst edition 1997
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

TABLE OF CONTENTS

Preface

1

DAY 1 SESSIONS 1-3

Session 1. The Redshift

HALTON ARP / The pair of X-ray sources across NGC 4258, its relation to

intrinsic redshifts, ejection and quantization

9

JACK W. SULENTIC and J. BRETT SMITH / A fresh look at discordant

redshift galaxies in compact groups

23

W.G. TIFFT / Evidence for quantized and variable redshifts in the cosmic

background rest frame

29

W.M. NAPIER and B.N.G. GUTHRIE / Testing for quantized redshifts. I. The

project

57

T.E. NORDGREN, Y. TERZIAN and E.E. SALPETER / The distribution of

galaxy pair redshifts

65

Session 2. Critical Properties of the Universe

LI-ZHI FANG and YI-PENG JING / Density fluctuations on super-Hubble

scales

73

S.A. GREGORY / The challenge of large-scale structure

81

ANTHONY L. PERATT / Electric space: evolution of the plasma universe

89

J.G. LAROS / Gamma-ray bursts: should cosmologists care?

105

Session 3. Statistical Methods

W.M. NAPIER and B.N.G. GUTHRIE / Testing for quantized redshifts. II. The

local supercluster

111

W.I. NEWMAN and Y. TERZIAN / Power spectrum analysis and redshift data

127

W. COCKE, C. DEVITO and A. PITUCCO I Statistical analysis of the occur-

rence of periodicities in galaxy redshift data

143

P.A. STURROCK I Zooming in on the redshift problem

159

DAY 2 SESSIONS 4-5 Session 4. New Approaches to Cosmology

G. BURBIDGE I Two universes

169

JAYANT V. NARLIKARI Anomalous redshifts and the variable mass hypothesis

177

W.G. TIFFT I Three-dimensional quantized time in cosmology

187

Session 5. Gravitation and Time in General Relativity

W.J. COCKE I The stress-energy tensor and the deflection of light in 6-

dimensional general relativity

211

P.C.W. DAVIES I Einstein's greatest mistake?

219

ROGER PENROSE I Time, space and complex geometry

229

D.E ROSCOE I Discrete spatial scales in a fractal universe

231

TOM VAN FLANDERN I Possible new properties of gravity

249

LEOPOLD HALPERN I On the cosmic limits of physical laws

263

MENDEL SACHS I Changes in concepts of time from Aristotle to Einstein

269

METOD SANIGA I On the transmutation and annihilation of pencil-generated

spacetime dimensions

283

DAY 3 SESSIONS 6-7 Session 6. Nuclear and Particle Physics

VINCENT ICKE I Particles, space and time

293

AVSHALOM C. ELITZUR I Time anisotropy and quantum measurement:

Clues for transcending the geometrical picture of time

313

ARI LEHTO I 3-D Period doubling and magnetic moments of particles

321

C. WOLF / Relics of the primordial origins of space and time in the low energy

world

329

L.W. MORROW I Unexplained empirical relations among certain scatterings

347

MARTIN KOKUS I Spherical rotation, particles and cosmology

353

Session 7. Mathematical Models and Methods

CARL L. DEVITO / A Non-linear model for time

357

W.M. STUCKEY / Defining spacetime

371

A.P. PITUCCO / Some elementary geometric aspects of extending the dimen-

sion of the space of instants

375

B.R. FRIEDEN / Fisher information as a measure of time

387

THE REDSHIFT CRITICAL PROPERTIES OF THE UNIVERSE STATISTICAL METHODS
DAY 1
Rodeway Inn, North
:~iP1"'r'"''""'li'it,;m;iitlru,iil r.~iitfl!rl!n~ on ModernMathematlCa1 MO(IelS Applications to Physics and Cosmology_
. April11-14. 1996 Tucson
Figu.re 1. Sketch art courtesy Janet A. Tifft

THE PAIR OF X-RAY SOURCES ACROSS NGC 4258: ITS RELATION TO INTRINSIC REDSHIFTS, EJECTION AND QUANTIZATION
HALTON ARP Max-Planck-Institut fur Astrophysik 85740 Garching, Germany
Abstract. The chance that the pair of X-ray sources observed across NGC 4258 is accidental can be calculated as 5 x 10-6. The recent confirmation
as quasars, and determination of the redshifts of the pair, at z = 0.40
and 0.65 by E.M. Burbidge enables the final accidental probability of the
configuration to be calculated as < 4 x 10-7. In addition there are a number
of observations which indicate the central Seyfert galaxy is ejecting material from its active nucleus.
The NGC 4258 association is compared to four other examples of close association of pairs of X-ray quasars with low redshift galaxies. It is concluded that in each of these five cases the chance of accidental association is less than one in a million. The ejection speed calculated from the redshift differences of the X-ray quasars is 0.12c. This agrees with the ejection velocity of O.lc calculated in 1968 from radio quasars associated with low redshift galaxies. When corrected for ejection velocities the observed redshift peaks become narrower - simultaneously strengthening the ejection origin for quasars and the quantization property of their redshift.
1. Introduction
The first associations of high redshift quasars with low redshift galaxies was made more than 30 years ago (Arp 1966b, 1967, 1968). The most recent, striking evidence has come from X-ray sources, paired across Seyfert galaxies, which have turned out to be quasars of considerably higher redshift than the galaxy (Radecke 1996, Arp 1996). Evidence for smaller intrinsic redshifts of galaxies has also accumulated (Arp 1994b). The evidence
Astrophysics and Space Science 244:9-22,1996. © 1996 Kluwer Academic Publishers.

10

HALTON ARP

demonstrates that part of the redshift of these extragalactic objects must be intrinsic (non-velocity).
The pairs are particularly important in that they allow us to estimate the ejection velocities necessary to get the quasars out of their parent galaxies. In the cases available, if the ejection velocities are subtracted from the component quasar redshifts, the two members have more closely the same redshift - as if material of the same intrinsic redshift was ejected in opposite directions. After correction for the velocity component, the redshifts also fall closer to the well marked peaks in the redshift distribution (Arp et. al. 1990). Therefore quantization of the redshifts becomes more clearly established. The fact of quantization independently reinforces the earlier result that the quasar redshifts are not primarily due to velocity but to an intrinsic property of matter. Perhaps most important of all, existence of quantization represents one of the strongest empirical clues to the physical reason for the intrinsic redshifts of these recently ejected, compact, energetic objects.

2. Ejection
It has long been accepted that radio galaxies eject material out in roughly opposite directions to approximately equal distances from their active nuclei. It has even been possible to study optical emission from material within these radiolobes (egs. see Fosbury 1984 and Morganti, Robinson and Fosbury 1984). More recently, as X-ray observations began to accumulate, it appeared that material which emits high energy X-rays also accompanies these radio ejections. Some well known examples are X-ray jets within the strong radio ejections from Virgo A and Cen A (egs. Feigelson et. al. 1981), the X-ray hot spots within the lobes of Cyg A and the X-ray material extending far out along the ejection direction in Cen A (Arp 1994a).
It seems, therefore, that both radio emission and X-ray emission are characteristic of the material ejected from galaxies. It should then perhaps not be surprising when the phenomenon of X-ray sources paired across active galaxies starts to turn up in the same way that pairs of radio sources were initially discovered across (what later turned out to be) galaxies with active nuclei. The study of these X-ray pairs and associations will have to proceed empirically as did the early association of radio pairs. Now, as then, the first step is to test the statistical significance of associations and build up a list of secure associations in which to study their empirical characteristics.
The identification of secure associations must utilize the a priori criterion of tendency toward: 1) opposite ejection 2) equal separation and 3) similarity of ejected sources. All these are demonstrated properties of

X-RAY SOURCES

11

accepted ejections and rule out any question of a posteriori probability calculations. Since in many of the X-ray cases (as in a number of previous radio and optical associations) objects of differing redshifts are identified, one cannot interpret them on the basis of a present theory or understanding of ejection mechanisms (if indeed it is solely an ejection phenomenon). A number of cases must be accumulated, studied and a working theoretical explanation suggested from an inductive analysis.
In order to make the a priori statistical criteria specific we refer to the early data of pairing of radio sources across active and disturbed galaxies: The Atlas of Peculiar Galaxies (Arp 1966a) showed numerous cases of radio sources paired across galaxies, particularly in that section containing galaxies with morphological evidence of ejection. The improbability of these paired radio sources being accidental resided principally in the closeness of the sources at their brightness and secondarily in the tendency for the sources to be aligned across the central galaxy and tertiarily to be equally spaced across the galaxy (Arp 1967). Although some sources were aligned to within ±1°, the average over the 26 original associations was 12°.7, of the order of alignment of radio lobes and knots which are conventionally believed to have been ejected from active galaxies.
A follow-up analysis of pairs of radio sources in the Parkes Survey (Arp 1968) showed those pairs which had galaxies located between them had similar properties, demonstrating physical association. Of these radio sources in pairs, 16 were identified as quasars and disturbances in some of the central galaxies indicated the time since ejection. This enabled calculation of ejection speeds for the quasars of O.lc. In an important result of the present analysis, just this predicted velocity is now calculated directly from the measured redshifts of the pairs of X-ray quasars across such galaxies as NGC 4258 as well as in previous associations of pairs of X-ray quasars.

3. The NGC 4258 Configuration
ROSAT X-ray measures of a 20' radius field around the active Seyfert II galaxy, NGC 4258 revealed a striking pair of X-ray sources aligned across the center of the galaxy (Pietsch et. at. 1994 and Fig.1 here). The authors commented: "If the connection of these sources with the galaxy is real they may be bipolar ejecta from the nucleus" .
Using the parameters listed in Tables 1 and 2 of Pietsch et. at. we construct Table 1 here showing the properties of the two sources. The fluxes (Fx) are computed in two steps: First the 0.4 to 2.4 keY band counts = B are obtained from B = s~ss (1+HR1). Then the count-to-energy conversion factor of 1.4 x lO-l1erg em-2 cts-1 (see Pietsch in Arp 1994a) is used to compute Fx. This Fx is close to the system of Hasinger et. at. (1993) and we

12

HALTON ARP

0

NGC 4258

•

o

o •

ROSAT 'pSp~ ·

. 0 .1-2,4 keV , .6 (j.

., •
.'!'
'0 <>

• ..

@

•

. •
0

. . .
®.
9 '.
•

•
5 arcmin .
, I

Figure 1. The pair of X-ray sources across NGC 4258 as discovered by Pietsch et. al.
= = (1994). #26, with z .65, is to the NE and #8, with z .40, is to the SW. The blue
stellar objects are seen at the center of each source.

can therefore use their log N(> S) - log(S) curve to compute the density of sources of the strength of #26 and #8 in an average field. That density comes out to be about 5 and 2 per deg.2 respectively.

TABLE 1. Parameters of X-ray Pair

Source #26 (NE) Source #8 (SN)

r arc min
9.66 8.57

p .a. deg
73.3 256.6

F", (0.4 to 2.4 keY) X 10- 13 (cgs)
0.8 1.4

HR1
-.4 - .2

ct rate xlO-3s-1
17.9 25 .1

X-RAY SOURCES

13

Therefore the chance of finding two such background sources accidentally within their measured distances of NGC 4258 is only PI = 0.052. Further the alignment is within 3.3 degrees giving an additional factor of
P2 = 0.018. The spacing across the nucleus differs by only 1.09 arc min.
Considering a posssible range for the spacing of 20 arc min., an additional factor of 2.18/20 =P3 = .109 is required. The total probability of two such bright sources pairing so closely across an arbitrary point in the sky is then PI x P2 X P3 = 1.0 X 10-4 .
It is necessary, however, to consider the similarity in hardness ratio and count rate of the two sources. This enables us to compute the probability that the two sources are not just randomly drawn from an average field of X-
ray sources. Using Table 2 of Pietsch et. at. (1994) one can compute that the
median range about zero hardness ratio (HR1) is 1.03. The chance therefore
of #8 and #26 falling within ±.2 of each other is P4 = 0.2. Similarly the
ratio of count rates for other sources in the field show a median range of 1.53. The chance of #8 and #26 falling within ±40% of each other is then Ps = 0.26. The combined probability of the two sources being only accidentally so similar in intensity and spectrum is then P4 x Ps = .052. Therefore the total probability of the pair being accidental, just from the
X-ray properties, is Ptot = 5 X 10-6 .
This formal calculation quantifies from the X-ray properties alone what the eye and qualitative judgement of the viewer takes in at a glance, namely that there is a very small chance that this is not a pair of X-ray sources physically associated with NGC 4258.

4. Evidence For Ejection
As early as 1961 gaseous emission filaments emanating from the nucleus marked NGC 4258 as ejecting material (Courtes and Cruvellier 1961). E. M. Burbidge, G. R. Burbidge and Prendergast (1963) as well as Chincarini and Walker (1967) showed that large deviations from circular motion occur in this galaxy, indicating large scale eruptive activity. Later van der Kruit, Oort and Mathewson (1972) from radio measures suggested the emission filaments and radio arms were caused by "... clouds expelled from the nucleus in two opposite directions in the equatorial plane about 18 million years ago, at velocities ranging from about 800-1600 km s-l."
Of course the X-ray pair is aligned within 13 and 17 degrees of the position angle of 60° (van Albada 1980) of the minor axis of NGC 4258, a direction in which one empirically expects ejection activity. In addition, however, is the fact that if one looks closely at the X-ray isophotes around source #26 it is clear that they are all elongated, both inner and outer isophotes, generally in the direction back towards the nucleus of NGC 4258.

14

HALTON ARP

The isophotes on the SW side of #26 are elongated at p.a. 237°, i.e. only 16° from a line back to the NGC 4258 nucleus. It can be ascertained from inspection of similar sources in representative ROSAT fields that this is not likely to be an instrumental effect.
Evidence from completely different wavelengths comes from the unusual water maser observations reported by Miyoshi et. al. (1995). They observe, within 8 mas of the center of NGC 4258, two small clumps of emission on either side of the nucleus. The one in the direction of the NE X-ray source has a redshift relative to the galaxy of 6.cz = +960 to +760 km S-1 and the one in the direction of the SW X-ray source has 6.cz = -940 to -860 km s-1. The authors place the major axis of a supposed disk at p.a. = 86° and interpret the redshift as due to Keplerian rotation around a black hole 40 times more massive than any previous candidate. Since black holes are commonly modeled to have accretion disks which have bipolar ejection, this would be an argument for unusually strong ejection activity in NGC 4258. The model would place such an accretion disk, very small, in the nucleus and presently oriented with its minor axis almost 90° to the supposed quasar ejection line. However, there are 5 different unpredicted aspects of this model for which the authors must invoke probable or possible explanations. But in simple essence, this observation merely consists of some points with a relative redshift of +900 km s-1 aligned in a direction only 13° different from the direction to X-ray source #26 and some points with a redshift of -900 km s-1 in a direction only 11° different from source no. 8. If #26 is identified as having an appreciably higher redshift than #8 this might be interpreted as evidence for #26 to have been ejected away, and #8 towards the observer from the nucleus of NGC 4258.
The degree of alignment found for the X-ray pair across NGC 4258 (3°), their alignment with the minor axis (13° and 17°) and their alignment with the water maser redshift anomalies (11° and 13°) are all then within the tolerances of normally accepted radio ejection phenomena.

5. Relation to Other Examples of Ejection from Active Galaxies
5.1. RADIO QUASARS ASSOCIATED WITH LOW RED SHIFT GALAXIES.
After radio source pairs were found across disturbed central galaxies in the Atlas of Peculiar Galaxies (Arp 1967) the analysis was turned around and pairs of radio sources were searched for in a region of the sky which was covered by the then new Parkes Survey at a frequency of 408 Mhz. In
the region between R.A. = 22h to 4h and Dec = +20° to -30°, thirteen
conspicuous, bright radio pairs on the sky were found which, in addition, had bright galaxies between them (Arp 1968). Between 10 and 12 of the radio sources in these pairs were quasars. Using the disturbances in the

X-RAY SOURCES

15

-100~---.-----.-----r-----r----'-----.-----r-----.----.

DEC.
(1950)

•. 616 B Ie 1767 •. 669

_13°~--~----~----~----~----~----~----~----~--~

OSm

2h 02m

l h 5am

54m

R.A.(1950)

Figure 2. The radio quasars PKS 0155-10 and 0159-11 are shown paired across the
= disturbed spiral galaxy Ie 1767. Their redshifts are similar to within ~z 0.05. All radio sources> 0.5 f.u. at 20 cm within the area are plotted. The z = .616 quasar has 8 = 2.0 f.u. while the z = .669 quasar has 8 = 2.9 f.u. (Arp 1968).

central galaxies to estimate a time since ejection of the order of 107 years, ejection speeds of the order of O.lc were calculated. It is very impressive to now see in Table 2 of the present paper just from the difference in redshift of the pairs of X-ray quasars, an average of about 0.I5c projected ejection velocity.
In addition Figure 2 shows the best case of aligned radio sources across a central galaxy found in 1968. It was known at that time that both were quasars but it went unremarked in the following years when their redshifts were measured, that they came out so extremely similar at z = 0.62 and 0.67. In fact, as we shall see now from examining the more recent pairings of X-ray quasars across low redshift galaxies, as significant as the new cases are, the best case of all as shown in Figure 2, has been known for the order of 27 years.

16

HALTON ARP

TABLE 2. Some X-ray Pairs Across Active Galaxies

Galaxy
NGe 4258 Mark 205 PG1211+143 NGe 3842 NGe 4472

zG
0.002 0.07 0.085 0.02 0.003

I I
Tl j T2
8.6;9.7 13.8;15.7
2.6;5.5 1.0; 1.2 4.4;6.0

6.0 0
3 44 8 33

F 2 ,1 XlO- 13
1.4cgs 2.3 0.2 1.0
~ 3000

Fz ,2 X10- 13
0.8cgs 2.7 1.4 0.3
~ 800

%1 j %:2
0.40;0.65 0.64;0.46 1.28;1.02 0.95;0.34 0.004;0.16

P1
5. 10-2 2.10- 2 1 . 10-2 7.10- 5 2.10- 4

Ptot
< 4.10-7
connected
< 10-6
6.10- 8
< 10-6

5.2. X-RAY QUASARS ASSOCIATED WITH LOW REDSHIFT GALAXIES.
If we restrict ourselves to just X-ray pairs across galaxies, there have been a number of notable cases discovered during the relatively short time that X-ray observations have been accessible. Some of these are listed here in Table 2. When all properties of each pairing are taken into account the
chances of any of these five cases being accidental is S 10-6• We see then
that NGC 4258 is merely the latest confirmation in a series of compelling examples of X-ray sources, mostly identified as quasars, which have been physically associated with low redshift galaxies in the same way that radio sources were in the past.
It is of interest to comment individually on each of the five cases listed in Table 2. In the table the subscript 1 designates the nearest source. The Fx values are estimated for the 0.4-2.4 keY band, except for the last entry which refers to M87 and 3C273 and uses the HEAO 1, 2-10 keY band. PI designates the accidental probability of finding the sources of listed Fx at TI and T2. 1 - Ptot gives the estimated probability of physical association.
NGC. 4258 Although the pair of X-ray sources across NGC 4258 was identified prior to September 1993, it was not until February 1995 that spectra were obtained by E.M. Burbidge (1995) which showed that the
two BSO, X-ray identifications were quasars z = 0.398 and 0.653. It was
calculated earlier that the chance of having two X-ray sources brighter than
the observed flux within the observed distance was PI = .052. When the
alignment,spacing and similarity of the sources is taken into account the chance of accidental pairing drops to 5 x 10-6. But this does not take into account the fact that both are now confirmed quasars with similarities in their optical magnitudes and redshifts. It is very unusual to observe two such similar redshifts for adjacent quasars. For example, of 26 quasars of
mv = 19 to 20 mag. observed by Arp, Wolstencraft and He (1984), only
two fell in the interval .1 < z < .8. This would reduce this improbability of
accidental association to 4 x 10-7• Still further we should take into account the tendency for the alignment of the pair to be in the direction of NGC

X-RAY SOURCES

17

4258's minor axis and also within 110 - 130 of the alignment of anomalous redshift water maser lines. (The high redshift water maser sources lie in the direction of the z = 0.65 quasar and the low redshift sources lie in the direction of the 0.39 quasar.) Finally there is the extension of the outer X-ray isophotes of the z = 0.65 quasar back toward the nucleus of NGC 4258. Overall we would have to say the chances of this being not a physical association are much less than one in a million.
Mark 205 It is striking how similar the Mark 205 association (Arp 1995a) is to that of the just discussed NGC 4258. In Mark 205 the two bright X-ray sources are somewhat more separated but the quasars they are identified with are optically and X-ray brighter than in NGC 4258 as if the whole system were a factor of 1.5 closer. It is particularly striking to note how similar the quasar redshifts are in the two systems. In fact if we propose that in NGC 4258 a pair of quasars of intrinsic z = 0.53 were ejected towards and away from us with a velocity of .13e then we could say that a pair of z = .55 quasars were ejected with .0ge from Mark 205.
Of course the two Mark 205 quasars are not at all well aligned in their observed positions. But the luminous X-ray connection from the z = .46 quasar curves back toward Mark 205 (Arp 1995a) in such a way that it must enter Mark 205 in a more northerly direction - in a direction initially
more aligned with the z = .64 quasar. Such a situation would be analogous
to ejected radio lobes when one side is bent or curved. There is also the possibility of a three way ejection that would conserve momentum.
But regardless of details of possible models, just the fact of finding two such optically bright quasars this close to an arbitrary point in the sky is of the order of 10-3 . As for the overall probability, the X-ray filament to the SSW contains two imbedded quasars, the z = .64 and a z = 1.259 quasar as well. (Arp1995a,d). If they are physically connected to the low redshift Seyfert, of course there is essentially zero probability of being accidental.
PG1211+143 Although classified as a quasar, this central galaxy has a Seyfert spectrum and properties very similar to Mark 205. It's associated X-ray sources, however, are fainter and closer to the central galaxy than either of the two preceding cases. The alignment and similarity of the two quasars makes the chance probability"" 10-6 (Arp 1995b). But of course, if the apparent alignment of radio sources so far observed (Kellerman et. al. 1994) is confirmed, its coincidence with the X-ray alignment would not only make certain the physical association but also the liklihood of an ejection origin for the quasars.
A recent spectroscopic observation by courtesy of IUCAA in Pune India and the Beijing Astronomical Observatory enables the redshift of the second quasar to be determined as z = 1.015. This is particularly important

18

HALTON ARP

-400.0 -200.0
0.0

' .. :

e18m BSO
.f a' l.s"•

-

-

-------

~:~:;
..

200.0

400.0
2'
600. 0 '--'--'--'--'---'---'---'--",--,---L..-'--'--'--'---'--'--'---'---'--'--I...-L-L.......I -400.0 -200.0 0.0 200.0 400.0 600.0
= Figure 9. The Seyfert-like object is PG 1211+143, flanked by quasars of z 1.28 and = z 1.02. The full line represents the direction and extent of a line of radio sources which
appears to coincide with the line of X-ray sources (Arp 1995b).
because it now gives ll.z for the first three pairs in Table 2 of 0.25, 0.18 and 0.26. If one wishes to interpret these pairs on an ejection hypothesis it, for the first time, gives a numerical estimate for the projected ejection velocity as about 0.12c - very close to the ejection velocity computed in 1968 from radio quasars. {Note: In Fig. 2 if the two quasars were ejected with", O.lc nearly perpendicular to our line of sight, and if IC 1767 were '" 2 times closer than Mark 205, the configuration would be similar in scale.}
NGC 3842 The close spacing of this X-ray pair across the central galaxy accounts for most of the improbability of its being accidental {the X-ray fluxes are from Bechtold et. al. , 1983}. It is important to note, however, that there is a third quasar associated with NGC 3842 which makes an approximate equilateral triangle with the first two. This not only lowers the improbability of chance association to 6 x 10-8 {Arp 1987, p13}, but it also offers a natural explanation for why, in a three way ejection event, the quasars would not need to be closely aligned. In view of the enormous significance of this association it would seem to be the one to which the properties of others would be compared for purposes of confirming the nature of the association. The most obvious property, which led to this

X-RAY SOURCES

19

-

N

•

II •

, '

•••

"

•• Q

E
•

SO I
•

•

•

•

. '~,'", '...,, "..,,''

•
2'
•
Figure 4. The E galaxy NGC 3842, brightest in a cluster, is seen flanked by two X-ray
sources which turned out to be quasars (QS01 and QS02). QS03 is a third quasar discovered as a radio source (Arp 1987).

discovery, was the existence of two point X-ray sources very close to a galaxy, as in NGC 4258.
NGC 4472 The X-ray fluxes of the two sources flanking NGC 4472 (M49) are so strong that HEA01 measures in the 2-10 keY band are tabulated in Table 2. The exact brightness is not of import here. The point rather is that M87 is one of the strongest X-ray galaxies in the sky and 3C 273 is the strongest X-ray quasar in the sky. Assuming we have'" 35, 000 deg2 unobscured of the 41,253 deg2 in the sky and that M87 is one of the three brightest X-ray sources and that 3C 273 is one of the first 10 we can compute PI ~ 2 x 10-4 that such bright sources fall so close to an arbitrary point in the sky. We see from Table 2 that this proximity of X-ray sources

20

HALTON ARP

3C 27.::.
J

Figure 5. The brightest galaxy in the Virgo Cluster is Atlas of Peculiar Galaxies #134 = NGC 4472 = M49. 3C 274 is one of the brightest radio galaxies, M87, and 3C 273 is
= the brightest apparent magnitude quasar in the sky at z .16 (Arp 1967). The latter
pair of sources are among the brightest X-ray sources in the sky.
is more improbable than NGC 4258 and better aligned. Of course, the total improbability of the association being accidental
was computed (Arp 1967) as f'V 10-6• But perhaps even more convincing was the qualitative question: Is it significant that the brightest radio, X-ray galaxy in the dominant galaxy cluster in our sky, and the brightest radio, X-ray quasar in the sky are near to and almost exactly aligned across the brightest galaxy in the center of that galaxy cluster? Most recently it has been shown that X-ray emitting material continuously connects M49 in one direction to M87 and in the other direction to 3C 273. (Arp 1995c) It would seem that the best evidence of all for linking higher redshift active objects to a lower redshift central galaxy had been already found in 1966.
6. Summary
It has been shown that, in agreement with visual impression, the alignment of the recently observed X-ray quasars across the nucleus of the Seyfert galaxy NGC 4258 is extremely significant. Further it is shown that NGC

X-RAY SOURCES

21

4258 is not an isolated case but there are a number of other associations of X-ray quasars with active galaxies that are of comparable or greater significance.In addition to the cases discussed here there are cases of X-ray jets pointing from active galaxies toward nearby higher redshift quasars (Arp 1995a). Undoubtedly it is the high energy wavelengths of the X-ray bbservations which emphasize the young, active objects like quasars, make easy their identification and render conspicious their relation to the active central objects. There is considerable evidence to support an ejection origin for these quasars in analogy with the characteristic ejection of radio lobes and radio sources from active galaxies. Of the five cases discussed in Table 2, four have central galaxies which are active and two show strong evidence for ejection from the active nucleus. It would be an obvious prediction that more cases like the ones discussed here would be available for study after carrying out systematic X-ray searches in the vicinity of active galaxies.
The quantized redshift peaks in the X-ray quasar range are: z = 0.061, 0.30. 0.60, 0.96 and 1.41 (Arp et. al. 1990). Table 3 shows the most recent pairs (Arp 1996), which when the ejection velocity components are averaged
out, gives an intrinsic z of 0.58. It is apparent that the value falls very close
to the z = 0.60 quantization peak, and drastically reduces the dispersion around the peak of the individual redshift values.

TABLE 3. Quasar Redshifts in X-Ray Pairs

Galaxy
Nee 5548 Nee 4258
Mark 205
Ie 1767
Average z

Redshifts
z = 0.56 and 0.67 z = 0.40 and 0.65 z = 0.46 and 0.64 z = 0.62 and 0.67
z = 0.58

Another pair recently measured across NGG 2639 (E. M. Burbidge, H. Arp, and H. D. Radecki in preparation) have redshifts of z = 0.307 and
0.325. In addition BL Lac objects of z = 0.308 and 0.615 have been shown
to be associated with NGG 1365 and NGG 4151 respectively (Arp 1996). In sum, the evidence for quantized redshifts in quasars is becoming stronger as more observations become available.
References
Arp, H.: 1966a, ApJS, 16, 1 Arp, H.: 1966b, Science, 151, 1214

22

HALTON ARP

Arp, H.: 1967, ApJ, 148, 321 Arp, H.: 1968, Astrofiska (Armenian Acad. Sci), 4, 59 Arp, H.: 1987, Quasars, Redshifts and Controversies (Interstellar Media) Arp, H.: 1994a, A&A, 296, 738 Arp, H.: 1994b, ApJ, 430, 74 Arp, H.: 1995a, in [AU Symp. 168 (Kluwer) in press Arp, H.: 1995b, A&A, 296, L5 Arp, H.: 1995c, Physics Letters A, 203, 61 Arp, H.: 1995d, A&A, 294, L45 Arp, H.: 1996, A&A in press Arp, H., Bi, H. G., Chu, Y., Zhu, X.: 1990, A&A, 239, 33 Arp, H., Wolstencraft, R D., He, X.T.: 1984, ApJ, 285, 44
Bechtold, J., Forman, W., Giacconi, R., Jones, C., Schwarz, J., Tucker, W., Van Speybrock, L.: 1983, ApJ, 265, 26
Burbidge, E. M.: 1995, A&A, 298, L1 Burbidge, E. M., Burbidge, G. R and Prendergast, K. H.: 1963, ApJ, 138, 375 Chincarini, G., Walker, M. F.: 1967, ApJ, 149, 487 Courtes, G. and Cruvellier, P.: 1961, C.R. Academy Sci., Paris 253, 218 Feigelson, F. D., Schreier, E. J., Delaville, J. P., Giacconi, R, Grindlay, J. E., Lightman,
A. P.: 1981, ApJ, 251, 1981 Fosbury, R A. E.: 1989, ESO Workshop Extranuclear Activity in Galaxies, p. 169 Hasinger, G., Burg, R, Giacconi, R, Hartner, G., Schmidt, M., Trumper, J., Zamorani,
G.: 1993, A&A, 275, 1 Kellerman, K. I., Sramek, R A., Schmidt, M., Green, R F., Schaffer, D. S.: 1994, A.J.
108,1163
Miyoshi, M., Moran, J., Herrerstein, J., Greenhill, L., Nakai, N., Diamond, P. Inoue, M.:
1995, Nature 373, 127 Morganti, R, Robinson, A. Fosbury, R A. E. 1989:, ESO Workshop Extranuclear Activity
in Galaxies, p. 433 Piccinotti, G., Mushotzky, R. F., Boldt, E. A., Holt, S. S., Marshall, F. E., Seriemitsos,
P. J., Shafer, R A.: 1982, ApJ 253, 485 Pietsch, W., Vogler, A., Kahabka, P., Jain, A., Klein, U.; 1994, A&A 284, 386 Radecki, H. D.: 1996, A&A in press van Albada, G. D.: 1980, A&A 90, 123 van der Kruit, P. C., Oort, J. H., Mathewson, D. S.: 1972, A&A 21, 169

A FRESH LOOK AT DISCORDANT REDSHIFT GALAXIES IN COMPACT GROUPS
JACK W. SULENTIC AND J. BRETT SMITH
Department of Physics and Astronomy University of Alabama Tuscaloosa, Alabama 35487
Abstract. We reexamine the statistics of discordant redshift galaxies in compact groups. We find that 43 out of 100 groups in the Hickson catalog contain at least one discordant redshift galaxy. We show that, despite the prevailing impression, all previous attempts have failed to explain this large number of discordant redshift galaxies. The order of magnitude excess survives all of our attempts to refine the sample.
1. Introduction
Compact groups are aggregates of four or more galaxies with surface density enhancements 102- 103 times their local surroundings. In addition to the challenges that such groups present to ideas about galaxy interactions, they also contain a large number of discordant redshift components. In this context, a galaxy redshift (expressed in velocity units where V= cz) is considered discordant if it differs from the median group value by ~V?. 1000 km S-l. The statistics of discordant components are insensitive to an increase of this limit by several times 103 km s-l. The median velocity dispersion for accordant redshift groups is 200 km s-l(Hickson et al. 1992). The standard paradigm requires that all of the discordant galaxies are chance projections of foreground or background interlopers.
The main problem with the chance projection hypothesis involves the rarity of physically dense and interacting compact groups. That makes the probability of such a chance projection quite small. Of course such an a posteriori probability estimate has little value. One needs a reasonably complete sample of compact groups in order to make meaningful estimates of interloper contamination. The belief in 1960 was that the vast majority of
Astrophysics and Space Science 244:23-2R, J996. © 1996 Kluwer Academic Publishers.

24

J. W. SULENTIC, J. B. SMITH

compact groups, when finally cataloged, would show accordant redshifts. The first discovered discordant system, Stephan's Quintet, would then be an example of a rare compact quartet made more prominent by the superposition of a bright discordant galaxy. The level of surprise grew considerably when redshifts were measured a decade later for two other famous compact groups (Seyfert's Sextet and VV172: Burbidge and Sargent 1970). Both quintets showed single discordant components (~V'" 11000 and 21000 km s-lrespectively) .

2. Statistics of Discordant Redshifts in Compact Groups
The statistics of compact groups have improved considerably in the past 15 years. A reasonably complete catalog of compact groups has been published (Hickson 1982) and the groups have been studied extensively. Near completion of the redshift measures reveals that 43 out of 100 groups have at least one discordant redshift component. This result would have caused considerable discussion had it occurred 25 years ago but, coming in recent years, it passed with very little comment. The result can be contrasted with the 51/602 discordant redshift binary galaxies (8-9%) found in a reasonably complete and similarly compiled catalog. If pairs and compact groups fall in regions with similar galaxy surface density then we expect similar levels of interloper contamination (allowing for differences in surface area).
How can we reconcile the discordant redshift galaxies in compact groups without challenging the redshift-distance relation upon which modern cosmology is constructed? There have been several attempts to explain the large number of discordant systems as chance projections. The efforts have focussed on estimating the number of discordant quintets that are expected given the observed population of accordant quartets. This approach evolved from the original discovery of three discordant quintets (4+1 systems) and because quartets comprise the largest subsample in the Hickson catalog. The arguments are identical for the next largest discordant population involving triplets with one or more interlopers (3+n systems where n= 1,2 or 3). The number of discordant quintets (ns), for example, can be estimated from the expression:
ns = n4 x (J x A

where (J is the field galaxy surface density (in galaxies deg-2) and A is the surface area subtended by the groups (in deg2). We have three possible variables that can be considered in attempting to explain the discordant quintets: we need a large value(s) for n4, (J and/or A. All three possibilities have been considered and are briefly summarized below.

DISCORDANT GALAXIES IN COMPACT GROUPS

25

2.1. MANY QUARTETS (N4 )
A few years after discovery of the three famous quintets, and several years before the publication of the Hickson {1982} catalog, a survey of galaxy quartets was published {Rose 1977}. This survey suggested that 400-500 suitably bright quartets existed on the sky. When combined with a reasonable extimate for aA, it was concluded that this quartet population could explain the {exactly three} discordant quintets known at that time. The most surprising thing about this claim was that redshifts were then known for approximately 12 of this vast population of quartets. Nottale and Moles {1978} showed that the probability of drawing the three expected discordant groups from such a small part of the purportedly large quartet sample was vanishingly small. Another quartet survey was made in the early eighties (Sulentic 1983) and it was demonstrated that the Rose {1976} estimate for the number of quartets was about an order of magnitude too high. This reanalysis was independently confirmed by the publication of the Hickson {1982} catalog which listed 100 compact groups north of declination -300 {including the three famous discordant quintets and approximately 35 accordant quartets}. The number of discordant quintets in the Hickson catalog has now increased to seven plus three additional quartets with two or three discordant companions. Even allowing for incompleteness in the numbers, it is clear that one can not account for discordant redshifts using any reasonable value for n4.

2.2. MANY POTENTIAL INTERLOPERS (0-)
There have been three attempts to estimate the accordant/discordant interloper population from local galaxy counts {Sulentic 1987; Rood and Williams 1989 and Kind11990: see also Palumbo et aL 1995}. Local surface densities were derived for each group using a range of magnitude limits and search radii with {generally} similar results being obtained. Typical surface densities are small with less than 10% of the Hickson groups found in rich group or cluster environments. Many others are associated with loose groups that are part of the large scale structure in the local universe. Much has been made of this fact in the past few years {Vennik et aL 1993; Ramella et aL 1994; Rood and Struble 1994} but it is not surprising to find that compact groups are associated with large scale structure. If groups avoid clusters and if no underlying "continuum" of field galaxies exists, what else could they belong to? What is surprising is how often compact groups are found in regions of very low galaxy surface density. If one takes the product of individual estimates of sigma and the sky areas subtended by each group {2:: Aa} one obtains expectations of 2-5 discordant redshift systems compared with the observed value of 43. One cannot explain the

26

J. W. SULENTIC, J. B. SMITH

discordant redshift population by arguing that compact groups lie in regions with higher than average galaxy surface density.

2.3. ADJUSTING SURFACE AREA (A)
The most recent attempts to reconcile the discordant excess involve the argument that one must not use the observed surface areas of the groups when calculating the interloper expectation (Hickson et al. 1988; Mendes de Oliviera 1995). Instead it is argued that many of the groups would satisfy the Hickson selection criteria even if another galaxy was located much farther from the accordant members. Hickson et al. (1988) reported Monte Carlo simulations of hypothetical groups with random projections of an interloper population. They show that one can reproduce the observed number of discordant systems by using the maximum possible group areas in the expectation calculation. Actually their procedure is equivalent to calculating the largest radius that each observed compact group could have (e.g. the largest radial distance where an additional galaxy could fall) without violating the imposed isolation and surface brightness criteria used in assembling the Hickson Catalog. The increase in surface area is quite dramatic in some cases (250x in the case of Seyfert's Sextet) since a doubling of A results from a modest (0.4) increase in group radius. Some cataloged groups are indeed so bright, compact and isolated that the addition of another galaxy many group diameters distant would still result in a compact group satisfying the formal definition.
We do not believe that this approach provides a solution to the problem. The observed population of discordant galaxies tend to fall near the accordant galaxies in each group. This is either a) an indication that they are physical (or lensed7) members of the groups or b) an indication of a selection bias in the group catalog. The chance projection hypothesis indeed predicts that many interlopers will fall at the outer edge of any selected search radius. The observed number of interlopers should be proportional to surface area (R2) so half of any complete interloper population will fall outside of 0.7R where R is the normalized group radius.
Figure 1 shows the radial distribution of the discordant redshift members in units of the maximum possible group radii that were employed by Hickson et al. (1988). We find a large excess of discordants within O.4R when we expect half of the sample to fall outside of 0.7R (which is approximately the result we obtain using the actual Hickson radii for the groups).
A two bin X2= 13.8 suggests that the observed distribution of discordants is
significantly different from the expectation (indicated by the dots in Figure 1). If the Hickson et al. (1988) maximum radii are the correct ones to use in estimating the interloper frequency then Figure 1 shows that the Hickson

DISCORDANT GALAXIES IN COMPACT GROUPS

27

expectation

\i

•

•

Ul

Q 7
u o ~

•

Ul 6

is

[:; 5
~
fIl 4
~
Z 3
•

• •
o~~-L~--~-L~--~~~~
o~U U M U U ~U M FRACTIONAL RADIUS

Figure 1. The radial distribution of discordant redshift galaxies in compact groups. Units are normalized maximum possible group radius. Dots represent expected distribution under a random projection hypothesis.

catalog is seriously incomplete. However use of the maximum radii resulted in an interloper expectation that approaches the currently observed value. Completion of the compact group catalog will add a large number of additional discordant systems. The result is that the problem does not go away.
3. A Refined Sample of Compact Groups
Having failed to account for the excess in any of the three ways discussed above we are left with the possibility that the Hickson catalog is somehow seriously incomplete and/or biased in a way that favors finding the discordant groups much more efficiently than accordant ones. This includes the possibility that many discordant groups are near limits, or in violation, of the stated selection criteria (see Hickson 1992). We reanalyzed the sample in order to verify that at least four members of each group satisfy all of the selection criteria. We found that 18 groups either 1) do not satisfy the stated isolation criterion or 2) show a larger scatter in (R band since Hickson searched the E prints of the Palomar Sky Survey in assembling his catalog) apparent magnitude than the stated maximum dispersion criterion (~m~3.0). We are left with 82 groups out of which 35 contain at least one discordant member. It is clear that the order of magnitude excess discordant population does not go away with sample refinement.
This is as far as we can go without considering redshifts. Of course we have already used the redshifts to identify discordant groups Further interpretation requires some conventional assumptions: 1) that redshift is

28

J. W. SULENTIC, J. B. SMITH

proportional to distance and 2) that true interlopers exist in the sample. We can then identify two populations of compact groups: 1) 22 false groups
containing n:::;3 accordant members and 2) 60 groups that represent "phys-
ical" (n2::4) multiplets in redshift space. The latter population contains 47 completely accordant multiplets and 13 discordant redshift (4+n) systems. If we play by the standard rules we can only treat the second population in
a statistically meaningful way. We are u,nable to consider the large number
offalse groups (mostly 3+n systems) without information on the statistics of accordant triplets on the sky. The small number of accordant triplets found in the only published survey (Karachentseva et al. 1979; see also Sulentic 1983)) suggests that the situation for 3+n systems closely parallels that for 4+n groups.
The 13 discordant groups containing n2::4 accordant multiplets are susceptible to statistical test. These systems come from an optimally defined sample including n4=43 groups with 33 pure quartets plus 10 quartets with one or more discordant members. Summing the surface areas and (J values for this sample yields an expectation of 0.98 interlopers compared with the observed number n= 10: the order of magnitude excess persists. An additional fact makes this result even more robust. The majority (9/10) of the accordant groups would have satisfied the Hickson selection criteria even without the interloper. In other words, the addition of the interloper did not push an otherwise too faint aggregate over the selection threshold. The underlying groups satisfy the Hickson criteria independently of the discordant component. The excess discordant redshift population in compact groups remain a paradox.

References
Burbidge, E. M. & Sargent, W.: 1970, In Nuclei of Galaxies, ed. D. O'Connell, (North Holland), p. 351
Hickson, P.: 1982, ApJ, 255, 382 Hickson, P. Kindl, E. & Huchra, J.: 1988, ApJ Lett., 329, L65 Hickson, P, Mendes de Oliveira, C., Huchra, J. & Palumbo, G.: 1992, ApJ, 399, 353 Karachentseva, V. et al.: 1979, Astroph. Issled., 11, 3 Kindl, E.: 1990, Ph.D. Thesis, University of British Columbia Mendes de Oliveira, C.: 1995, MNRAS, 273, 139 Nottale, L. & Moles, M.: 1978, A& A, 66, 355 Palumbo, G., Saracco, P., Hickson, P. & Mendes de Oliveira, C.: 1995, AJ, 109, 1476 Ramella, M., Diaferio, A., Geller, M. & Huchra, J.: 1994, AJ, 107, 1623 Rood, H. & Williams, B.: 1989, ApJ, 339, 772 Rood, H. & Struble, M.: 1994, PASP, 106,413 Rose, J.: 1977, ApJ, 211, 311 Sulentic, J. W.: 1983, ApJ, 270, 417 Sulentic, J. W.: 1987, ApJ, 322, 605 Sulentic, J. W.: 1993, In Progress in New Cosmologies: Beyond the Big Bang, ed. H. Arp,
R. Keys, K. Rudnicki, (Plenum), p. 49 Vennik, J., Richter, G. & Longo, G.: 1993, Astron. Nach., 314393

EVIDENCE FOR QUANTIZED AND VARIABLE REDSHIFTS IN THE COSMIC BACKGROUND REST FRAME
W. G. TIFFT
Steward Observatory University of Arizona Tucson, Arizona 85121
Abstract. Evidence is presented for redshift quantization and variability as detected in global studies done in the rest frame of the cosmic background radiation. Quantization is strong and consistent with predictions derived from concepts associated with multidimensional time. Nine families of periods are possible but not equally likely. The most basic family contains previously known periods of 73 and 36 km S-1 and shorter harmonics at 18.3 and 9.15 km S-I. Several approaches to evaluating the significance of quantization are employed and the dependence on redshift, the width and shape of 21 cm profiles and morphology is discussed. Common properties between samples define several basic classes of galaxies. Quantization is consistently optimized for a transformation vertex very close to the vertex of the cosmic background dipole. Relationships between cosmocentric and galactocentric rest frames are discussed.
1. Introduction
This paper presents evidence for global redshift quantization and examines its properties. By global quantization we mean that redshifts of homogeneous classes of galaxies from all over the sky contain specific periods when viewed in an appropriate rest frame; the redshift is not a continuous variable as conventionally expected. Work prior to 1992 is summarized eleswhere (Tifft 1995a). Early discussions of cosmology are contained in Tifft (1995b) and Tifft, Cocke & DeVito (1996). A current empirical model is discussed elsewhere (Tifft 1996a).
Two advances in quantization work occurred in 1992 and early 1993. The 3 degree cosmic background radiation rest frame was recognized to be the
Astrophysics and Space Science 244:29-56,1996. © 1996 Kluwer Academic Publishers.

30

W. G. TIFFT

primary reference frame for global quantization (Cocke & Tifft 1996), and a possible model (Lehto, 1990) was identified which predicts redshift periods in terms of the Planck energy. The model, henceforth the 'temporal model', views time as three dimensional and connects the structure of matter to redshift effects and cosmology.
Early work on global redshift quantization used a galactic center rest frame (Tifft 1978a,b Tifft & Cocke 1984). Quantization was found for galaxies with wide and narrow 21 cm profiles, but not for intermediate objects. In the CBR rest frame it is now possible to work with all types of galaxies. The cosmic frame appears to be fundamental. The effect can induce large non-random effects in other rest frames, especially the galactic center where Guthrie and Napier (1991, 1996) independently confirm periodicities.
Before 1993 redshift periods were empirical and related by simple factors to a period near 72 km s-l. One important period is near 36 km s-l. Precise predicted periods given by the 3-d temporal model now remove any ambiguity introduced by period uncertainty. One aspect of this paper is to show how accurately these periods fit observations. The first work with the CBR reference frame used the old periods. By combining the CBR rest frame and the 3-d temporal concepts we can simultaneously demonstrate the period match and the presence of a consistent CBR vertex. See Tifft (1996b) for details.
From the earliest studies it has been apparent that redshift periods and phasings depend upon properties of the galaxies involved; it is essential to use accurate homogeneous data sets or periods and transformations are masked or distorted. Accuracy largely limits studies to 21 cm redshifts where measures can achieve sub km s-l precision (Tifft & Cocke 1988, Tifft 1990). With 21 cm data, homogeneity is improved by sorting according redshift, 21 cm profile width, W, sometimes profile shape or asymmetry, A, and standard morphology, the t index. Low quality data is rejectd using signal-to-noise, SjN, or flux-to-width, F jW, ratios. F jW also separates samples by luminosity in deep redshift surveys. Studies of 21 cm redshift precision suggests that variability is present; redshifts seem to shift within the periodic pattern. Because of this, redshift sources are rarely combined, and samples are limited to defined time intervals.
The most recent galactic center transformation is (232.2, -36.6,0.9) km S-I. The numbers are the transverse, radial, and perpendicular components in galactic coordinates. This transformation is now usually applied relativistically. Older values rarely differ by more than 1 or 2 km s-l. The most recent CBR transformation is (-243, -31, 275) km S-I. It is usually applied as a Galilean transformation sequential with a relativistic galactic center transformation. A direct Galilean CBR transformation of (-241.7,-30.8,275.1) km s-lhas also been used. Differences are negligible

QUANTIZED REDSHIFTS

31

except at very short periods. It seems likely that a relativistic transformation to the CBR is not correct but further studies of vertices and the form of the transformation are needed. The present uncertainties do not affect any important conclusions.
The association of redshift quantization with the CBR reference frame provides one link with cosmology. A second link comes from nonlinearity in the periodicity with lookback time. Before redshifts are analyzed a correction is applied according to

Vcorr = 4c[(1 + z)1/4 - 1] + .. ..

(1)

Higher terms are a function of qo, and cancel for qo = 1/2. See Tifft (1991) for a derivation. A demonstration that qo = 1/2 is appropriate is given in
Tifft (1996b). The correction is important only for short periods and high
redshifts.

2. The Periodicity Rule

Lehto (1990) describes properties of matter by assuming a minimum unit of time, the Planck time, and expanding it into observable time intervals by a doubling process. The Planck time is.

JhG to = -1 = -5 = 1.3506 X 10-43 s,

(2)

Vo

c

where h is Planck's constant, G the gravitational constant, and c the speed of light. Vo is a corresponding maximum frequency which defines a maximum unit energy and mass.

Eo = hvo = -h = 4.905 X 1016 erg,

(3)

to

rno = 2Eo = 5.458 x 10-5 gm.

(4)

c

These units alone are sufficient to model the properties of fundamental

particles and redshift periodicities. Only time and energy, in energy or

mass form, is involved. This is all that is assumed in the temporal model.

Lehto (1990) also includes a minimum spatial unit, the Planck distance

ro = cto = 4.049 x 10-33 cm.

(5)

Recent work in quantum gravity suggests that such minimum spatial intervals could be a property of space. In a discrete space-time lattice structure the basic unit of velocity is

Vo = -ro = c.

(6)

to

32

W. G. TIFFT

As noted above spatial quantization is not required to quantize redshifts. The present temporal model assumes that space is continuous.
Given basic units, Lehto assumed a period doubling process, known to operate in some chaotic decay processes, to extend the Planck units into the observable domain. The simplest doubling process relates observable values to the fundamental by a factor 2±D, where D is the number of doublings. Such a scheme requires that fundamental masses, energies, etc be related by integer powers of 2. What Lehto found was that exponents seemed to concentrate at 1/3 integer values. He interpreted this in terms of threedimensional time. One dimensional perceived time could be related to a three dimensional volume in temporal 3-space. Volume doubling is reduced to one dimension by taking cube roots; perceived time is a scalar with sign and magnitude only. Lehto wrote perceived times as

= = = L

N.,+NIl+Nz

3DtM

t to2a to2 3

to2 3 •

(7)

N values are individual axial doublings, D is the net doubling and M is a

temporal fraction, 0, 1 or 2. The D, M notation distinguishes three doubling

families; values with constant M are related by powers of two.

Equation (7), combined with (3) and (4), permits calculation of particle

masses and particle pair energies. Lehto found that the mass corresponding

to L = 227 is equivalent to the electron mass within the uncertainty in the

physical constants defining to. Recent extensions model most of the basic stable particles and forces (Tifft & Lehto 1996).

Equation (7) assumes that volumes follow a doubling rule where all

three axes scale by 21/ 3 simultaneously. Removing this restriction allows

growth in steps of 21/ 9

t

=

to2

9DtT 9

•

(8)

The integer T ranges from 0 to 8 and defines 9 period doubling series. Possible redshifts, in velocity units, are given by

= = 9DtT
V P c2- 9 •

(9)

This equation also represents all first order velocity differences, hence possible periods, P. This is the periodicity rule which is found to fit observed redshift periods very well. The basic T = 0 sequence contains periods of 73.2 and 36.6 km S-1, which closely match the empirical periods discovered in the 70s. Although the 3-d temporal model has proven to be quite fruitful, this paper is intended primarily to show how well equation (9) fits redshift data without regard to any interpretation of the equation.

12 10
J &
12 10
I &

QUANTIZED REDSHIFTS

33

Virgo CIUlter W.8G-l00

Period

Virgo elulter W.40-150

I •
Virgo CI••,or W.7G-ll0
0 20

Period

P.rlod
Figure 1. Power spectra of the Virgo region sample subdivided into 21 cm profile width intervals, W, in km S-l. The abscissa is redshift period in km S-l. Vertical lines mark predicted periods. The power at a given period depends upon the profile width interval utilized but the locations of the peaks do not.
3. First Tests, Virgo Dwarfs
Certain classes of local galaxies show periodic redshift patterns in the galactic center rest frame; the patterns are not seen in 21 cm data on Virgo cluster dwarf galaxies by Hoffmann et al (1987). Early tests of the CBR association also used primarily local galaxies (Cocke & Tifft 1996). The Virgo galaxies provided the first test combining the CBR association with periodicity predictions of equation (9). Clear periodicities matching the predictions are present; details are given in Tifft (1996b). Significance has been examined several ways, but the simplest way to show the periodicities is by spectral power analysis. As used here the average power and power dispersion for random data should be close to unity. The probability of finding a given power at one specified frequency is approximately inversely exponential in the power. See Cocke, DeVito & Pitucco (1996).
Figure 1 contains power spectra for galaxies in overlapping intervals of 21 cm profile width, W. Three periods stand out; two match the original 36 and 72 km s-l periods. Essentially all significant peaks match predicted periods as shown with vertical lines. Table 1 summarizes the three main

34

W. G. TIFFT

TABLE 1. Spectral Power Data for Virgo

Width Pk Pow Pk/Per Pk Pow Pk/Per Pk Pow Pk/Per

km 8-1 P=73.2

P=36.6

P=49.8

50-90 60-100 70-110 100-250

5.6 1.0004 4.2 1.0029 <4

<4 8.3 0.9966 9.8 0.9947

7.7 1.0084 7.1 1.0033 4.1 0.9980 4.8 0.9912

60-125

<4

5.0 0.9926

7.1 0.9979

40-150 All

5.1 1.0111

<4

4.0 1.0126

<4

6.3 0.9975 6.1 0.9970

periodicities. The peak power and the ratio of the period at peak power to the predicted period (the pk/per ratio) are given as a function of profile width. The following statements summarize findings and some results to be brought out later:
1) As W is varied, power may shift between periods, especially harmonics within one T family, but the peaks closely track the predicted periods. Width adjustment varies the power but does not 'tune' periods.
1a) Distinct phase shifts within the same period occur near certain profile widths. This is not apparent in the dwarf-dominated Virgo sample but will be shown later. Certain periods or T values tend to associate with particular morphology and profile width intervals.
1b) Redshifts generally concentrate in absolute phase around simple common fractions of the periods. Concentrations are not randomly spread in phase. This is again most easily shown with later samples.
2) The pk/per ratio is a measure of the quality of fit to the set of predicted periods. The ratio between adjacent predicted values is 1.0801, the ninth root of two. Power peaks concentrate strongly around 1.00.
a 3) Periods are not distributed randomly in Tj the basic T = family is
usually dominant along with the T = 6 cube-root family. Some ninth-root families tend to occur with the dominant families, T = 1, 5 and 7 being the most important. The 49.8 km s-1 Virgo period has T = 5.
Figure 2 shows the mapping of power, at the 36.6 km s-1 period, around expected values of the transverse and radial transformation components appropriate to the CBR and galactic center rest frames. The small box is the

QUANTIZED RED SHIFTS

35

Virgo Dwarfs

~ zP..3o6.'9'8

200

N·48 70<W<110

\00 -400

-200

-\00

\00

-200

-\00

\00

Pi

P;

Figure 2. Contour diagrams of power, at the 36.6 km S-l period, for a sample of Virgo cluster galaxies. W is profile width in km S-I. Power is shown scaled by a factor of 10. The axes are the f) and 7r components, in km S-I, of the vector used to transform to the CBR rest frame (left) or galactic center (right). Each diagram refers to a constant Z component as indicated. The box is the COBE error box for the CBR dipole vertex. The x in each frame is the approximate location of the rest frame vertex based upon previous quantization studies. The Virgo periodicities associate with the CBR vertex, but not with the galactic center.

COBE error box for the CBR vertex. X symbols mark adopted quantization vertices. The Virgo galaxies, not widely spread on the sky, show a broad power concentration associated with the CBR but not the galactic center.
4) Power at predicted periods is maximized when redshifts are transformed to a rest frame close to the COBE CBR vertex. The radial component is typically slightly more negative than the COBE value.
The significance of the periodicities and the match to equation (9) has been evaluated three different ways. The fact that the most prominent power peak matches the previously known period near 36 km s-l with a power of 10 is significant by itself. About 20 predicted periods fall in the range studied; a match at any period at power 10 has a likelihood of accidental occurrence below the 0.001 level. Since at least three periods are matched above power 6 and no high power peaks fail to match periods, we conclude that equation (9) well describes the periodicities present.
Since questions have been raised about using extreme power values to estimate likelihoods we have used a binomial test to evaluate the degree to which all peaks above power 4 fit predicted periods. The power spectra for all the profile width intervals in the 20 to 100 km s-l period range contains 14 independent power peaks greater than 4.0. The fits vary slightly but 8 of the 14 peaks lie near or within 0.005 of unity in the pk/per fitting
index. The index should be uniformly populated between 1.00 ± 0.04 for a
random distribution, hence the probability of falling within 0.005 of unity is

36

W. G. TIFFT

2.0 1.8 1.6 1.4 1.2
I 1.0
I 0.8
0.6 0.4 0.2

··II
•

I • • •

I 2.5
W-60-100 W-70-1I0

W. 60-125

2.0

• •

• • a •

a •

•
A I: 8
II •

O.S

. •

I•I
• a

.
0

I ·· I • WW--6700--110100 W_60-125

a
•• ••i I

1\

• • • A
•

A •

II II

a

0·S.9S 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 Scale Factor

0·S.9S 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.0S Scale Factor

Figure 9. Mean power and power dispersion for 25 periods between 23 and 146 km s-l. Symbols distinguish profile width subsets of Virgo galaxies; W is in km S-l. Samples with open symbols cover the complete redshift range; samples with filled symbols omit redshifts below 500 km S-l. Power is measured at periods scaled from the predicted periods by the scale factor on the abscissa. Power and dispersion peak at the predicted periods.

about 1/8. The likelihood of 8 or more accidental fits in 14 trials within this
tolerance is 8 x 10-5. The likelihood of finding more than 4 fits is < 0.05.
A third test uses the unit mean and dispersion in power expected for a random distribution. Eight sets of periods were generated by scaling the predicted periods by factors 0.97, 0.98, .. " 1.04 to cover the range between predicted periods. The mean and dispersion in power was then found for the 25 periods between 23 and 150 km s-1 using three data sets in the 60 to 100 km s-1 width range. Figure 3 shows the result as a function of the scaling factor. The distributions peak sharply at 1.00, the predicted period set. Comparing the mean and dispersion at 1.00 with the values midway between the predicted periods using a Student's t test yields t = 4.1, or about a 10-4 likelihood that they arise from the same parent population. Using power levels, peak locations, or the power distributions we find consistent significant results. The Virgo dwarf galaxies contain periodicities uniquely consistent with equation (9) when viewed from the CBR rest frame.
The third test confirms that adjusting profile width intervals does not arbitrarily tune periods. Ifthis were not the case we should have found many intermediate periods. Real periods will shift only slightly and show power variation according to their actual profile width dependence as is observed. To test for tuning of spurious periods one must use periods which are not predicted, but such periods are not found in significant numbers. Arbitrary periods are rare since the redshift distribution is not random, it contains stable predicted periods.

QUANTIZED RED SHIFTS

37

4. A Second Sample, The Perseus Supercluster

A second sample uses redshifts from the deep Arecibo survey of the Perseus supercluster from Giovanelli and Haynes (1985, 1989). There is a special reason for this choice. A common criticism of periodicity studies is that parameters are adjusted to optimize power and period fits; in the first samples discussed here all parameters were set prior to the discovery of the ninth-root rule. See Tifft (1996b) for details. The samples were defined in older studies. In 1984 Tifft & Cocke (1984) found that local galaxies with 21 cm profiles wider than about 420 km S-l contained a 36 km s-1
galactocentric periodicity. Martin Croasdale (1989) generally verified this using independent data, some of which came from the 1985 Perseus survey. To examine and extend Croasdale's work the 154 galaxies with unblended 21 cm profiles wider than 400 km s-1 were compiled from both Perseus region studies. Only 22 of the galaxies are in common with Croasdale.
This ready-made sample was used in 1992 in an early study of the CBR
association, prior deriving equation (9). 73 galaxies with SIN < 4 were set
aside as lower in quality. Using the 81 best redshifts it was noted that galaxies with small flux-to-width ratios contained a 36.05 km s-l period which
appeared to associate with the CBR rest frame. The F IW ratio provides
a rough luminosity distinction. Using this distinction the 81 galaxies were
divided into 53 with FIW < 0.01 and 28 with FIW > 0.01 to roughly
optimize the 36.05 km s-1 periodicity; this period is not one of the periods predicted later by equation (9). By defining the samples using this period we introduce some sample homogeneity but no bias relating to the periods predicted later.
Figure 4 shows redshift phase, plotted in a double cycle to show periodic clumping, for the 81 galaxies with SIN> 4. The predicted 36.5859 T = 0
period is used; The abscissa is F IW. The right hand frame shows part of the
53 point power spectrum. Table 2 summarizes period fits giving the peak
power and the (peak period)I (predicted period) ratios. The dominant peak
fits the T = 0 family at the 18.3 km S-1 harmonic. There is no significant change if galaxies in common with Croasdale (1989) are deleted. The 18.3 km S-1 period is present. This period along with the 36.6 km s-1 and 9.15 km s-1 harmonics is often dominant. The period is aligned on phase 0.0, simply phased with the CBR rest frame. The Perseus data also illustrate the general preference for cube-root families; the T = 3 family is distinct. The ninth-root families flanking T = 6 are present and match the detection in Virgo. T values do not occur randomly; there are similarities between samples. The low SIN data are also consistent. When the low quality data are combined with the 28 point sample the longer period T = 3 periods are reinforced. Low quality data destroy short periods but preserve long ones.

38

W. G. TIFFT

. I. 2

_I' •.
•t"Jp;,•-~:.• ,"\ .•.,

•
•

'"

fl.".. ,. ! I• ..,•••

•t..p.•....\,'_. •• '"

..IJ·!.tul""•..,•I.,

Perseus Region Period. 36.5958
•

40

60

80

(FluxIWidth)x1 00

Perseus. W > 400
Period

Figure 4. (left) Phase diagram for Perseus galaxies with wide 21 cm profiles. Points
are plotted twice in a double phase cycle at the 36.6 km S-1 period. The abscissa is the flux-to-width ratio scaled by 100. There is a regular 18.3 km S-1 pattern aligned at phase
0.0 and 0.5. (right) A section of the power spectrum for the 53 point subsample of wide profile Perseus galaxies; W is in km 8- 1. The abscissa gives periods in km S-1. Three predicted periods are shown with vertical lines. A disproportionate fraction of peaks in excess of power 4 associate closely with predicted periods.

To evaluate significance we found all power peaks greater than 4.0 in the period range 17 to 250 km s-l. The limits are set by the breadth of power peaks at long periods and excess noise at short periods. We then count the matches within a limiting pk/per range and apply binomial statistics. The 53 point sample has 9 fits within 0.004 of unity (1/10 the possible range) and 27 power peaks above 4. The probability of 9 or more accidental hits in 27 trials is only 0.0009. The 28 point sample has 4 hits out of 9, unlikely at the 0.008 leveL If we raise the cutoff period to 36 km s-l to reduce noise, the 53 point sample returns 6 hits out of 10, unlikely at the 0.0002 leveL Table 3 summarizes some of the binomial test results for both the Virgo and Perseus investigations. We again note that there was no optimization for the wide profile Perseus samples; they were defined before equation (9) was found.
The Giovanelli and Haynes (1989) data were next examined using galaxies with narrower 21 cm profiles. Findings are similar; Some of the results are given in Table 3. One subsample of the 472 galaxies available used 179
galaxies with SIN > 4 and 200 < W < 400 km s-l. A period matching
study found 10 of 21 power peaks above 4 falling within 1/5 of the range around predicted periods. This returns a random likelihood of 0.004. Of special interest is the continuity of the 18.3 km s-l period at W = 400 km s-l. Table 2 (lower part) shows that the pk/per ratio match is within 1% on both sides, 1.0003 and 1.0002; the power values are 6.9 and 7.1. Such continuity between width intervals, here with a phase shift, is extremely unlikely by accident but is not considered in evaluating significance. Periods

QUANTIZED REDSHIFTS

39

TABLE 2. Spectral Power Data for Perseus

Period T Power Pk/Per Power Pk/Per Power Pk/Per

km S-l

N=53

N=28

28+73

36.5958 0 18.2979 0

4.4 0.9990 7.1 1.0003

232.3689 3 116.1845 3 58.0922 3 29.0461 3

4.8 0.9999 4.9 0.9977

5.0 0.9968 4.4 1.0029

7.6 0.9984

99.5984 5

4.9 1.0016

85.3802 7

6.8 1.0029

TABLE 2. Spectral Power Data for Perseus
= Comparison Above and Below W 400

V

W

km S-l km S-l

SIN (F/W)

N Pow(Pk/Per) P=18.2979

4500-17500 > 400 « 0.01) 53 7.1(1.0003)

0-20000 300-400 0-20000 200-400

>4 76 >4 179

6.9{1.0002) 6.0{1.0003)

are intrinsic to the data, power but not periods can be tuned by selecting profile width intervals.
The samples on either side of the W = 400 km S-l boundary also show the stability of the CBR association. Figure 5 contains power maps, at P = 18.3 km S-l, for a range of the tangential and radial transformation components near the COBE vertex as shown earlier for Virgo. The independent maps agree closely.
5. A Third Sample, The Cancer Superc1uster
A deep Arecibo survey of the Cancer region by Bicay & Giovanelli {1986ab, 1987} provides additional information. The 643 galaxy study provides a good illustration of the common T = 0 periods. For detail see Tifft {1996b}. The familiar 36 km S-l periodicity is strong in low redshift foreground galaxies viewed from the CBR rest frame. The top part of Figure 6 show

40

W. G. TIFFT

TABLE 3. Binomial Tests of the Distribution of Power Peaks

Sample N Virgo 137

V km/s
All

W km/s
All

P km/s
20-100

Fit Pks Hit Prob

1/8 14 1/4 14

8 0.00008 9 0.002

Per-W 53 S/N>4 *

All > 400* 17-250 1/10 27 36-250 1/10 10

9 0.0009 6 0.0002

28

All > 400* 17-250 1/10

**

Per-565 179

All 200-400 16-250 1/5

31

All 225-250 16-250 1/4

56 6-8000 50-250 10-100 1/16

34 6-8000 200-350 10-100 1/16

* Predetermined F/W<0.01, ** F/W>O.Ol

9 4 0.008

21 10 0.004

10 7 0.004

8 4 0.0009

9 3

0.02

-240

-250 ~e!~;~~r
Z-27S N -179 200<W<400 -260

-so

-40

-30

-20

Pi

Pi

Figure 5. Contour diagrams of power, at the 18.3 km S-1 period, for samples of Perseus galaxies with 21 em profiles wider and narrower than 400 km S-l. Power is shown scaled by a factor of 10. The axes are the () and 11" components, in km S-l, of the vector used to transform to the CBR rest frame. The diagrams refer to a Z component of 275 km S-l. The box is the COBE error box for the CBR dipole vertex; the x is the approximate
location of the vertex from previous quantization studies. Samples on opposite sides of a phase shift, which occurs near W = 400 km s-l, define the same period and vertex.

the 36.6 km s-1 phase-width pattern and power spectrum for the 58 galaxies
with redshifts below 2000 km s-1. The narrow profiles and 36 km s-1 period
resemble the Virgo galaxies. The power spectrum sharpens and peaks very
near the predicted period for the 33 galaxies with 90 < W < 190 km s-1.
The lower right panel shows the CBR association for the 33 objects. The

QUANTIZED RED SHIFTS

41

.\:,.."'.l.i,...~...". .
.•.·.1••-•· • · •
... . ....- ",.:..~,...#,..,"...~.,....\...." .

All V < 2000

c-:.r Resioa

P.36.S9S8

10

!II 6

Vc-<:2.0rGR0esiOD

00

100 200 300 400 SOO 600 700

Profile Width

Period

. ,-..::..... .. -.-. \

.~• • I ·. .• •

-210

4

,

•••, , , . c-:.r

-220

. : . - , . . . • • ~..

P.18.2979

" •#•.'. ......., .· .:Ir,..... :

-230 ·240

•

. ·

.• e,• .,-·,I

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I
.ft::

••
'.....

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-. •

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.. ... . ., .:., •

,. , ~

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~ I

•

••

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.

I, ". " ••~ "",' :'!".

o 0

100 200 300 400 SOO 600

~ -2S0
-260 -270 -280 -290 700 -300-8~0-'---:!::----~--::-=~--==--~c-"-_~IO~O~--:'IO=-'

Profile Width

Pi

Figure 6. The left panels show phase-profile width diagrams for Cancer galaxy samples. Phase is plotted in a double cycle. Periods, P, profile widths, W, and redshift, V, are in km S-l. The upper left panel shows the 36.6 km S-l periodicity for low redshift galaxies.
The lower left panel shows an alternating periodicity pattern found for higher redshift
= galaxies when P 18.3 km S-l. The selection criterion, discussed in the text, changes at = W 400 km S-l where a phase shift occurs. The power spectrum (upper right) refers to
the low redshift sample. The solid line is for all 58 low redshift galaxies; 33 galaxies with 90 < W < 190 km s-l produce the dashed spectrum. A line marks the predicted period. The lower right frame shows the power concentration, for the 33 galaxy set, associated with the CBR dipole vertex. See Figure 5 for a description of axes and symbols.

first part of Table 4 summarizes the foreground analysis. The lower redshift end of the Cancer complex, including the Cancer cluster, shows the 36.6 km s-1 periodicity among the wider profile galaxies. The 18.3 km s-1 period dominates when lower luminosity sources are included and can be traced through nearly the entire sample.
The lower left panel of Figure 6 and the last part of Table 4 trace the T = 0 periods through the higher redshift data. The 9.15 and 18.30 harmonics alternate as a function of profile width. F/W and S/N levels are set high to show the shorter period clearly. Periods track precisely, usually within 1%of the pk/per range about predictions, through successive independent width intervals while remaining aligned at 0.0 and 0.5 in phase on the 18.3 km s-1 scale. Above W = 400 km s-1 an expanded sample shows the phase break which occurs near W = 400 km S-l. As found for

42

W. G. TIFFT

V/I03 km/s
0-2

TABLE 4. Spectral Power Data for Cancer

W SIN N

Pow(Pk/Per)

km/s

P=9.1490 P=18.2979 P=36.5958

All All 58

90-190

33

9.1(1.0043) 10.7(0.9998)

3.5-7 2-10

> 250 All

>8 128 All 184
562

4.7(1.0023) 6.9(1.0027) 6.6(1.0022)

7.8(0.9907)

5-10 0-175
175-275 275-400

* 30

4.2(1.0032)

40 6.7(1.0002)

31

7.3(1.0000)

0-400 0-10 > 400
* F/W > 0.015

100 8.4(1.0003) >8 49 4.3(0.9999)

Perseus data there is no change in period but there is a phase shift. These Cancer data give a clear picture of how phase, harmonics, and width can be interrelated.
6. Short Periods and qo Determinations
Studies of short periods over wide redshift intervals are sensitive to the nonlinearity in z from equation (1). This equation was derived as a Taylor expansion about qo of 1/2 (Tifft 1991); higher order terms permit a
determination of qo. Short periods in the basic T = 6 cube-root family
are strong in Perseus, Cancer and local redshift data (Tifft 1996b). Precise period matches occur when qo is equal to 1/2. Table 5 contains examples. The peak power location, near power 10 in these examples, shifts slightly as qo is varied. The pk/per ratio passes through 1.00000 when qo approaches 1/2. This result, found for several independent samples, gives considerable confidence in the significance of both equations (1) and (9). A classical interpretation of qo is unlikely in the temporal model.
The determination of qo is quite insensitive to the CBR vertex assumed. Figure 7 shows peak power maps as a function of the transverse and radial transformation components. Two large independent samples from the Cancer data are shown; one includes 89 narrow, the other 128 wide profile galaxies. Peak power exceeds 10 close to the standard vertex we have
assumed. At this high resolution (P = 2.88 km s-l) only the edge of the

QUANTIZED REDSHIFTS

43

-237 -238
i -241
-243 -244 -245 -246
-36 -35 Pi

-237 -238 -239 -240
i -241 -242 -243 -244 -245

CaDcer W>250 V K 3500-7000 Pz2.8817
75 8

a />

-246 ·36 Pi

Figure 7. The power distribution, in the vicinity of the CBR dipole vertex, for two subsets of Cancer region galaxies. Wand V give profile width and redshift ranges in km S-l. SIN refers to signal-to-noise limits and N gives the sample size. At the short period shown the power peaks are sensitive to qo, and match predicted periods when qo= 0.5. The independent samples conform closely to the same vertex. See Figure 5 for description of axes and symbols. Only the edge of the COBE error box, the line at right, falls within the frame for such short periods.

TABLE 5. Estimation of qo

Period km/s

qo Peak Pk/Per km/s

5.76348 0.52 5.7626 0.99985 0.51 5.7633 0.99997 0.50 5.7641 1.00011 0.49 5.7650 1.00026 0.48 5.7659 1.00042 0.46 5.7678 1.00075

N

V W F/W

km/s km/s

88 4300-17900 >450 <0.015 (-241.5, -24.2,275.0)

2.88174 0.51 2.8815 0.99992 128 3500-7000 >250 S/N>8 0.50 2.8818 1.00004 (-241. 7, -30.8,275.1) 0.49 2.8821 1.00012 0.47 2.8826 1.00030

COBE CBR dipole error box is visible at the right.
7. Local Data
The samples so far discussed involve single epoch studies of non-local galaxies, including ones in external superclusters. We now turn to multi-epoch data for local galaxies, drawing primarily on 21 em data from the Fisher-

44

W. G. TIFFT

Tully (1981) survey from the 70s and data from Tifft & Cocke (1988) and Tifft (1990) from the 80s. Using different epochs we can investigate variability. The new data also include quantitative measures of 21 profile shape, the A = asymmetry index. Some material here is from Tifft (1996b); details about variability will be discussed in Tifft (1997).
Quantization effects change near certain profile widths. One such change occurs near W = 400 km s-l; a second occurs near 200 km s-l. The top frames of Figure 8 compare an original study of the CBR association using Fisher-Tully galaxies with the lower left frame from Cancer work in Figure 6. Below W ~ 175 km S-1 the Fisher-Tully data are periodic. The periodicity blurs but returns, with a phase shift, by W ~ 300 km s-l. We see the same shift in Cancer at the 18.3 km s-1 T = 0 period, and recognize the shift as a transition through the 9.15 km s-1 harmonic. local galaxy
work focussed on the 100 < W < 300 km S-1 interval to verify the dom-
inance of T = 0 periods and investigate the transition region. Detail are revealed by the way 'deviations', redshift differences between epochs, relate to phase and asymmetry. 'Phase-deviation' diagram are used. Deviation usually refers to the redshift difference Tifft & Cocke (1988) minus FisherTully (1981), written TC-FT. The TCF sample contains 454 galaxies for which this difference is available.
Figure 9 contains phase-deviation diagrams for TCF galaxies. The up-
per left frame includes all 249 galaxies with 100 < W < 300 km S-I. The
peak power is above 9 in the CBR rest frame as shown at upper right. The pklper ratio is 1.0010; the peak falls within the central 2.5% of the range between predicted periods. The systematic shift between modern redshifts and Fisher-Tully values is apparent. The lower panels show enhanced periodicity when profile asymmetry is restricted to less than 10%, and mor-
phology to t < 9. The lower right frame shrinks the width interval. The
transition region contains a finer harmonic structure and is the same in Cancer and locally. SIN has little effect; scatter in phase is not due to observational uncertainty, it is due to finer structure. Scatter, from modern redshifts, is not much larger than the point size. Scatter in Fisher-Tully data affects deviations only.
To see finer structure we must introduce redshift variability. Figure 10 repeats a variant of the lower right frame of Figure 9. The vector shows that if a redshift were to decrease by one period between epochs a galaxy could shift from one end of the deviation pattern to the other and remain in phase. This is what seems to occur, occasional rapid transitions retain a periodic phasing and generate periodic deviations. A secular downward drift seems to occur from the high redshift end of levels. Intermediate steps mayor may not be seen. Data from galaxies with wider profiles (lower right) show a staggered pattern which would be generated if intermediate levels

QUANTIZED REDSHIFTS

45

2.0

1;. ..., . !It ,_ .... ,:'"...
•,iI .' . • • t. .., •• ~

1.5

N

.\.0

t:-
~

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0.5

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•

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, · l~':4:;' . ••

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• ,
••

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10 • • • •

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0.0

0

100

200

300

400

500

600

700

2.0

',!!'J..:'...".. ·

1.5
N
!..\.0 .c 0.5
0.0

..'.... .. ". .... Line Width

.I.",,CC•.,...'.••.,.,-,~t1;t..~\.}:.II.J,.-.J.i.'o'1·:'..·...: '-•..·'...• ....:,...·.1~• ..''...'·.:,.,f.l.·.•...•·...• •......'....

• • • •

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100

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300

400

500

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~
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0

.... ':' X.•• I "'....

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·to:.·~•.· "·.

•

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0

100 200

300

400

500

600

700

Profile Width

Figure 8. The upper two frames are phase-width diagrams for local galaxies using Fisher-Tully data; W is in km S-I. The diagrams are from a study of the association
of redshift quantization with the CBR rest frame before precise periods were predicted; an empirical 72.1 km S-1 period was used. There are distinct periodicities, with a large phase shift, on either side of a transition region near W = 200 km S-I. The lower frame repeats a Cancer region phase-width diagram from Fig. 6 to show that the same type of transition, involving subharmonics of the period, occurs at this width. The phase shift effect at W = 400 km S-1 can also be seen in both samples.

occur. Periodicity in such cases cannot be recognized without deviation information. A Student's t test comparing deviations in the half phase intervals dividing at .0 and .5 easily shows the periodicity.

46

W. G. TIFFT

:;r.. .. . . --r-,-/~~~.-•~~~.~r..-.T~·~'-~-'~~'-I~-'-d-OO~

~ ~

1.6 1.4

.. 1.2

"i 1.0

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Deviation (TC.PT)

-248 -2S0
-~2~~~~~,u~~~~~~~~~ -40 -38 ·36 ·34 Pi

2.0 ,.---.--.---,-,.r..;-r.---::.:r--'~-r--.--.., 2.0,.---.--.--.--,----r--.,.---,.-.--.

1.8
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•

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... •• • • .I~: e.
. .1 e.: •• :

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.1

~

170<W<250 -1.1<01.<11 SIN> 10 T<9 N.U

Deviation (TC·PT)

DeviatiOll (TC.PT)

Figure 9. Phase-deviation diagrams, and a cosmocentric power map, for local galaxies. The 18.3 km S-1 predicted period is used. Deviation is the redshift difference, in km
S-I, Tifft-Cocke minus Fisher-Tully (a 10± year interval). The upper left diagram shows
a complete set of 249 galaxies with profile widths, 100 < W < 300 km S-I; points
concentrate around phase 0.5. At upper right the association of power with the CBR rest frame is shown. Refer to Fig. 5 for a description of axes and symbols. More restricted samples are shown in the lower frames. Restrictions, in W, profile asymmetry (A index), signal-to-noise, and morphology (t index), improve homogeneity and enhance power, but have no significant affect on the period or vertex location (compare Fig. 10).

The upper right panel of Figure 10 contains the power spectrum of the sample at upper left. The dashed line shows the spectrum without an asymmetry restriction. As with width adjustments, narrowing a parameter range can affect the power, but does not significantly affect periods. The periods are intrinsic to the galaxies. The lower left frame shows the CBR association of the restricted sample. As with periods, restricting the sample does not significantly affect the vertex location. The second peak in the power spectrum matches the T = 1 period at 16.94 km s-l. The adjacent ninth root families seem to appear when the cube-root families show evidence of recent or current change. Near the beginning or end of a doubling process one axis may be out of synchronization with the others.
Asymmetry restrictions often improve the resolution of periodicities. If phase scatter is due to intermediate states, asymmetry may discriminate.

QUANTIZED REDSHIFTS

47

: ,
.••«•••••••,:•e:: ••• ..~

TCFSample

170<W<250 p K 18.2979

12

·1.1 <A<I.l

• S/N>tO

10

, :

~
... 6

. . •«.......

,:~
..;,

-.
••

0:

~20 ·15 .10 ·5

0

10 15 20 25

Deviation (TC·PT)

TCF Sample 110<W<2S0
Period

·230

·240

·250

·260

·50

-40

·30

·20

Pi

• I.~.:

•

.' \.~ : .

~<;~;;ple

• •...... ,. •• •• ~!8.2979

~ 1

. . . .. .... .. .-\-...:.'.• ...)• .'::::...-

o •.

...... . .- \- :..:.:...~

::
:

• S1N>10

o

i" ~::...

·20 ·lS ·10 ·S 0 5 10 15 20 25

Deviation (TC·FT)

Figure 10. Redshift variability effects in a restricted local sample (see Fig. 9). The vector in the P = 18.3 km S-1 phase-deviation diagram (upper left) shows how a shift of one cycle between epochs will shift a point, produce a related deviation, and retain the periodicity. Intermediate levels seem to occur in other width intervals, (lower right), yielding a characteristic staggered pattern. The power spectrum (upper right) of the 36-point restricted sample shows a precise period match; predictions are marked with lines. Removing SIN and asymmetry, (A), restrictions generates a 92-point sample. Power drops slightly (dashed spectrum) but does not affect the period or CBR association (lower left, see Fig. 5 for a description). The power spectrum contains the next shorter predicted period; such periods seem to occur when recent or current variation is suspected.

Figure 11 shows positively asymmetric galaxies; they concentrate on the
wide side of the 200 km s-l transition, populate the 9.149 km s-l T = 0
harmonic and show a sharply staggered pattern consistent with stepwise
redshift decay. Objects with A < 0 tend to favor the narrow side of the 200
km s-l transition with a shift in phase. In the 0 to -10 km s-l deviation
range the A > 0 objects show a power, at 9.149 km s-l, in excess of 10.
They map into the standard CBR rest frame as shown at upper right.
This negative wing is expanded at lower right where points seem to clump laterally at still higher T = 0 harmonics. Redshifts seem to change in
discrete steps, cascading between relatively stable levels in ways associated
with the width and shape of the 21 cm profiles. The velocity distribution function appears to determine transition likelihoods. Multiple epoch data and detailed profile shape information are essential for the study or even

48

W. G. TIFFT

2.0 1.&" 1.6 is 1.4
i 1.2 1.0
~ 0.8 .. 0.6 0.4 0.2 0.0 -20

... .·.... · •• • .:: •

•• •

•I.1'1ft : .:.... •

....·..·.·...·... ..· .... • •

• " • C',.~..
,;
.:
;,

•
• •

I .(" ~:. . . . .

·. . . • .'F.:... .'

ISO<W<300 A>O

-234 -236 -238 -240
~ -242 -244 -246 -248 -250 -252

i
A 0 >0 -I :c::Dcv<l Z.275
\

-IS -10 -s

0

S 10 15 20

-40 -38 -36 -34

Deviation (TC·PT)

...
-32 Pi

-24 -22

2.0
1.8 l-
1.6 is 1.4
i~ 1.2 1.0
l 0.8 fe 0.6
0.4 0.2

·.. .. · .. .,:

· ·. · •'Jt i •o 0 • •

/.' /,~

•
'

..
if

....f?I~~.

' • 'j>.

•
.. •
• .'

·..... · · i : 0

00

·. .... fl· ... ..

2.0

150<W<300

1.8

A>O 1.6

is 1.4 1.2

1.0

! 0.8
if 0.6

I

I .(, :.~ . . .
. . • •' ~'':-:i.' •' ..

0.4 I 0.2

. .

... . .. . ,', o·

•

. . . • 0

t(. 0

0

:.
. .: ':

0:

.. . . .. .. e::'"•

~"
.~ ~

. . o .

0 0

0:

:0

.o:'

0 0:

.:

.;

.~

0'~20 -16 -12 -8 -4 0 4 8 12 16 20

0.0 -10 -9 -8 -7 ~ -S -4 -3 -2 -I 0 I 2

Devialion (I'C-PT)

Deviation (TC-FT)

Figure 11_ Phase-deviation diagrams and a power contour map for local galaxies with
positive asymmetry and profile widths in the upper portion of the 100 < W < 300 km
S-l transition region_ A strong negative deviation is present and periodic at 9.15 km S-l.
The pattern is consistent with discrete changes (lower left) involving a substructure at
still hipher harmonics (lower right). Power contours for galaxies with -10 < dev < -1
km s- (upper right, see Fig_ 5 for a description of axes and symbols) show power in excess of 10 very close to the adopted CBR dipole vertex_

the detection of such variability. Lookback time may cause differences as a
function of distance so samples in different redshift ranges should not be
casually combined.
The basic T = 0 doubling family dominates intermediate width profile
galaxies consisting of relatively normal spirals. There seem to be three other
categories, two classes of dwarf galaxies with narrow 21 cm profiles, and a
general class of wide profile objects. Extreme dwarf galaxies, morphology
t = 9 or 10 with W < 75 km S-1, are locally periodic in the T = 7 family
with a clear asymmetry dependence. This is shown in Figure 12 for the
extreme dwarfs in the TCF sample. Objects with negative asymmetry or
symmetric profiles show strong negative deviations periodic at the 10.6726
km s-1 T = 7 period. Galaxies with positive asymmetry are sharply phaseshifted. The sample, independent of the T = 0 sample, shows a clear CBR
association and hypothetical transition patterns tuned in absolute phase.
The 10.67 km S-1 period and its 5.33 km s-1 harmonic were detected

QUANTIZED REDSHIFTS

49

. 0 . 2.0 r---r-----,-----,----r~__r-__,__-__,

1.8 1.6

0; . ..

~....
.0

•

:.: ...

T.9~0
W<7S A<1.0S

t ::~ r---,------,r----+'+"Tt. -----=.+<'T"7"/'.-II:--~<-<1-<-1-.05'1

1.6

:_:+ ....... 4·: L-.+__A_>I_.0_4-,----JJ

G 1.4
~ 1.2
l 1.0

• .to •••:;::.:~ . : .: ... .
e: ... "

CD 1.4
5 1.2 lc;j
1.0

• ~ !A.:;t:':':
* ..- +e: t
+: {".o+f..

T-9)0 W<75

! 0.8 f
0.6

.. ~ • • •
.0
_.: ..... :.

f! 0.8 0.6

+...
:.:

• __..~~•••...•

-+

0.4

• "". •••: j-: :t\.:

0.2

... .: ....

0.4

• ~ !".:..::.;':

0.2

t .: +e:

0'~2':-0--:_I'-='S--:-1'::-0--'-S:--~-----:-----:':10----:'IS'

0'~2':-0--:_I'-:-S--:-

1'::-0-

-'

-S

::

-

of:
"'-

'

.'+ :O-

-

• --

-:

-

--

-

-:

':

10,-

---

'

1 S

Deviation (TC-PT)

Deviation (TC-FT)

2.0 ,------,r-------,----r-r---=::-...-----j----,

-232

P -10.672S

+- +t ....f

• A<O

1.8

++ .. ~.,'"

.. O<A<1.0S

-234 -236 -238
~ -240

Z-27S
N~32

1.6
~ 1•4 ~ 1.2
l 1.0

r :.: ....... "!-:-+-r-,==+c--A__>1_.0_4

• ..0. +0••.-j~.''.;4.

T-9.10

t'::;: .. ... +-1 +
+

W<75

-242 -244 -246 -248

+

~ :::
0.4

0.2

.. .. /.~ ;~
... •:':...r~it: ~ .•

+

;! .~ ~~ ~ ..- + •.

,+ •

-2S0-4LO-'----"~-:'-:-"---!-~7:-='C:=--~__:::____:_;_'___=_'

0'~2'-:-O--:-I'-='S---:-1-=-0---:_S~"--':------:------:':10---,J15

Pi

Deviation rrc-PT)

Figure 12. Phase-deviation diagrams and power contours for local galaxies with extreme
dwarf characteristics, t = 9, 10 and W < 75 km S-l. A strong negative deviation is present
for galaxies with symmetric and negatively asymmetric 21 cm profiles (upper left). The period is 10.67 km S-l, shifted one ninth-root cycle from the common T = 6 family of periods. Galaxies with positively asymmetric profiles, are phase shifted (upper right). The pattern is consistent with discrete changes (lower right) where asymmetry distinguishes between stages. Power contours for the negative wing of galaxies (upper left) show power in excess of 11 very close to the adopted CBR dipole vertex (lower left, see Fig. 5 for axes and symbols)

prior to the derivation of equation (9) (Tifft 1991). Their precise fit into
the pattern of predicted periods helped to focus attention on equation (9).
The T = 7 ninth-root family bears the same shifted relationship to T = 6
as the T = 1 periods have with T = O. The shifted ninth-root patterns may
characterize regions undergoing changes. The W = 75 km s-l boundary for
this group is not arbitrary; it is the narrow cutoff width for dwarfs found in the original global redshift studies (Tifft & Cocke 1984).
Between the extreme dwarfs and normal spirals of t = 8 or earlier, there
is a large class of objects. They can be characterized by t = 9 or 10 with 75 < W < 250. These common local galaxies show no overt periodicity
until deviations are examined. The T = 6 cube-root family is then ap-
parent. Figure 13 shows the 46.1078 km s-l period where a characteristic
staggered phase-deviation pattern appears. A Student's t test, comparing

50

w. G. TIFFT

.,'~••:J~ '" • TCF Sampl.

..... :; .... • \-'1: •• ,. ,

....
1,,'

75 < W < 250 P.46.1078

~I
0-25

-20

·.. 't... ' . ••

• • •~: :~.

~ .~.
•

'~
.: •• I ••

·AllA,SIN>IO T-910
'.

• ",... .. I,..:;a,. •

.. ........ ... . " . I•• , .,

~

:~.

.. . .-e" :. • '~.. ,il-.,: .. •

-IS -10 -5 0 5 10 15 20

~I
0 -5

Deviation crC-FI')

.,:-....

.. ...'.'~~".:.•·•..
...III: •••

. . ..

":. · ..

~
:

•

.'..\0

Deviation CfC86-TC84)

C41 Sample W<125 P-46.1078 All A, SIN > 10 AlIT
10

Figure 13. Phase-deviation diagrams for local dwarf galaxies; a staggered deviation pattern, associated with variability, occurs at the 46.1 km S-l period. The comparison
= between modern redshifts and Fisher-Tully data is shown at left for galaxies with t 9, 10
and 75 < W < 250 km S-l. The pattern continued to develop between 1984 and 1986 as shown for dwarf galaxies with W < 125 km S-l at right. The deviation scale, in km S-l,
is expanded by a factor of 3 in the right frame.

mean deviations in half phase intervals dividing .at .0 and .5, indicates that the segments have only an 0.001 chance of being from the same deviation distribution. One interval shows no deviation; the other deviation is consis-
tent with the 5.7635 km s-1 T = 6 period, a subharmonic of the 46 km s-1
period. This class of objects is interesting since recent observations alone show changes. The right panel of Figure 13 compares galaxies of the same general type using 1984 and 1986 observations. The same periodic wave is present with a low amplitude consistent with the short time interval involved; the change was still in progress in 1984. Evidence for variability is not limited to Fisher-Tully data. Consistent shifts for spirals can also be found in some of the oldest available 21 cm data.
The wide profile galaxies show a strong 5.7635 km S-1 T = 6 periodicity. This is illustrated in Figure 14, first for a restricted class of symmetric
profile galaxies with W > 250 km S-1, then for an unrestricted sample of objects with W > 200 km s-1. A staggered pattern is present with the
negative wing aligned on phase 0.0. The power spectrum of galaxies in the deviation interval from -2 to -8 km s-l peaks at power 17 for P = 5.7631
for the 36 symmetrical profiles, and at power 16.3 for P = 5.7624 for all
64 objects. The period is matched within one-half of one percent of the Pk/Per range in phase with the CBR rest frame.
Sample adjustments have no significant effect on power, period or the CBR association shown at lower right. This pattern is clear in the wide profile Perseus galaxies, and its harmonic in the wide-profile Cancer galax-
ies, where it was used in qo determinations. The short T = 6 periods seem

QUANTIZED REDSHIFTS

51

. .. . ..... ..:. •

: ...
-;

... , , ~·"·r ~

•

TCPSampie
W>250 P.5.7635 -\.1<1.<1.1

. .

o

....••

-25 -20 -15 -10 -5

10 IS 20

-10 -8 -6 -4 -2 0

10

Deviation (TC-FT)

Deviation (TC-FT)

-8 < Dev < -2

-241

-242 16

12
I
Period

-247 -248

-249

""

-2S~3'-:-6'""'-:'_3":-S---=-3-:-4"""-'-_33:--"'---':-""""------"'--,c-::<=c..........:.:L---"'---'------J

Pi

Figure 14. Phase-deviation diagrams, power spectra and power contours for local super-
cluster spirals with wide 21 em profiles. Galaxies with W > 250 km S-1 and symmetric
profiles (upper left) show a staggered pattern of deviations at the 5.76 km S-1 period. This period is common in galaxies with wide 21 cm profiles. Deviations between -8 and -2 km S-1 are aligned on phase 0.0 and achieve a power of 17 (lower left) precisely at the predicted period. When asymmetry restrictions are removed and the W range lowered to 200 km S-1 (upper right) there is no significant change of power or period (dashed line in spectrum). The power peak occurs at the adopted CBR dipole vertex (lower right, see Fig. 5 for axes and symbols)

to be quite common among the wide profile galaxies. The T = 0 family
dominates in galaxies with intermediate profile widths, then longer period
T = 6 periods return among the dwarfs. The extreme dwarfs shift to the
adjacent T = 7 family. Specific classes of galaxies associate with different T
values and dominant period ranges; the T = 0 and T = 6 cube-root families
stand out. Periods are not randomly distributed in T. Table 6 summarizes
the major sets of periods.

8. Relationship Between the CBR and Galactocentric Frames
There seem to be two significant quantization rest frames. To understand this we believe it is necessary to abandon the idea that galaxies move with respect to one another. Such motion for our Galaxy can explain the CBR dipole observation, but combined with similar random motions for other

52

W. G. TIFFT

= TABLE 6. Selected Redshift Periods P c2- 9DtT

D\T

7

6

5

1

0

17

2.2872

16 2.6681 2.8817

4.5745

15 5.3363 5.7635

9.1490

14 10.6725 11.5270

16.9416 18.2979

13

33.8831 36.5958

12

46.1078 49.7992

73.1916

11

92.2157 99.5984

146.3833

10

184.4313

galaxies would destroy global quantization. If we accept quantization we require a non-velocity explanation of the CBR transformation. In the temporal model, described in a separate review, galaxies are quantized structures dispersed, and evolving, in three-dimensional time. The CBR transformation places the observer in the quantized frame associated with 3-d temporal space. We see quantized patterns which depend only on lookback time and the character of the type of galaxies involved.
At the same time we cannot overlook the fact that within our Galaxy we have real spatial motion with respect to the galactic center. When we apply the galactocentric transformation we remove this motion, but this is not sufficient to place us in the quantized temporal frame. As a 3-d temporal object the Galaxy has certain properties; the CBR transformation removes these along with the spatial solar motion. The galactocentric transformation removes only the spatial part. This seems to be sufficient to induce local resonant patterns which appear as strong fluctuations rather than a regular global pattern.
The two transformations appear to be linked; within scatter in local random stellar motions the tangential components are equal and opposite (-243 and +232 km s-l) while the radial terms are the same, (-31 and -36 km s-l). In the temporal model the dynamics of a galaxy may be associated with the temporal structure. The CBR vertex is nearly opposite the galactocentric one in longitude; transformation terms in longitude simply change sign. Given strong tuning in the CBR frame one might expect resonances opposite the longitude of the CBR vertex using only the spatial correction. This is especially true if one examines galaxies with similar characteristics.
Figure 15 (left) takes the sample of local spirals, V < 1000 km s-1,
used by Guthrie and Napier (1991), and refers them to the galactic center

QUANTIZED REDSHIFTS

53

..,. " ,..,~.
'. :-~.

"' .

...... .. . . ... '

; - " 0

0

..~:

,,.,. ! I
IE

:-
"

"'o~~1C"'.0

0
"

,.,

.0 ,.

"

I ....
••1. • •
... ... '. ','
\. ,." '.s.:~~~.

Period • 36.'958 T.O-8 V<IOOO ON Objccta
.

2~~~~~~~~~~~~~

..., :...',..... . -.:".....

.. ..., ·~0I"'0 ·.-".·

II .;:........ " . , ,~O

00

T.'Period = 36.59'8
• N-98 All Te. T o

.. ..... . : .. I' • I' .:~.!
•·•.i.-..'':;:,,,;·.'.:t.~"t".:*.' •".-...•'•

00 100 200 300 400 '00 600 700 800 900 1000

00 100 200 300 400 '00 600 700 800 900 1000

Profile Width

Profile Width

Figu.re 15. Phase-profile width diagrams, in the galactocentric rest frame, for spiral galaxies. The basic 36.6 km S-l period is used; W is in km S-l. The left frame contains a
106 point Guthrie-Napier sample of nearby spirals. These very local objects are periodic
but are heavily dwarf dominated. The right frame contains 98 classical Sc (t = 5) galaxies.
The periodicity is again detectable in specific width intervals, but is not phased with other
= types and shows a distinct change near W 200 km S-l. Such periodicities, much more
regular in the CBR rest frame, may induce strong periodic fluctuations in local galaxy
samples observed in the galactocentric frame.

for the predicted 36.6 km s-1 period. The galaxies are mostly dwarf object but similar enough internally that just the removal of dynamical motion reveals the periodicity. This is also true (right) for all Sc galaxies (t = 5) with recent Tifft-Cocke or Tifft redshifts. These extend further in redshift, show the basic periodicities at 36.6 and 18.3 km 8-1, and the 200 km s-1 profile width transition. They are not in phase with the local dwarf objects, however. Given such periodic clumping any local sample can be far from random in its redshift distribution. A search near the galactic center, or the anti-longitude of the CBR vertex, should detect fluctuations.
A search was carried out using a recent 104 point set of spirals defined by Guthrie and Napier. Figure 16 shows the locations of strong power peaks for an 18.8 km S-1 period related to the Guthrie and Napier findings. A pattern of power peaks is concentrated around the anti-longitude of the CBR dipole vertex (shown as a cross). Our standard galactocentric vertex is shown with an X. Triangles mark strong 37 km s-1 periodicities mapped by Guthrie and Napier (1996). The close proximity of the galactocentric vertex and the CBR anti-longitude point makes it difficult to separate galactic and CBR correlations. All or most galactocentric findings may be traced back to the cosmocentric effect through connections between the transformations.

-

-

-

-

-

-30 u·L.....J.._L-I~-JIL.....-...I...--JIL.....-...I...--JIL.....-~_IL.....-~....J 60 70 80 90 100 110 120
Gal Long
Figure 16. Locations of power peaks, in galactic coordinates, for 104 local supercluster galaxies examined recently by Guthrie and Napier. An X marks the standard galactocentric quantization vertex; the cross and open circle mark points, in the galactic plane, opposite the longitude of the cosmocentric quantization and COBE vertices. Large power
fluctuations (filled symbols) at P = 18.8 km S-l, half of the 37.5 km S-l period studied
by Guthrie and Napier, associate with the anti-CBR point. Power varies from 9 for the smallest symbols to 17 for the largest. They were found in a 106 point search through a velocity cube using a 2 km S-1 resolution. Open symbols identify other periodicities found by Guthrie and Napier. These features occur at frequencies greatly in excess of random expectations and may be local fluctuations induced by a basic cosmocentric pattern.

9. Summary
In 1992 and 1993 redshift quantization was associated with the CBR rest frame, and a model involving 3-d time was developed which permits predictions of global periodicities. Two equations now exist, one linearizes periodicities in z, and the other defines periods. They are:

Vcorr = 4c[(1 +z)1/4 - 1] +...

and

P

=

_9D±T
c2 9 .

(10)

The equations are consistent with a model combining 3-d time with 3d space within which fundamental particle properties at one extreme, and cosmological observations at the other, may be related. The following statements summarize and expand on characteristics introduced in Section 3.

QUANTIZED RED SHIFTS

55

1) Width, redshift range, and profile asymmetry adjustments influence spectral power but do not tune periods. As parameters are varied, power may shift between periods, especially harmonics within one T family, but peaks closely track predicted periods.
1a) Distinct phase shifts within the same period occur near certain profile widths. The shifts involve steps through subharmonics which suggest that redshift transitions occur from time to time. Patterns of offset redshift deviations between different epochs are consistent with such changes.
1b) Redshifts concentrate in absolute phase around simple fractions of the periods. Concentrations are not randomly spread in phase.
2) The pk/per ratio is a measure of the quality of fit to the set of predicted periods. Power peaks concentrate strongly around 1.00 and avoid values near 1.04 midway between predictions. Short periods at high redshifts in-
dicate that qo = 1/2.
3) Certain periods or T values tend to associate with particular morphology and profile width intervals. Four major classes have been identified in local redshift data.
3a) Periods are not distributed randomly in T; two cube root families, T = 0
and 6, dominate. Ninth-root families often associate with the dominant
families, T = 1, 5 and 7 being the most important. Table 6 summarizes
common periods associated with classes of galaxies.
4) Power at predicted periods is maximized when redshifts are transformed to a rest frame close to the COBE CBR vertex. The radial component is slightly more negative than the COBE value. The galactocentric rest frame seems to be intimately related to the CBR frame.

10. Acknowledgements
The author is indebted to John Cocke who was instrumental in the derivation of equation (1) and the pursuit of the CBR connection, and to Ari Lehto for his original work with 3-d temporal concepts, particularly those relating to fundamental particles. Carl DeVito and Anthony Pitucco also contributed ideas which assisted in developing the current 3-d temporal model.

References
Bicay, M. D. and Giovanelli, R.; 1986a, AJ, 91, 705 Bicay, M. D. and Giovanelli, R.: 1986b, AJ, 91, 732 Bicay, M. D. and Giovanelli, R.: 1987, AJ, 93, 1326 Cocke, W. J. and Tifft, W. G.: 1996,Astroph. fj Space Sci., in press

56

W. G. TIFFT

Cocke, W. J., DeVito, C. and Pitucco, A.: 1996, this conference Croasdale, M. R.: 1989, ApJ, 345, 72 Fisher, J. R. and Tully, R. B.: 1981, ApJS, 47, 139 Giovanelli, R. and Haynes, M. P.: 1985, AJ, 90, 2445 Giovanelli, R. and Haynes, M. P.: 1989, AJ, 97, 633 Guthrie, B. N. G. and Napier, W. N.: 1991, MNRAS, 253, 533 Guthrie, B. N. G. and Napier, W. N.: 1996, A&'A, in press Hoffmann, G. L.,Helou, G.,Salpeter, E. E., Glosson, J., Sandage, A.: 1987, ApJS, 63, 247 Lehto, A.: 1990, Chinese J. Phys., 28, 215 Tifft, W. G.: 1978a, ApJ, 221, 449 Tifft, W. G.: 1978b, ApJ, 221, 756 Tifft, W. G.: 1990, ApJS, 73, 603 Tifft, W. G.: 1991, ApJ, 382, 396 Tifft, W. G.: 1995a, Astroph. &' Space Sci., 227, 25 Tifft, W. G.: 1995b, Mercury, 24, 12 Tifft, W. G.: 1996a, this conference Tifft, W. G.: 1996b, ApJ, in press (Sept. 10) Tifft, W. G.: 1997, in preparation Tifft, W. G.,& Cocke, W. J.: 1984, ApJ, 287, 492 Tifft, W. G.,& Cocke, W. J.: 1988, ApJS, 67, 1 Tifft, W. G., Cocke, W. J., & DeVito, C.: 1996, Astroph. &' Space Sci., in press
Tifft, W. G.,& Lehto, A.: 1996, in preparation

TESTING FOR QUANTIZED REDSHIFTS. 1. THE PROJECT
W. M. NAPIER Armagh Observatory College Hill, Armagh BT61 9DG, Northern Ireland AND B. N. G. GUTHRIE 5 Arden Street Edinburgh EH9 lBR, Scotland
Abstract. A project intended to examine the long-standing claims that extragalactic redshifts are periodic or 'quantized' was initiated some years ago at the Royal Observatory, Edinburgh. The approach taken is outlined, and the main conclusions to date are summarized. The existence of a galactocentric redshift quantization is confirmed at a high confidence level.
1. Introduction
Persistent claims have been made over the last 25 years or so that at least some extragalactic redshifts are non- cosmological in origin. Perhaps the least credible of these claims is that the redshifts of galaxies are periodic or 'quantized', tending to occur at intervals of ",72 km S-l within binaries, groups and clusters (Tifft 1976, 1977, 1980; Arp & Sulentic 1985; Arp 1987), with a related global redshift periodicity of ",24 or ",36 km S-l for field galaxies when a suitable correction for the solar motion is made (Tifft & Cocke 1984, hereinafter TC). The quantization claim is extraordinary, and if confirmed would have profound repercussions for cosmology. Given the perceived success of standard paradigms, a correspondingly high standard of proof would be required before the alleged periodicity could be accepted (say at the level where a cosmological model which failed to incorporate it would lack credibility). Testing for the quantization is however a 'clean', well-posed statistical problem, while new high- precision 21 cm redshifts are now available in adequate numbers for confirmation or otherwise of the
Astrophysics and Space Science 244:57-63,1996. © 1996 Kluwer Academic Publishers.

58

W. NAPIER, B. GUTHRIE

claim to be possible. A series of research programmes was therefore initiated at the Royal Observatory, Edinburgh to investigate the issue. Rigorous statistical analysis, utilising power spectrum analysis (PSA), was employed throughout: the pitfalls in the latter, and our means of avoiding them, are described in the companion paper (Paper II). Two pilot studies, involving 48 and 40 high-precision redshifts respectively, yielded positive results, and so were followed by a major analysis involving over 200 spiral galaxies in the Local Supercluster. We summarize herein the progress of this work.

2. The Virgo Cluster
We first examined the distribution of the most accurately measured HI redshifts of galaxies in the region of the nearby Virgo cluster, which had not previously been used in formulating the quantization hypothesis (Guthrie & Napier 1990). We compiled two samples of galaxies within 10° of the central galaxy M87, comprising 112 bright spirals and 77 dwarf irregulars. Their heliocentric redshifts cz are <3000 km S-l (the upper limit for the cluster) and have stated accuracies of ±1O km s-l or better.
We first tested each sample for the existence of a redshift periodicity somewhere in the range 70-75 km s-l , in accordance with the original claim made by Tifft (1976). No significant periodicity in this range was found for either sample of heliocentric redshifts. However, when the individual redshifts were corrected for the estimated solar motion with respect to the centroid of the Local Group [V0=252 km s-l towards (l0, b0 )=(100°, 0°)], a possible periodicity of ",71.3 km S-l emerged for the sample of 112 spirals. The periodicity appeared to be stronger for the 56 outer spirals at 5°-10° from M87. Accordingly, a sub-sample of 48 spirals in low-density regions of the cluster was compiled from a chart of bright galaxies in the region, the criterion for low density being adjusted to maximize the periodicity signal. Taking account of the number of independent trials involved in testing the period range 70-75 km s-l and the number of trials used in selecting the optimum criterion for low density, we found that the periodicity (71.1 km s-l) was significant at a confidence level 0.997;S C;S 0.999.
Since the Virgo cluster covers only a small area of sky, the differential correction for the solar motion is small and the exact choice of solar vector is not critical. When the apex was varied over the whole sky, it was found that the periodicity appeared most strongly for correcting vectors
(l0, b0 )=(98°, 60°) and (101 0, -30°); the previously adopted apex (100°,0°)
lies on a north-south ridge encompassing these twin peaks (see figure 8 in Guthrie & Napier 1990). The significance of the peaks was assessed by comparison with 60 whole-sky maps constructed for sets of 48 synthetic, random redshifts with the same overall distribution in space and redshift as

TESTING REDSHIFTS I

59

the real data. These non-periodic datasets failed to reproduce the observed
power contours, and periodicity was preferred over chance at a confidence level 0.996;S C;S 0.999. For the real data, whole-sky maps for other solar speeds between 150 and 300 km s-l yielded broadly similar results, the twin peaks and ridge (and therefore the underlying periodicity which generates them) being significantly stronger for V0 ~200 km S-l .

3. Nearby Field Galaxies
For our second pilot study (Guthrie & Napier 1991) we compiled samples of nearby field galaxies (corrected redshifts <1000 km s-l) to test the TC hypothesis of a global periodicity of ",24 or ",36 km S-l . Since these periods are small, high redshift accuracy is very important. Redshifts with listed standard errors O"cz;S 4 km s-l were taken from the extragalactic HI database compiled by Bottinelli et al. (1990). Excluding galaxies in the region of the Virgo cluster, we had 106 spirals and 62 irregulars. Eliminating also the galaxies previously used by TC, we obtained an independent sample of 89 spirals of which 40 had redshift errors O"cz ~3 km s-l .
The heliocentric redshifts of the 89 spirals were individually corrected for the solar vector found by TC (233.6 km s-l, 98.°6, 0.°2), and a preliminary PSA was applied to the corrected redshifts to search for periodicities in the range 20-200 km s-l . A prominent peak was found at P=37.1 km S-l, close to the periodicity of 36.3 km s-l claimed by TC for galaxies with broad HI line profiles, but there was no evidence for the periodicity of 24.2 km s-l claimed for narrow-line galaxies. The significance of the peak at 37.1 km s-l was assessed by Monte Carlo trials: synthetic datasets were constructed by adding to each of the 89 redshifts a random displacement in the range 0-60 km S-l as well as the correction for the TC solar vector. Thus all the essential features of the real dataset were preserved except for the local redshifts. PSA of 3 000 synthetic datasets showed that the probability of obtaining a periodicity of the observed strength in the range 70-75 km S-l or one of the submultiple ranges 23.3-25 and 35-37.5 km s-l by chance in a single trial is ",0.003. Thus the TC hypothesis of redshift periodicity is preferred over the null hypothesis of a random redshift distribution at a confidence level C ",0.997. No significant periodicity was found for the uncorrected, heliocentric redshifts.
There is inevitably some uncertainty in the solar vector found by TC by maximizing the periodicity signal, but it is fairly close to estimates of the solar motion around the Galactic centre. We therefore tested a wide range of vectors around the solar motions relative to the Galactic centre and the centroid of the Local Group, and found two strong peaks at P = 37.2 and 37.5 km s-l respectively, both close to the adopted galactocentric solar

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motion. Taking account of the proximity of these peaks to this latter vector, and noting that the periodicities were stronger for the 40 spirals with (fez ~3 km s-l than for the other 49 'less accurate' spirals (as would be expected for a real phenomenon), the overall probabilities of chance coincidence were found to be '" 3 x 10-5 for the 37.2 km s-l periodicity and '" 1 x 10-4 for the 37.5 km s-l one. On the other hand, no significant periodicities were found for the sample of 62 irregular galaxies.

4. The Local Supercluster
Our two pilot studies raised a number of questions. In particular the existence of multiple peaks clearly complicated the matter of determining the unique solar vector (if such existed) for which the periodicity was seen most strongly. Trials with synthetic data revealed that a single redshift periodicity, for a specific solar vector V 0, yielded a plethora of ghost peaks or side lobes for many V 0, some far from the genuine one. Thus while the existence of a periodicity might readily be inferred, it was not always easy to discriminate the 'true' peak from the 'ghosts' in a velocity map. Further, our derived probabilities were obtained in part from the proximity (in velocity space) of individual high peaks to the galactocentric solar vector derived from Galactic HI data. They were thus an example of extreme value statistics, and sensitive to uncertainties in the true V 0'
On the other hand, these preliminary analyses also yielded positive results: periodicities were observed in the independent datasets, at reasonably high confidence levels, close to the (P, V 0) values previously claimed. We therefore undertook a much more extensive analysis involving over 200 galaxies out to the edge ofthe Local Supercluster (Guthrie & Napier 1996). We employed a more robust statistical procedure, for example using the overall power in a volume of (P, V 0) space as a statistic rather than the height of individual high peaks; we used pattern-matching of peaks obtained from synthetic datasets to find the 'true' vector corresponding to the periodicity; and we compared with the recent estimate of the galactocentric solar vector due to Merrifield (1992). Various tests for robustness (partitioning of data, sub-division by radio telescope and so on) were also applied. This study is reported elsewhere in these proceedings and is only summarised here.
First, we compiled a list of 97 spirals with corrected redshifts <2600 km 8-1 and (fez ~3 km s-l , not previously used by TC. The overall power distribution in (P, V 0) space was found and compared with distributions obtained from properly constructed synthetic datasets. We found that, when corrected for related vectors close to recent estimates of the Sun's galactocentric motion, the redshifts are strongly periodic (P ~37.6 km S-l).

TESTING REDSHIFTS I

61

Thus the basic hypothesis of redshift quantization is confirmed at an extremely high formal confidence level. However we also found evidence that the intrinsic strength of the global periodicity slowly weakens with distance from the Sun, while remaining strong for galaxies linked by group membership. Thus while the above trials establish that the hypothesis 'redshifts are periodic' is strongly preferred over the hypothesis 'they are not', the evidence may also indicate that the periodicity is strongest for adjacent galaxies but weakens as their separation increases (as would happen, for example, with an imperfectly coherent wave). This of course represents a significant modification of the original hypothesis, and in accordance with orthodox statistical procedure it was tested against a further sample. The latter comprised 117 spirals for which HI profiles with signal-to-noise ra-
tios >10 had been obtained with the 300-foot Green Bank telescope; these
galaxies have a higher mean redshift than the 97 and are more widely separated. The new sample indeed provided only weak evidence for a periodicity consistent with that found for the 97 spirals; the additional group-linked galaxies in the combined samples, on the other hand, were found to have a very strong galactocentric redshift periodicity of ",38 km S-l. The differential redshifts of the group-linked galaxies in the combined samples exhibit an extremely strong periodicity which is virtually impossible to ascribe to chance (Fig. 1). For both the Virgo cluster and the field samples, the vector with respect to which the periodicity holds was found to lie within the error box of the solar galactocentric motion. The hypothesis we tested was, however, limited and specific, and we cannot exclude the possibility that other vectors (such as the COBE one) and periodicities may exist for other samples, as claimed by Tifft (1996) in recent work.

5. Discussion and Conclusions
In physics, observation and reproducibility are as important as formal statistical verification. In treating the quantized redshift question purely as an exercise in statistics, there is a risk of obscuring the fact that the periodicity is easily seen by eye. This is particularly so in the case of high-precision differential redshifts within groups (Fig. 1). In general, the more precisely the redshifts are measured, the stronger the effect is seen to be; conversely, it vanishes rapidly as the precision of the redshifts employed degrades. Likewise as the size of the samples increases, so also does the strength of the imbedded signal, while the correcting vector holds with remarkable stability. Simulations reveal this behaviour to be consistent with those of a real periodicity at a quantitative level. The galactocentric nature of the periodicity in the samples studied so far is difficult to reconcile with an artefact, which would of course create a spurious periodicity in the frame of reference

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o

OCZcorr (kill s-I)

400

Figure 1. Distribution of weighted differential redshifts for 80 galaxies linked by group membership in the combined samples of 115 and 117 Local Supercluster galaxies (Paper II). The {) cz have been corrected for the galactocentric solar vector V (') = (213 km S-1 , 93°,2°) obtained from Galactic modelling, but as the correction is differential the precise value of V (') is not critical. The vertical dotted lines represent, not the best fit, but the solution obtained from the earlier pilot study (period 37.5 km S-1 , phase 0 km S-1 ). A Parzen smoothing has been applied.

of the observer, not the Galactic centre!
The periodicity can be seen in the data of several papers but, presumably because it is so unexpected, it is generally overlooked. As one recent example, Karachentsev & Makarov (1996) have determined a running apex for the Sun, Galaxy and Local Group with increasing volume out to 8 Mpc around the Sun; this study involves 103 galaxies with cz <500 km s-1 . They find the peculiar velocity dispersion of their sample to be remarkably constant, at ",,72 km s-1, independently of the volume sampled or the galaxy type (dwarf or giant). However such behaviour is clearly nonGaussian, since in the Gaussian case the dispersion of the peculiar velocities
should vary as 0.7J-l/ /ii, yielding an expected 72±5 km s-1 at 8 Mpc (103
galaxies), 72±7 at 3.25 Mpc (50 galaxies) and 72±12 km s-1 at 0.7 Mpc (16 galaxies). An examination of the redshift residuals reveals that they are indeed non-Gaussian, clustering around values of "" ±36, f'V ±75 and f'V ±114 km s-1 .
To sum up, over the range of redshifts tested, the redshift quantization has been consistently and reproducibly observed in all data sufficiently accurate to reveal it: our statistical analysis merely formalizes an empirical result.

TESTING REDSHIFTS I

63

WMN wishes to thank Bill Tifft and the Pima Community College for their invitation to attend the conference, and their hospitality and support during it.

References
Arp, H.: 1987, l. Astroph. Astron., 8, 241 Arp, H. & Sulentic, J. W.: 1985, Apl, 291, 88 Bottinelli, L., Gouguenheim, L., Fouque, P. & Paturel, G.: 1990, ACiA Suppl., 82, 391 Guthrie, B. N. G. & Napier, W. M.: 1990, MNRAS, 243, 431 Guthrie, B. N. G. & Napier, W. M.: 1991, MNRAS, 253, 533 Guthrie, B. N. G. & Napier, W. M.: 1996, AClA, 310, 353 Karachentsev, 1. D. & Makarov, D. A.: 1996, Al, 111, 794 Merrifield, M. R.: 1992, Al, 103, 1552 Tifft, W.G.: 1976, Apl, 206, 38 Tifft, W.G.: 1977, Apl, 211, 31 Tifft, W.G.: 1980, Apl, 236, 70 Tifft, W.G.: 1996, Apl, 468, 491 Tifft, W.G. & Cocke. W.J.: 1984, Apl, 287, 492 (TC)

THE DISTRIBUTION OF GALAXY PAIR REDSHIFTS
T. E. NORDGREN, Y. TERZIAN AND E. E. SALPETER
Cornell University Ithaca, New York 14853
Abstract. High signal to noise neutral hydrogen observations of a complete sample of 132 galaxy pairs show a velocity difference distribution which decreases monotonically from zero. There is no strong indication of redshift periodicity for the entire sample and no indication at all for a subset of 79 isolated galaxy pairs. In addition, when redshifts are corrected for the solar motion around the Galactic Center there is no indication of a redshift periodicity of 37.6 km s-lin .6.Vfor galaxy pairs (as suggested by Guthrie and Napier 1996).
1. Introduction
Work on galaxy pairs at 21 cm first began at Cornell with Peterson (Peterson 1979) who used the 300 ft Green Bank radio telescope to study a sample of 279 galaxy pairs. The aim of this work was primarily to determine mass to luminosity ratios and to search for extended halos. This work was continued by Schneider (Schneider et a1.1986) who extended the observations to small groups. Since much of the information derived from the study of galaxies in groups and pairs is statistical in nature, the validity of the results is only as good as the sample from which they are drawn.
Starting in 1990 a method was developed by Chengalur (Chengalur et al.1993) whereby galaxy pairs are chosen in a predetermined and systematic way from published optical redshift catalogs. Through the use of redshift information in the CfA catalog (Huchra et al.1983) and the Southern Sky Redshift Survey (da Costa 1988) galaxy pair candidates can be found solely on the basis of proximity in projected separation and velocity. Unlike in previous studies, no consideration is needed, or given, to choosing pairs on the basis of Rimilar magnitude and angular separation being less than an
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arbitrary multiple of the diameter (Peterson 1979, Schneider et al.1986). In addition, by counting the number of galaxies in a truncated cone (with a base radius of 4.5 Mpc and depth of 335 km s-1) about each galaxy in a catalog, galaxies can be separated or classified by the number density of galaxies around them (Chengalur et al.1993). Chengalur divided the galaxies in the catalogs into quartiles (i.e the number density below which one quarter of all the galaxies in the catalog can be found corresponds to the first quartile, the median number density corresponds to the upper limit of the second quartile, etc.). The information in redshift catalogs makes possible the evaluation of environmental effects on any derived galaxy pair sample.
Previous HI galaxy pair surveys using single dish telescopes have avoided pairs with separations small enough to cause confusion of the 21 cm lines (Chengalur 1994, Tifft & Cocke 1989). For the Green Bank 300 ft telescope (for example) all galaxy pairs with separations smaller than the beam FWHM of ""lO'will be excluded from the sample. In order to remove this selection bias from the current study, use is made of the high spatial resolution of aperture synthesis telescopes such as the Very Large Array. The pairs in this study are therefore made up of a close pair sample which has been imaged in HI using synthesis arrays, and a wide pair sample which has been observed using traditional single dish 21 cm techniques.
Nordgren et al.(1996) have completed the observation of all the pairs in the Chengalur wide and close pairs sample. In addition, observations were conducted at the VLA, Australia Telescope Compact Array and Westerbork Synthesis Radio Telescope which allow for comparison between close galaxy pairs in the lower two quartiles with pairs in higher quartiles.

2. The Close Pair Survey
The close galaxy pairs of the combined Chengalur-Nordgren database were determined by the following selection criteria:
1) To be a pair, each galaxy must have an independent listing in the redshift catalog. A galaxy pair in the very latest stage of merger which may only have one redshift listing will therefore not be included in this sample.
2) At least one member of the galaxy pair must have a number density of surrounding galaxies within the lower two quartiles.
3) Both galaxies in the pair must have redshifts between 1100 km 8-1 and 4500 km S-1 for the CfA (or 5300 km s-1for the SSRS). The lower velocity bound insures that no galaxies from the Virgo Cluster are included within our sample. For a magnitude or diameter limited survey, the incompleteness of the catalog is a function of redshift (Charlton & Salpeter 1991,

GALAXY PAIR REDSHIFTS

67

Chengalur et al.1993 and Chengalur 1994). The upper velocity limit insures that the catalog is complete to ten percent (Chengalur 1994).
4) In order to maximize the likelihood of detecting sufficient HI, both galaxies must be of type Sa or later.
5) The projected separation (rp) must be less than 75 kpc (100 kpc for the SSRS).
6) The velocity difference (.6.V) must be less than 200 km s-l. 7) No third galaxy within 1.0 Mpc or 400 km s-l. 8) In order to insure detectable amounts of HI, the published integrated HI sum for the pair must be greater than 10 Jy km S-l. (This requirement was relaxed for the SSRS due to the fewer number of galaxies for which there was published HI information). In order to test the effect of environment on close galaxy pairs an additional sample has been observed where: 1) The restriction to pair members having densities in the lower two quartiles has been relaxed to allow for galaxies with densities in the third quartile. 2) rpcan be as great as 100 kpc. 3) .6.Vcan be as great as 300 km S-l. 4) The restriction to no neighbors within 1.0 Mpc and 400 km s- l has been removed.

3. The Wide Pair Survey
The wide galaxy pairs of the combined Chengalur-Nordgren database were determined by the following selection criteria:
1) Each galaxy must have an independent listing in the redshift catalog. 2) At least one member of the galaxy pair must have a number density of surrounding galaxies in the lower two quartiles. 3) Both galaxies in the pair must have redshifts between 1100 km s-l and 4500 km s-l for the CfA (or 5300 km s-l for the SSRS). 4) Both galaxies must be of type Sa or later. 5) The projected separation (rp) must be less than 1.5 Mpc. 6) The velocity difference (.6.V) must be less than 250 km s-l. In order to account for the limited declination range of the Arecibo telescope, the declination of both galaxies in the efA must be between OOand 40°. Only limited observing time was available for observations at Parkes. Two further constraints were therefore placed on the SSRS wide paIrs: 7) rpmust be less than 1.0 Mpc unless either galaxy member has a surrounding number density in the lowest density quartile, in which case rpcan be as large as 1.5 Mpc.

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8) A declination range of -200to -64.5°is imposed for those galaxies with surrounding number densities in the second quartile.

4. Observations
Observations were conducted using six telescopes from around the world (Table 1). 115 galaxies were observed using the Arecibo radio telescope while 81 galaxies were observed using the Parkes radio telescope. Due to the limited observing time available at Parkes, HI velocities from the literature were used whenever available. HI velocities for an additional 51 galaxies were obtained in this way. In total, neutral hydrogen was detected in 132 pairs (25 close pairs and 107 wide pairs). Table 1 lists the telescope, the minimum angular beam size (FWHM), the mean uncertainty in the derived 21 cm velocity and the number of pairs detected.

TABLE l. Telescope observations

Tel.

()

a(km S-1 ) Num. Pairs

Arecibo 3'

4

48

ATCA 3D"

5

9

Parkes 14'

7

58

VLAC 3D"

5

6

VLAD 45"

5

8

WSRT 3D"

5

2

Spectra for many of the wide pair galaxies have already been published (Chengalur et al.1993). Analyses of the close pair HI "moment-maps" can be found in Chengalur et al.1994 and Nordgren et al.1996.
5. Statistical Analysis
If galaxy pairs truly have some arbitrary range of real three-dimensional velocity differences, then randomly orienting them in the sky relative to the observer will produce a histogram of their redshift differences which is maximum at zero and decreases monotonically with increasing velocity difference. This can be easily seen by noting that a galaxy pair with a particular true velocity difference will, depending on its orientation to the observer, always be seen to have a velocity difference between zero and its true difference. Whatever the true velocity of a pair, oriented properly, it will always be able to be viewed as having a velocity difference of zero. In the past, histograms of .6.Vfor samples galaxy pairs have not demonstrated this

GALAXY PAIR RED SHIFTS

69

trend (Tifft & Cocke 1989, Schneider & Salpeter 1992, Figure 4.2 Chengalur 1994). Although the distribution is seen to be maximum at zero there is a second peak near 70 km s-1. The motivation for including potential pairs with separations as large as 1.5 Mpc in the Chengalur-Nordgren sample is to address the hypothesis that the secondary peak in the AVdistribution (and all non-zero velocity peaks) is the result of a selection bias in previous samples. If wide galaxy pairs tend to be on radial orbits (Schneider & Salpeter 1992) then by excluding the very widest pairs from a sample one will exclude a set of galaxies with potentially very small velocity differences. The suppression of this population of galaxy pairs could result in a non-zero peak in the distribution of AV.
Figure 1a shows the histogram of heliocentric AVfor the entire sample of 132 galaxy pairs. Bin widths are chosen to be 20 km s-1in width which is larger than the uncertainty in any individual HI measurement. Although the distribution of AVdecreases rapidly from zero as velocity difference increases their are still non-zero peaks present. If the fluctuation in the number of pairs per bin is indicative of Poisson statistics then the uncertainty in the bins surrounding and including the non-zero peaks in Figure 1a is on the order of 4 pairs each. This uncertainty is comparable to the difference in counts between bins surrounding the non-zero peaks, and thus the observed distribution of AVis consistent with a monotonic function.
To investigate the effect of neighboring galaxies on the distribution of AV, we define a galaxy pair as being isolated if there is no other galaxy within 750 kpc and 250 km s-1 0 f at least one member of the pair. Figure 1b shows the observed velocity difference for this new set of 81 pairs. The shaded histogram is the sample of 81 isolated galaxy pairs. For comparison, the total sample of 132 galaxy pairs is shown in white. There is no longer any indication of a periodicity in the distribution of D.V. With the exception of the second bin being higher than the first by only one pair the distribution of observed velocity differences monotonically decreases from zero velocity.

6. Galactocentric Velocities
Guthrie and Napier (1996) observe a 37.6 km s-1periodicity in HI redshifts of spiral galaxies once heliocentric velocities have been corrected using a vector which is close to the Sun's galactocentric motion. In order to test the claim of periodicity we follow the prescription of Guthrie and Napier and use their solar vector of 10 = 96°, b0 =-3°and V0 = 210 km s-1to apply this galactocentric correction to the galaxies in the Chengalur-Nordgren sample. We will refer to velocities which have been corrected in this manner has being galactocentric. Due to the small size of the reported velocity period it is important to have velocity measurements of high precision (Guthrie &

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T . E.NORDGREN ET. AL.

27

27

2.

2.

21 18 15

.· 21 18
. 15

12

"0
·e 12
· z

18 12

15

..i•i 9

~ 12

·e·
z

"0
· e
· z

Figure 1. The distribution of velocity differences for the Chengaiur-Nordgren galaxy pair sample. Figure (a) is for the full sample of 132 pairs. Figure (b) shows the full sample in white with the subset of isolated pairs shaded. Figure (c) is the wrapped distribution of 66 pairs where the velocities are now galactocentric. Figure (d) is the same sample wrapped over the range 0 to I8.8km S-l. The dashed line is the mean of the five bins.
Napier 1996). To be certain of the quality of the HI velocities, we have used only those pairs where both galaxies were observed as part of the current study (i.e. no pairs were used where one galaxy measurement was quoted from the literature). This requirement resulted in a sample of 66 galaxy pairs being transformed into a galactocentric velocity reference system. Figure 1c shows the ~Vdistribution for the galactocentric pairs where the velocities have been wrapped over the range 0 to 37.6 km s-l(e.g a galaxy pair with ~V= 38.6 km s-lwill be binned as if it were 1.0 km s-l, while a pair with t1V= 74.2 km s-1 will be binned as if it were 36.6 km s-1). Each bin is 3.76 km s-lwide. A periodicity of 37.6 km s-lwill manifest itself as a peak at zero and a peak at 37.6 km S-l. The peak at zero velocity observed in Figure 1c can be explained as the natural peak of the overall distribution

GALAXY PAIR RED SHIFTS

71

at zero velocity. There is no corresponding increase at 37.6 km s-l. Figure 1d is the same sample wrapped over the range zero to 1/2 the periodicity. Each bin is 3.76 km s- lwide. A periodicity of 37.6 km s- lwill manifest itself as a peak at zero with a depression at 18.8 km s-l. The dashed line is the mean number of pairs in the five bins: 13.2 pairs. There is no indication of a 37.6 km s-l periodicity.

7. Summary
In order to minimize the effect of selection biases on the analysis of galaxy pair statistics we are engaged in a program of systematically compiling a complete sample of galaxy pairs. We have therefore created a database which includes the very closest galaxy pairs observed with aperture synthesis telescopes as well as the potentially very widest pairs out to separations of 1.5 Mpc. The observed velocity difference distribution for this sample decreases rapidly with increasing velocity and is monotonic well within the uncertainties in each bin. The distribution of DoVis therefore consistent with that produced by a randomly oriented sample of galaxy pairs. There is no indication in the full sample of pairs of statistically significant peaks at a periodicity around 70 km s-l. Nor is there any indication at all for the isolated subset of any peaks in the distribution other than at low DoV. Finally, no indication is seen of any 37.6 km s-lperiodicity for galaxy pairs transformed to a galactocentric velocity reference.

8. Acknowledgements
This work was supported in part by the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation.

References
Charlton, J. and Salpeter, E. E.: 1991, ApJ, 375, 517 Chengalur, J. N.: 1994, PhD thesis, Cornell University Chengalur, J. N., Salpeter, E. E., Terzian, Y.: 1993, ApJ, 419, 30 Chengalur, J. N., Sa1peter, E. E., Terzian, Y.: 1994, AJ, 107, 1984 da Costa, L. N., Pellegrini, P. S., Sargent, W. L. W., Tonry, J., Davis, M., Meiksin, A.,
Latham, D. W., Menzies, J. W., Couson, I. A.: 1988, ApJ, 327, 544 Guthrie, B. N. G. and Napier, W. M.:1996, A&A, in press Huchra, J. P., Davis, M., Latham, D. W., Tonry, J.: 1983, ApJ Supp, 52, 89 Nordgren, T. E., Chengalur J. N., Salpeter, E. E., Terzian, Y.: 1996, in preparation Peterson, S.: 1979, ApJ, 232, 20 Schneider, S. E., Helou, G., Salpeter, E. E., Terzian, Y.: 1986, AJ, 92, 742 Schneider, S. E. and Salpeter, E. E.: 1992, ApJ, 385, 32. Tifft, W. G. and Cocke, W. J.: 1989, ApJ, 336, 128

TWO UNIVERSES
G. BURBIDGE Center for Astrophysics and Space Sciences and Dept. of Physics University of California, San Diego La Jolla, California 92093-0424
Abstract. The community of astrophysicists see the universe in two different ways. Most of them believe that the evidence points to a hot big bang universe. The minority, largely represented at this meeting, believe that if proper weight is given to all of the observational evidence, rather than only a part of it, a very different model of the universe is indicated. Here I summarize that part of the evidence ignored by the majority, which shows (a) that not all redshifts are due to expansion, and (b) that galaxies and other coherent objects probably did not form from the condensation of diffuse gas.
1. Introduction
We all live in one universe, but we see it through two very different pairs of spectacles. Thus, we are really talking about two universes. I shall call them A and B. Almost everyone at this meeting sees it one way (B) and the bulk of the astronomers who attend almost any other meeting on cosmology and extragalactic astronomy (say the Princeton meeting held in June 1996) see it the other way (A).
What are the major differences between the two positions? There is one overriding effect which separates the two positions. Observational results which are not easily explained by conventional ideas are disregarded or claimed not to be correct by those in the majority position (A), but they are taken seriously by those in the minority (B). If this occurred on a small scale, it would be considered natural, since many early observational or experimental results in physical science are initially questioned if theory has not already predicted them. However, in
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the present situation we are dealing with something on a much larger scale which has built up over some thirty years or more.

2. Universe A
Since the fundamental work of Hubble and Humason on galaxies which started in the 1920s, and which was based on the earlier observations made by V. M. Slipher, the redshifts were interpreted using Friedmann and Lemaitre's solutions to Einstein's equations as showing that we live in an expanding universe. From about 1930 on, this view was generally accepted.
While it was speculated at early times by a minority that the redshift might not be due to the expansion of the space-time metric, it took more than 60 years for an observational test to be carried out which showed that the bulk of the shift for normal galaxies is an expansion shift and is not due to other causes. Time reversal of such a universe would lead to contraction to an exceedingly small volume. Thus the concept which has become widely held is that the universe has expanded from a very small volume "the primeval atom" of Lemaitre and, the "Big Bang" in the common parlance today.
From the 1930s on this model was generally accepted but no physics was put in. Starting in the 1940s attempts were made to understand how all of the chemical elements could have been made from fundamental particles at such an early stage. Gamow, and Alpher and Herman showed that deuterium and helium could be built in an early universe, but it was impossible to build elements beyond mass 5 (which is not stable). Starting in 1946, Hoyle proposed that the heavier elements were built in the interior of stars, and in a series of investigations culminating in 1957 Cameron, and Burbidge, Burbidge, Fowler and Hoyle (1957) showed that all of the elements beyond helium, together with some helium, were built in stellar interiors (we are neglecting here Li, Be and B, whose origin is probably in cosmic rays, etc.).
In the course of their studies of the physics of the early universe, Gamow and his colleagues realized that with an expanding cloud of protons, neutrons, electrons, positrons and neutrinos, there would also be a hot ball of radiation which would cool as a black body as the universe expanded. They estimated that its temperature would be 5-10° K at the present epoch, but they did not consider the possibility of detecting it.
Had the connection been made, it would have been clear that the observations of McKellar (1941) and his colleagues on the interstellar CN, CH, and CH+ molecules already suggested that a microwave background flux must be present with an intensity such that T ::s; 3° K. Also it had become

TWO UNIVERSES

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clear that to attain the observed helium abundance from hydrogen burning in stars, it was required that there be a radiation field produced either by galaxies at an earlier stage in their evolution, or in an early universe (cf Bondi, Gold and Hoyle 1955; Burbidge 1958), and that the temperature of this radiation if it were transformed into black body radiation would be about 2.7° K, though this was not specifically stated by either Bondi et.al. or Burbidge.
In the early 1960s, Robert Dicke with the Princeton group traveled again along the road laid out by Gamow et.al., but went further and started looking for the black body radiation, on the assumption that there was a big bang. Also calculations of the D, He3 and He4 produced in a big bang were made (Hoyle and Tayler 1964, Peebles 1966, Wagoner, Fowler and Hoyle 1967). With the discovery by Penzias and Wilson (1965) of the microwave background radiation, and confirmation of its black body form (cf COBE 1990) it was concluded that we have a strong observational basis for the belief in the hot big bang model.
Galaxies in this scheme must have formed from the collapse of higher than average density fluctuations which are invoked ad hoc in this model. Thus all of the phenomena involving discrete objects - galaxies, and QSOs, and anything else that is found, must be attributed to the evolution of the density fluctuations as a function of time and space.
The discovery of phenomena which imply that not everything can be traced back to evolution and gravitational interaction, means that this picture is either incomplete or just plain wrong.
Above all, it is necessary to argue that apart from the small effect due to peculiar motions of galaxies ~ 300 km S-l, and the random motions expected in groups and clusters, the whole of the observed redshifts are expansion shifts. The belief that all of the groups and clusters have characteristic ages corresponding to the age of the universe leads to a general belief that for all such systems the virial theorm holds, and it is this argument which forms one of the observational bases for the belief in the large scale existence of dark matter.
To summarize, believers in category A (most astronomers) require that
(i) Almost all of the redshifts of all extragalactic objects are due to the expansion of the universe. Their distances can be determined from the redshifts.
(ii) The universe began in a hot big bang which already contained the seeds of galaxies.
(iii) All groups and clusters are bound so large amounts of dark matter are present.

172

G. BURBIDGE

3. The Universe B
There have been a number of observational discoveries, many of which are being discussed at this meeting, which if accepted contradict (i) a part of (ii) and (iii). It is these which force us toward viewpoint B. We discuss the evidence under several headings.

3.1. EXPANSION PHENOMENA IN GALAXIES AND IN GROUPS AND CLUSTERS
Forty years ago Ambartsumian (1958 and other references) by analogy with expanding associations of 0 and B stars argued that the evidence was growing that there were expanding associations of galaxies. He was particularly intrigued by early work on compact groups like Stephan's Quintet, Seyfert's Sextet, and VV 172 each of which has one member with a highly discrepant redshift. We now know that out of 100 compact groups cataloged by Hickson nearly 40% have one member with a discrepant redshift greater than 1000 km s-1 from the mean of the others. Many attempts have been made to explain this phenomenon as due to statistical accidents - but they fail.
This suggests that some galaxies have quite significant intrinsic redshift components, or that very high speeds of ejection are present in some cases (both discrepant redshifts and blueshifts are present).
Even if the galaxy with a discrepant redshift is ignored the remaining group is a problem for the conventional view. This is because the groups are so small that the crossing times are'" 2 x 108 years and the ratio of galaxy diameters to size of the group is such that there would be many inelastic collisions if the group were as old as 1010 years; i.e. the group members should not exist as separate dynamical systems.
In some cases, the X-ray flux from hot gas shows that much dark matter must be present, but that does not solve the dynamical or timescale problems. In large clusters also it is well known that the kinetic energy of the visible matter is much greater than the potential energy and this is usually interpreted, applying the virial expression, as evidence of the presence of dark matter. In clusters which from their form and regularity are clearly relaxed, this is appropriate but in many systems, e.g. the Virgo cluster and the Hercules cluster. it is clear that they are far from being relaxed.
There are two ways of interpreting these results. The first is to argue with Ambartzumian that these systems are all coming apart. This is the case if we attribute the whole of this redshift dispersion in the group or cluster to the Doppler effect. The consequences of this is to conclude that the systems are much younger than'" 2/3Ho • Thus the conventional view of galaxy formation cannot be correct.

TWO UNIVERSES

173

The alternative explanation is to suppose that part of the differential redshift is due to an intrinsic component so the actual velocity dispersion which determines the crossing times and the amount of dark matter (through the virial theorem) is significantly reduced.

3.2. ANOMALOUS REDSHIFTS IN QSOS AND RELATED OBJECTS
Since about 1967 extensive evidence has been found which shows that many QSOs with large redshifts are physically associated with galaxies with low redshifts. This work has been extensively described by Arp and his collaborators and by Burbidge et.al. in a series of papers (cf Arp 1987, Burbidge 1996, Hoyle and Burbidge 1996, Burbidge et.al. 1990 for many references). The evidence involves a few cases where there are luminous connections between low redshift galaxies and high redshift QSOs, many statistical samples, and many geometrical configurations which strongly suggest that QSOs are ejected from the galaxies. If Zo is the observed redshift, Zc is the cosmological redshift, Zd is the Doppler (velocity) component of the redshift and Zi is the intrinsic redshift component

For nearby galaxies with Zc ~ 0.02, and close QSOs, Zo ~ Zi but there are some associations involving fainter galaxies where Zc 2:: 0.2.
There is also a correlation between the QSO-galaxy angular separation and the distance of the galaxy, of the form Od ~ constant. (Burbidge, Strittmatter and O'Dell 1972; Burbidge et.al. 1990). Also some QSOs have redshifts approximately equal to the companion galaxies. Thus sometimes O. Zi f',.J
The existence of finite Zi in many QSOs must be due to something intrinsic to the QSO. It means that all distances derived from the Hubble relation for QSOs are highly suspect. The intrinsic redshift cannot be a Doppler shift (cf Burbidge and Burbidge 1967) because we see no blueshifts - which would dominate. Thus there is hard evidence of intrinsic redshifts in a special class of objects which are dominated by a non-thermal process; Zi can range from 0 to f',.J 3 at least.
3.3. EJECTION OF COHERENT OBJECTS
The geometric configurations in many galaxies and ejected QSOs and other systems (e.g. NGC 4258 and the QSOs aligned across it) - (cf Burbidge 1995), and M84 lying in exactly the same position angle as the non-thermal jet coming from the center of M87 (Wade 1960), show clearly that coherent objects with masses up to those of galaxies can be ejected from parent galaxies.

174

G. BURBIDGE

Of course this suggests that galaxies and related objects have a very different origin from that believed by those who subscribe to A.

3.4. QUANTIZED REDSHIFTS
The existence of quantized redshifts as an observational fact is now well established. It has been discussed extensively here.
(a) Normal Galaxies
Starting more than 20 years ago Tifft (1976) showed that the differential redshifts of galaxies in the Coma cluster showed distinct periodicities with a value of ~cz '" 72 km s-1. These results were confirmed by Weedman and over the years the phenomenon has been found in pairs of galaxies (Tifft and Cocke 1989) and in the redshift differences between satellite galaxies and the central galaxies in small groups (cf Arp and Sulentic 1985). Tifft (1995, 1996) has extended the work to the global scale, and Guthrie and Napier (1996) have confirmed that these quantized effects, with ~cz ~ 37 km S-1 are found in accurate observed redshifts of normal galaxies within the local supercluster.
In addition to this, there is growing evidence from pencil beam surveys of faint galaxies that a periodicity with a large value ~cz = 12800 km s-1 is also present (Broadhurst et.al. 1990). Arp (1987) has also shown that in a few cases intrinsic redshift components with c~z up to '" 10000 km s-1 are present.
(b) Quasi-Stellar Objects and Related Objects
In 1968, it was first shown that the redshifts of these objects form quan-
tized sheets with ~z = 0.061. Peaks could be easily seen in n~cz from n = 1
to n = 10 (Burbidge 1968). With time the effects have strengthened. With
more than 700 objects with z < 0.2, the same effect has been seen. Ninety-
four of the objects have z between 0.055 and 0.065 (Burbidge and Hewitt
1990). Burbidge and O'Dell (1972) and later Duari et.al. (1992) carried out statistical tests on the samples and showed that the strong periodicity is real - the exact value of ~zo of 0.0565 and its significance is increased when the redshifts are transformed to the galactocentric frame. A second period ~z = 0.0128 is also found at high significance. In addition to these effects peaks in the wider redshift distribution have been known since the early days. These peaks come at z = 0.3, 0.60, 0.96, 1.41 and 1.95. It was shown by Karlsson (1977) that they can be fitted by the periodic formula
~ log(1 + z) = 0.223. There has been much debate about the peaks but
when selection effects are taken out the peaks at 0.3, 0.6, 1.41 and 1.95 in particular are unquestioningly present.

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175

All of the observed phenomena discussed above must be taken into account when we try to determine what sort of cosmological model is viable, and what pattern of formation, and evolution has been followed by galaxies.

4. Summary
Those who accept all of the observational data - those in category B, find it hard to accept the simplistic viewpoint espoused in A. The main stumbling block comes when we try to interpret the redshift simply as a distance indicator. For normal galaxies it can still be argued that the bulk of the redshift is due to expansion, together with a small term involving quantized effects which are intrinsic. There is no accepted theory of the quantized effect though Tifft and Cocke (Tifft, Cocke and DeVito 1996, Tifft 1997) are exploring various possibilities.
The redshift phenomena involving QSOs and related objects suggest: (1) That many QSOs are not at the distance derived from the redshifts. (2) That they are ejected from galaxies. (3) That coherent objects in general are ejected from galactic nuclei. (4) For Redshift components which are intrinsic, probably the masses of the fundamental particles are not the same as those in our own Galaxy. It is possible, but not certain that these results point to a cosmology very different from that espoused in A. It certainly requires a change in the conventional approach to galaxy formation and evolution starting from a very dense phase in the universe. How long will it be possible for the community to believe in A, and by ignoring the observational basis for B, treat it as irrelevant? This depends on the sociology of science and not on theory and observation. As long as astronomers are rewarded for following the herd, and punished for behaving independently, we are in trouble.

References
Ambartsumian.: 1958, Solvay Conf. Reports, ed. R. Stoops, (Bruxelles) Arp, H.: 1987, Quasars, Redshifts and Controversies, (Interstellar Medium, Berkeley) Arp, H. and Sulentic, J. W.: 1985, ApJ, 291, 88 Bondi, H., Gold T. and Hoyle, F: 1955, Observatory, 75, 80 Broadhurst, T. J., Ellis, R. S., Koo, D. C. and Szalay, A. S.: 1990, Nature, 343, 726 Burbidge, E. M.: 1995, A&Ap, 298, L1 Burbidge, G.: 1958, PASP, 70, 83 Burbidge, G.: 1968, ApJ, 154, L41 Burbidge, G.: 1996, A&Ap, 309, 9 Burbidge, G. and Burbidge, E. M.: 1967, Quasi Stellar Objects, (W. H. Freeman, San
Francisco) Burbidge, G., Burbidge, E. M., Fowler, W. and Hoyle, F.: 1957, Rev. Mod. Phys., 29,
547 Burbidge, G. and Hewitt, A.: 1990, ApJ, 359, L33

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G. BURBIDGE

Burbidge, G., Hewett, A., Narlikar, J. V. and Das Gupta, P.: 1990, ApJS, 74, 675 Burbidge, G. and O'Dell, S. 1.: 1972, ApJ, 178, 583 COBE; Mather, J. C., Cheng, E. S., Eplee, R. E., et.al.: 1990, ApJ, 354, L37 Duari, D., Das Gupta. P. and Narlikar, J. V.: 1992, ApJ, 384, 35 Guthrie, B. N, G., and Napier, W. N.: 1996, A&Ap, 310, 353 Hoyle, F. and Burbidge, G.: 1996, A&Ap, 309, 335 Hoyle, F. and Tayler R.: 1964, Nature, 203, 1108 Karlsson K. G.: 1977, A&Ap, 58, 237 McKellar A.: 1941, Dam. Ap. Obs. Publ. Peebles, P. J. E.: 1966, ApJ, 146, 542 Penzias, A. and Wilson R.: 1965, ApJ, 142, 419 Tifft, W. G.: 1976, ApJ, 206, 38 Tifft, W. G.: 1995, Ap&SS, 227, 25 Tifft, W. G.: 1996, ApJ, 468, 491 Tifft, W. G.: 1997, Ap&SS, these Time Conf. proceedings Tifft, W. G., and Cocke, W. J.: 1989, ApJ, 336, 128 Tifft, W. G., Cocke, W. J., DeVito, C. L.: 1996, Ap&SS, 238, 247 Wagoner, R., Fowler, W. and Hoyle, F.: 1967, ApJ, 148, 3 Wade C. M.: 1960, Observatory, 80, 235

DENSITY FLUCTUATIONS ON SUPER-HUBBLE SCALES
LI-ZHI FANG Department of Physics University of Arizona, Tucson, AZ 85721 , USA AND YI-PENG JING Max-Planck-Institut fur Astrophysik Garching, Germany
Abstract. According to causality, the existence of density perturbations on scales
larger than the present Hubble radius y = 2c/Ho is crucial for discriminating between inflation and non-inflation models of the origin of inhomogeneity of the universe. Observations of the cosmic background radiation anisotropies favor a super-Hubble suppression on scales Amax in the range 0.5 - 3.0y. Many of non-inflation models are consistent with such a suppression. Inflation models are certainly not in conflict with this suppression; however one important parameter, the duration of the epoch of inflation, may need to be fine-tuned.
1. Introduction
The most popular theory of structure formation in the Universe is based on the assumption that the structures started from small amplitude density perturbations which grew by gravitational instability. The primeval density perturhations are assumed to arise as vacuum fluctuations of scalar fields during the inflation era [1]. It predicts that the fluctuation spectrum is scale invariant with index'" 1. The subsequent evolution of these seeds of the density perturbations was brought about by gravitational interaction among baryonic and dark matter. The temperature fluctuations of the cosmic background radiation (CBR) and the formation of galaxies, clusters of galaxies , and even high-redshift objects were found to be consistent with
Astrophysics and Space Science 244:73 -XU,1996. © 1996 Kluwer Academic Publishers.

74

L.-Z. FANG, Y.-P. JING

this standard model if appropriate compositions of dark matter are taken

into account. Nevertheless, there are still models for the origin of density

fluctuations, such as cosmic strings and other defects of phase transitions,

which cannot be discriminated by these observations[2].

A possible way to distinguish between the mechanisms of planting the

perturbation seeds is to detect the density perturbations on scales larger

than the Hubble radius H- 1, where H is the Hubble constant at the time

being considered.

In the inflation era, the causal horizon grew exponentially, while the

Hubble radius was almost unchanged. Since the onset of inflation, the causal

horizon became much larger than the Hubble radius. The inflation scenario

is then characterized by the existence of a special region of length scales

larger than the Hubble radius, but less than the causal horizon. During

inflation, sub-Hubble perturbations were stretched into super-Hubble scales

by the expansion. Cosmologically interesting perturbations underwent an

evolution from sub- to super-Hubble scales. Therefore, inflation can produce

physically super-Hubble perturbations.

Perturbations on scales larger than the present Hubble radius have not

reentered the Hubble radius yet. This kinematical feature is common for

various versions of inflations regardless of their dynamical details. One can

then typically describe the spectrum of inflation- generated perturbations

by a power law

P(k) oc kn

(1)

without a cutoff related to the Hubble radius. On the other hand, non-inflation evolution requires that the causal hori-
zon is always about the same as the Hubble radius. No causally physical mechanism can seed perturbations on super-Hubble scales. All microphysics is impotent on scales larger than the Hubble radius. Even in the case that the seeds have scales larger than the horizon, causality will guarantee that there is no net density perturbation on superhorizon scales [3]. The spectrum of perturbations falls at least as fast as k4 on superhorizon scales [4]. Instead of eq.(l), the spectrum on large scales should be suppressed as P(k) oc knf(k), with f(k) being

1

f(k) oc 1 + (kmin/k)m'

(2)

where the suppression index m ~ 4 - n, kmin '" 7rH/ c. The suppression
factor f (k) in the power spectrum has also been directly found in models
like cosmic string plus cold or hot dark matters[5]. Therefore, the super-Hubble behavior of the perturbations is crucial to
studying the origin of fluctuations. It has been shown that the existence of

DENSITY FLUCTUATIONS

75

perturbations on scales larger than the Hubble radius before the recombination epoch can be tested by small-scale fluctuations of the CBR [6]. In this paper, we examine the perturbations on scales larger than the present Hubble radius. The existence of such super-Hubble scale perturbations can be tested by the CBR fluctuations on very large scales.

2. Fluctuations With Super-Hubble Suppression
Since COBE detected the CBR anisotropy, it was shown that the spectrum (1) can match the observations of the CBR anisotropy [7]. However, this success doesn't mean that the spectrum suppressed on scales larger than 2c/Ho is ruled out by the observations. In fact, right now, no statistical test has been done yet for these distinctive power spectra. It is worth studying whether the spectrum with long wavelength suppression is consistent with current observations.
Let's consider the large-scale fluctuations in the CBR temperature in a flat universe with a cosmological constant A = O. The fluctuation in direction 0 is[8]:

"k !:IT (0) = _ H6 '" 8(k) -ik·y

T

2c2 k2 e ,

(3)

where y = (2cH01, 0) is a vector of length 2cHOl pointing to 0 on the sky. 8(k) is the Fourier amplitude of the density contrast 8(r). The power spectrum P(k) = (18(k)12) with super-Hubble suppression can be written as
(4)

where VJ.! is a large rectangular volume, and !:lfi is a constant determined
by the variance of the perturbed potential.
The observed temperature fluctuations of the CBR on the celestial
sphere are usually expressed with spherical harmonics as !:IT/T(O) =
Elm arYr(O), where llm(o) are the spherical harmonic functions. Defin-
ing a rotationally invariant coefficient CI == (1/41T) Em(larI2), one finds
from eqs.(3) and (4) that

"k C = H6(2l + 1) '" P(k) .2(k )

l

4c4

k4 JI Y,

(5)

where j l (x) is the spherical Bessel function. For spectrum (4), eq. (5) becomes
(6)

76

L.-Z. FANG, Y.-P. JING

Instead of .using the amplitude ~~, one can also normalize the spectrum
using the quadrupole amplitude defined by Q = C~/2T, where T = 2.726
K is the mean temperature of CBR. Strictly speaking, eqs.(3) and (6) were derived under the assumption
that all the density perturbations are primordial, i.e. produced before recombination. They cannot be directly used to calculate the CBR fluctuations from density perturbations induced later. Many non-inflation models like those of phase transition defects do assume that partial, or even entire, perturbations were generated after recombination. The CBR fluctuations should be a mixture of the "primordial" anisotropies [eq.(6)] and those induced by perturbations generated later. Obviously, in this case the total CBR anisotropy will depend on the mechanism of the generation and evolution of perturbations after the last scattering.
However, for a very wide class of non-inflationary models, eq.(6) has been found to be still valid for describing the CBR anisotropy from latetime perturbations if the amplitude ~~ in eq.(6) is replaced by a factor describing the temporal dependence of the perturbations [9]. Therefore, if we treat ~~ and n in eq.(6) as phnomenological parameters, the results given by fitting the observational data to eq.(6) are valid for models of " primordial" and/or late-time induced anisotropies. Especially, the suppression factor j(k) is model-independent, therefore, the fitting result of kmin should also be available to judge between models. Moreover, we will not consider the temperature fluctuations caused by tensor (gravitational wave) perturbations, because in most models CBR anisotropies are dominated by scalar perturbations, and the tensor perturbations also obey the suppression eq.(2). The power spectrum of tensor perturbations generally has a different index n from that of scalar perturbations eq.(I). Considering this point, we will investigate two extreme cases of the suppression on super-Hubble scales: 1) sharp cutoff, m = 00; 2) softer cutoff, m = 4 - n.

3. Statistical Analysis
To test the models of eq. (6) with fil1ite cutoff Amax = 27f/ kmin we first use the COBE observations of the two-point angular correlation function C(O) of the CBR temperature [7]. The two-point angular correlation function C(O) is determined by Cl as
(7)

where Pz(x) is the Legendre function, and W(l) = exp{ -1/2[l(l +l)/17.82 ]} is a window function. The influence of cosmic variance [10] can be treated by the standard X2 technique [11]. For a given n, we estimate the goodness-

DENSITY FLUCTUATIONS

77

of-fit of models with parameters of kmin and Q by minimizing X 2 over the
data:
(8)

where Gi and ai are, respectively, the observed values and errors of the angular correlation at Oi, and acv (0) is the 1a cosmic variance of the G(0).
In eq.(8) we assumed that the variances in different bins are mutually independent. Strictly speaking, this assumption does not consider the binbin correlation of cosmic variances, and we should use statistics applicable for a covariance matrix of Gil such as a likelihood analyses. However, the approximation of eq.(8) is already suitable for our purpose: to estimate a statistical confidence of rejecting the supper-Hubble suppression model of eq. (6) by observations. Generally, considering more variances will lead to a lower probability of the rejection for a given model, and a higher confidence of the acceptableness of the model. Therefore, eq. (8) should safely provide an underestimated confidence limit of the consistence of the supper-Hubble suppression model with current observation. In fact, the likelihood analyses of a cubic toroidal (T3 ) universe gave almost the same best-fit values for Q and kmin as eq.(8) does[ll, 12]. This indicates that under the current precision of the data, the statistics of Q and kmin do not significantly depend on the nondiagonal part of the covariance matrix of Gi. Mathematically, testing the suppression scale Amax of model (6) is completely the same as testing kmin of a T3 universe. Therefore, it would be reasonable to apply the statistic eq. (8) to estimate the acceptableness of model with supper-Hubble suppreSSlOn.
Since acv is also proportional to Q, we adopt an iteration procedure to
conduct the X2 minimization. First we assume a zero acv and find out the best-fitting value of Q. Using this value we calculate the (Jcv based on 100 Monte Carlo realizations of Gl, and do the minimization again and find a new fitting value of Q. Using this new Q we repeat the minimization and find another more accurate value of G2 rms-PS. The iteration procedure is stopped until the differences of X2 and of Q between the two consecutive
minimizations are less than 0.1 %. The final Q and X2 are our desired values. The goodness of the X2-fit of the sharp (m = 00) and softer (m = 4 - n)
cutoffs are shown in Figure 1, in which P(> X~in) is the probability that the experimental data are drawn frum a realization of the Inmjel. It can clearly be seen from the figure that there are remarkable peaks with respect to Y/ Amax· It shows that the suppressed spectrum eq. (4) is acceptable. even improves the fitting to the observed CBR temperature fluctuations.
In Table 1, we list our fitting results of the )...max / Y ranges acceptable by the COBE observations at 95% confidence level. The results of Amax/Y do not sensitively depend on the suppression index m. For the cases of the

78

L.-Z. FANG, y'-P. JING

Figure 1a

Figure 1b

0.8
0.6
.1" 0" :
0.4

m=oo
- - n=l n=1.6
- - - - n=0.6

0.8
0.6
.1" 0" :
0.4

m=4-n

I

- - n=l

I

I

n=1.6

I

I

- - - - n=0.6

.,
"

0.2

0.2

'.. i - ' - ' - ' - - ' - ' - ' - ' - ' -

0

0

0.1

10

0.1

Figure 1. Probability P(> X;"in), i.e. X2-fit goodness, as a function of Y/>"max. Here X;"in is calculated by fitting the spectrum with suppression (2) to the COBE-DMR two-point angular correlation function of the cosmic temperature fluctuations. The index
n of the power spectrum is taken to be 0.6, 1.0 and 1.6. The dot-dash line denotes
P(> X;"in) = 5%.

index n ~ 1 which are favored by current observations of galaxy distributions, the upper limits on Amax/Y are determined to be about 3. For n=1.6, although the most likely values of Amax/Y are about 2, no significant upper limit on Amax/Y can be deduced from the COBE observations. The upper or lower limits given above will change slightly if one includes the nondiagonal part of the error matrix in the fitting procedure. As mentioned above, the nondiagonal part will generally increase the confidence of the acceptableness.

TABLE 1. Super-Hubble sup-
pression wavelength >"max/Y given by C(O)

n m=O

m=4

0.60 1.05-2.20 0.64-2.13
1.00 1.11-2.70 0.77-3.03
1.60 > 1.25 > 1.11

Figure 2 plots the best-fitting quadrupole, i.e. Q = cV;ms-PS' as a
function of y/ Amax . The thick line denotes the RMS quadrupole measure-
ment and the dotted area is its 10" region, i.e. Qrms = 6 ± 3 J.l K [7]. For

DENSITY FLUCTUATIONS

79

Figure 2a

Figure 2b

- - n=1 .... . n=1.6 n=0.6

m= oo

- - n.1 .... . n=1.6 n=0.6

m=4-n

10-' L-~~--'-~........1L---,---,-~~.w10---'
0. 1
y/ A_.

10-' L-~~--,-~........L_--,---'-~~-'-'---'

0.1

1

10

y/ A_.

Figure 2. The best fitted quadrupole , ie.. C; I;ms-Ps, as a function of the wavelength of the suppression on super-Hubble radius, Y/)..max, The thick line denotes the RMS quadrupole measurement C; I;ms' and the dotted area is its 10' region .

the suppression scales allowed by the X2 tests, the best-fitting quadrupole agrees with the observed one. The result is weakly dependent on the power
law index n and the suppression index m, though the n = l.6 case with-
out suppression gives a worse match of the best-fitting quadrupole with the observed one. Considering that the measures of C(8i ) and Qrms are independent, these results seem consistently to warn us of the existence of suppression on the super-Hubble scales.
4. Discussions and Conclusions
For a large class of non-inflation models like "late-time" cosmological phase transition [13], there is no mechanism for the growth of super-Hubble scale perturbations. It requires that the suppression scales Amax should not be larger than about l.5y [4]. For the models like topological defects, in which the perturbations are produced both before and after recombination, the super-Hubble suppression scale Amax depends on the dynamics of the defects . For instance, Amax is found to be in the range of '" 0.8 - 3.0y for models of cosmic string plus hot or cold dark matter [5]. From Table 1, the suppression scales for the n ~ 1 power spectra are consistent with these models. In the case of n = l.6, the confidence level for a suppression scale to be larger than 1.5y is 80%, which is probably difficult to survive in some models of late-time phase transition. Overall, many of the non-inflation models are consistent with the two years of COBE data.

80

L.-Z. FANG, Y.-P. JING

Our formal error analysis shows that the COBE data favor models with finite suppression Amax on scales larger than but close to the Hubble radius. In the "standard" inflationary model, a super-Hubble suppression in the spectrum of primordial density perturbations can be given by the duration of the epoch of inflation. Because the longest wavelengths of the density perturbations should come from the perturbation which crosses the horizon at the time when inflation just began, a suppression scale would be determined by the number of e-folds of cosmic scale growth in the whole epoch of inflation. Therefore, in order to explain why the suppression scales in the spectrum of the primeval density perturbations are so close to the Hubble scale, the duration of the epoch of inflation may need to be fine-
tuned. In the case of n = 1.6, the goodness of the fit of the Amax = 00 model
with the COBE observations is comparable with models with finite Amax, although a finite value of Amax '" 2y is still favored. However, the current observations of galaxy distributions can hardly accommodate n = 1.6.
YPJ is supported by an Alexander-von-Humboldt research fellowship.

References
1. Kolb, E. W., and Turner, M. S.: 1990, The Early Universe, (Addison-Wesley, NY) 2. Bennett D. P., Stebbins, A. and Bouchet F. R.: 1992, ApJ, 399, L5; Bennett, D.
P. and Rhie, S. H.: 1993, ApJ, 406, L7; Pen, U. L., Spergel, D. N. and Turok, N.: 1994, Phys. Rev. D, 49, 692 3. Traschen, J.: 1985, Phys. Rev. D, 31, 283; Veeraraghavan, S. and Stebbins, A.: 1990 ApJ, 365, 37 4. Abbott L. F. and Traschen, J.: 1986 ApJ, 302, 39; Robinson, J. and Wandelt, B. D.: astro-ph/9507043 5. Albrecht, A. and Stebbins, A.: 1992, Phys. Rev. Lett., 68, 2121 and 69, 2615 6. Critenden, R. G. and Turok, N. G.: 1995, astro-ph/9505120; Albrecht, A., Coulson, D., Ferreira, P. and Magueijo, J.: 1995, astro-ph/9505030 7. Bennett, C. L. et al.: 1994 ApJ, 436, 423; Bennett, C. L. et al.: 1996, astroph/9601067 8. Peebles, P. J. E.: 1982, ApJ, 263, L1 9. Jaffe, A. J., Stebbins, A. and Frieman, J. A.: 1994, ApJ, 420, 9 10. Abbott, L. F. and Wise, M. B.: 1984, ApJ, 282, L47 11. Jing Y. P. and Fang, L. Z.: 1994, Phys. Rev. Lett., 73, 1882; Scaramella R. and Vittorio, N.: 1993, MNRAS, 263, L17 12. Seljak, U. and Bertschinger, E.: 1993 ApJ, 417, L9 13. Wasserman, I.: 1986 Phys. Rev. Lett., 57,2234; Press, W. H., Ryden, B. and Spergel, D.: 1990 Phys. Rev Lett., 64, 1084; Fuller G. and Schramm, D. N.: 1992 Phys. Rev. D, 45, 2595; Frieman, J. A., Hill C. T. and Watkins, R.: 1992 Phys. Rev. D, 46, 1226

THE CHALLENGE OF LARGE-SCALE STRUCTURE
S. A. GREGORY Dept. of Physics and Astronomy fj Institute for Astrophysics University of New Mexico Albuquerque, New Mexico 81131
Abstract. The tasks that I have assumed for myself in this presentation include three separate parts. The first, appropriate to the particular setting of this meeting, is to review the basic work of the founding of this field ; the appropriateness comes from the fact that W. G.Tifft made immense contributions that are not often realized by the astronomical community. The second task is to outline the general tone of the observational evidence for large scale structures. (Here, in particular, Icannot claim to be complete. I beg forgiveness from any workers who are left out by my oversight for lack of space and time.) The third task is to point out some of the major aspects of the field that may represent the clues by which some brilliant sleuth will ultimately figure out how galaxies formed.
1. Discovery
G. deVaucouleurs 1975 (and references therein) followed up suggestions made in 1937 by E. Holmberg and identified the Local Supercluster in the 1950s. The general significance of this work was quite controversial; many thought that this structure might just be a statistical local overdensity. Real progress could not be made until the 1970s when large, statistically complete redshift surveys could be conducted as a result of the introduction of image intensifying tubes. Among the first of these surveys was my dissertation (results published in Gregory 1975) in which all galaxies with
mp < 15.7 within a radial distance of r < 3 degrees from the Coma cluster
center were surveyed spectroscopically. It was in an early discussion of this data in 1973 that Tifft pointed out the lack of a foreground . Isuggest that this is the birth of the concept of cosmic voids. Tifft and L along with Laird Thompson, further developed the observational status of large structures
Astrophysics and Space Science 244:81-88,1996. © 1996 Kluwer Academic Publishers.

82

S. A. GREGORY

(Tifft and Gregory 1976 [first wedge diagram] & 1978) culminating with the paper covering the Coma/A1367 region that is often cited as the first full presentation of voids and superclusters as the fundamental features of large-scale structure (Gregory and Thompson 1978).
A great deal of discovery-phase work was also done by Chincarini and Rood 1976, Joeveer and Einasto 1978, Tarenghi et. al 1979, and by Tifft, Hilsman, and Corrado 1975 who discovered the supercluster in Perseus (more on this later - the Rosetta Stone of galaxy formation?). I note that not much mention was made of the fact, but those of each of these groups that I talked to at the time all noted that the then-known superclusters had the interesting properties of having mean redshifts of approximately 3,000 km s-l (Hydra - Centaurus), 5,000 km s-l (Perseus), 7,000 km S-l (Coma) and 9,000 km S-l (Hercules). Chincarini and Rood went so far as to describe these structures as having a "fabric" nature. The regularity and our seeming location as the center of perhaps concentric shells were disturbing to the standard view.
Additional observations of note include Tully and Fisher 1987 (and references therein) who greatly elaborated on the structure of the Local Supercluster showing it to have sheetlike and linear features similar to those found in external superclusters and Kirshner, Oemler, and Schechter 1979 who found the Bootes void which was much larger than any previously known. Potentially important alignments were reported by Gregory, Thompson, and Tifft 1981 for galaxies in the Perseus supercluster and by Binggeli 1982 for the alignments of clusters with nearby clusters.

2. Bulk Motions
Rubin et al. 1976 studied ScI-II galaxies and found systematic motions, but Chincarini and Rood 1979 argued that these observations were also well interpreted as a mapping of large-scale structures. Aaronson et al. 1986 developed the IR Tully Fisher relation for spirals and Dressler et al. 1987 developed the Dn - e relation for ellipticals. This body of work gave us two means of estimating distances that were independent of redshift. Hence, the difference between predicted Hubble flow distances and those found by the new methods enabled these two groups to investigate bulk motions. Various levels of refinements to these methods have yielded the concept of a Great Attractor located at a redshift distance of about 4500 km s-l near to but not coincident with the Hydra and Centaurus clusters.

3. Intermediate Results and Implications
Batuski & Burns 1985 found unprecedentedly large structures in the distribution of Abell clusters. These include a supercluster (including the Perseus

LARGE SCALE STRUCTURE

83

supercluster at the near end) of length approximately 1 billion light years and a void covering much of the northern galactic hemisphere that includes the Bootes void on one side. The CfA group (de Lapparent et al. 1986) showed a strip survey around Coma; the well defined boundaries of the voids suggested a bubble-like topology. In the Perseus supercluster Giovanelli, Haynes, and Chincarini 1986 found morphological segregation. They found that the filamentary nature of the supercluster was well defined by early morphological types but that later types showed increasingly diffuse structures.
A series of papers investigated the degree of emptiness of the Bootes void (Tifft, et al. 1986, Moody, et al. 1987, and Wiestrop and Downes 1988). These papers noted that one could find galaxies in the void by means of emission line surveys. However, the voids did not "fill up" with these galaxies; voids were still extremely underdense with respect to the mean.
A large amount of theoretical work has been generated by the observations reported above. I do not have the time or space to give justice to these important studies. I suggest that the reader look at a reasonable overview such as Deckel 1988 and more recent work. The concepts involved examine whether or not the Universe is dominated by hot dark matter (neutrinos) which accounts for the largest structures but has trouble with small groups and cold dark matter which seems to work in the opposite manner. Hybrid models seem promising, but perhaps Gaussian origins for the perturbations will be superseded by cosmic strings. Out of the bubble concept came explosive models for the amplification of density perturbations. These can account for small voids but have trouble at the larger scales.

4. Some Recent Work
A. In the early 1990's the COBE satellite (Wright et al., 1994 and references therein) found 1) the dipole nature of the background radiation and 2) the (probable) evidence for the seeds of large-scale structures.
B. Szalay et al., 1993 combined the results from 4 deep redshift surveys near both the NGP and SGP. They believe that they have found a significant periodic structure with a spacing of 12,700 km s-J .
C. Praton and Schneider 1994 showed that wedge diagrams can have important artifacts induced by infall and transverse motion. Features of their diagrams appear very similar to bubbles in the slice survey, and they derive bulk motions that are "not consistent" with the COBE results. This work possibly explains the concentric appearance of features in redshift space.
D. The group including R. Kraan Kortevig and P. Henning 1996 conducted several HI and optical surveys/searches in the zone of avoidance.

84

S. A. GREGORY

--CJ)
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Figure 1. The 2-D distribution of Zwicky galaxies in the Perseus supercluster region. Note the obvious gently curving filamentary nature of the dominant structure.
There is very strong recent evidence for the discovery of a major cluster at the predicted position of the Great Attractor. This evidence comes from the discovery of a very large number of galaxian images on the sky survey that are strongly concentrated near the predicted position on the sky of the Great Attractor.
E. New results presented here: Results from the Arizona/New Mexico spectroscopic survey conducted by S. Gregory, W. Tifft, S. Hall, J. Moody, and M. Newberry
i. Details on filamentary structures in Perseus supercluster - We find that there are three intersecting filaments that are differentiated in 3-D. Figure 1 shows the general distribution of galaxies in the Perseus supercluster region. Figure 2 expands the western region that represents our new survey and shows that the two parallel filaments are separated in redshift space with the northern filament being on the near side and intersecting a third filament that extends to the northeast.
ii. Morphological Segregation - We confirm the results of Giovanelli, Haynes, and Chincarini with our new and differently defined data (we use the 4,000 A break to find morphologies). Figures 3, 4, and 5 show the same region as Figure 2 with different morphological mixes (Fig. 3 - all types, Fig. 4 - early types, and Fig. 5 intermediate and late types).
iii. Emission Line Incidence - If morphological segregation is thought of

LARGESCALE STRUCTURE

85

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Figure 2. Here we have isolated the galaxies that lie in filaments that intersect the main
supercluster. Circles indicate those galaxies with cz < 6,000 km S-I, and triangle indicate those with cz > 6, 000 km S-I. The northern of the two parallel filaments intersects with
the third filament that extends to the northeast. The two parallel filaments join with the main supercluster near the eastern border of this fipure. The mean separation between
the two parallel filaments is about v = 1,600 km s- in redshift space.

as a sequence of star formation epochs, then emission line activity can be thought of as an extension to late type absorption spectra (at least the HI! type spectra). The distribution of emission line objects in the filaments is consistent with other indicators of morphological segregation. Also, one of the three filaments has no emission objects. Figure 6 shows the distribution of galaxies with emission line spectra.
5. Concluding Thoughts
Can we answer such questions as 1) what is a filament , 2) how empty are voids, 3) what are the topological properties of superclusters and voids sheets, filaments, connectedness of these two, bubbles, sponges, and 4) what is the reason for morphological segregation (is it as simple as disk galaxies get turned into spheroidal systems by encounters?)
There appears to be an analogy: Spiral arm tracers in disk galaxies and filament tracers in superclusters. Can the analogy be extended? Is there an evolutionary sequence?
What is the nature of the observations of the regularity of the large-

86

S. A. GREGORY

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Figure 3. Here we show the distribution of all morphological types in our western Perseus supercluster survey region. Morphologies are estimated from the nuclear spectral type.

• •

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LARGESCALE STRUCTURE

87

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Figure 6. Same as Figure 3 except that those galaxies with emission lines in their spectra are shown. Note that the distribution is very diffuse, and that the filament extending to the northeast is largely missing from this diagram.

88

s. A. GREGORY

scale structures? Are the concentric shells real? Is there quantization at the level of 12,700 km s-l?
What is the nature and significance of alignments?

References
Aaronson, M., Bothun, G. D., Mould, J., Huchra, J., Schommer, R., and Cornell, M.: 1986 ApJ, 302, 536
Batuski, D. J. and Burns, J. O. 1985: AJ, 90, 1413 Binggeli, B. 1982: AtM., 107, 338 Chincarini , G., and Rood, H. J. 1976: ApJ, 206, 30 Chincarini, G., and Rood, H. J. 1979: ApJ, 230, 648 Deckel, A.: 1988, in Large-Scale Motions in the Universe, ed. Rubin, V. C. and Coyne,
G. V. (Princeton University Press) de Lapparent, V., Geller, M. J., and Huchra, J. P.: 1986, ApJ Lett., 302, L1 Dressler, A., Faber, S. M., Burstein, D., Davies, R. L., Lynden-Bell, D., Terlevich, R. J.,
and Wegner, G. W.: 1987 ApJ Lett., 313, L37 Giovanelli, R., Haynes, M. P., and Chincarini, G. L.: 1986 ApJ, 300, 77 Gregory, S. A.: 1975 ApJ, 199, 1 Gregory, S. A. and Thompson, L. A.: 1978 ApJ, 222, 784 Gregory, S. A., Thompson, L. A., and Tifft, W. G.: 1981, ApJ, 243, 411 Henning, P. A.: 1996, private communication Joeveer, M. and Einasto, J.: 1978, in fA U Symp. 79 ed. J. Einasto and M. S. Longair
(Dordrecht:Reidel), 241 Kirshner, R. P., Oemler, A., and Schechter, P. L.: 1978, AJ, 83, 1549 Moody, J. W., Kirshner, R. P., MacAlpine, G. M. and Gregory, S. A.: 1987, ApJ Lett.,
314, L33 Praton, E. A. and Schneider, S. E.: 1994, ApJ, 422, 46 Rubin, V. C., Ford, W. K., Thonnard, N., Roberts, M. S., and Graham, J. A.: 1976 AJ,
81, 687 Szalay, A. S., Broadhurst, T. J., Ellman, N., Koo, D. C., and Ellis, R. S.: 1993, Proc.
Nat. Acad. Sci. (USA), 90, No. 11, 4853 Tarenghi, M., Tifft, W., Chincarini, G., Rood, H. J. and Thompson, L. A.: 1979, ApJ,
234, 793 Tifft, W. G., Hilsman, K. A. and Corrado, L. C.: 1975, ApJ, 199, 16 Tifft, W. G. and Gregory, S. A.: 1976, ApJ, 205, 696 Tifft, W. G. and Gregory, S. A.: 1978, in fAU Symp. 79 ed. J. Einasto and M. S. Longair
(Dordrecht: Reidel), 267 Tifft, W. G., Kirshner, R. P., Gregory, S. A., and Moody, J. W.: 1986, ApJ, 310, 75 Tully, R. B. and Fisher, J. R.: 1987, Nearby Galaxies Atlas, Cambridge University Press. Vaucouleurs, G. de: 1975, in Stars and Stellar Systems, Vol. 9, pp. 557-600 Wiestrop, D. and Downes, R. A.: 1988, ApJ, 331, 172 Wright, E. L., Smoot, G. F., Kogut, A., Hinshow, G., Tenorio, L., Lineweaver, C., Ben-
nett, C. L. and Lubin, P. M.: 1994, ApJ, 420, 1

ELECTRIC SPACE: EVOLUTION OF THE PLASMA UNIVERSE
ANTHONY L. PERATT
Los Alamos National Laboratory Los Alamos, New Mexico Scientific Advisor, Office of Research and Development, United States Department of Energy, Washington D.C.
Abstract. Contrary to popular and scientific opinion of just a few decades ago, space is not an 'empty' void. It is actually filled with high energy particles, magnetic fields, and highly conducting plasma. The ability of plasmas to produce electric fields, either by instabilities brought about by plasma motion or the movement of magnetic fields, has popularized the term 'Electric Space' in recognition of the electric fields systematically discovered and measured in the solar system. Today it is recognized that 99.999% of all observable matter in the universe is in the plasma state and the importance of electromagnetic forces on cosmic plasma cannot be overstated; even in neutral hydrogen regions ('" 10-4 parts ionized) , the electromagnetic force to gravitational force ratio is 107 .
An early prediction about the morphology of the universe is that it be filamentary (Alfven, 1950). Plasmas in electric space are energetic (because of electric fields) and they are generally inhomogeneous with constituent parts in motion. Plasmas in relative motion are coupled by the currents they drive in each other and nonequilibrium plasma often consists of current-conducting filaments. This paper explores the dynamical and radiative consequences of the evolution of galactic-dimensioned filaments in electric space.
1. Introduction
Contrary to popular and scientific opinion of just a few decades ago, space is not an 'empty' void. It is actually filled with high energy particles, mag-
Astrophysics and Space Science 244:89-103,1996. © 1996 Kluwer Academic Publishers.

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A. L. PERATT

netic fields, and highly conducting plasma. The ability of plasmas to produce electric fields, either by instabilities brought about by plasma motion or the movement of magnetic fields, has popularized the term 'Electric Space' in recognition of the electric fields systematically discovered and measured in the solar system. Today it is recognized that 99.999% of all observable matter in the universe is in the plasma state and the importance of electromagnetic forces on cosmic plasma cannot be overstated; even in neutral hydrogen regions ('" 10-4 parts ionized), the electromagnetic force to gravitational force ratio is 107.
Among the earliest predictions about the morphology of the universe is that it be filamentary (Alfven, 1950, 1981, 1990). Plasmas in electric space are energetic (because of electric fields) and they are generally inhomogeneous with constituent parts in motion. Plasmas in relative motion are coupled by the currents they drive in each other and nonequilibrium plasma often consists of current-conducting filaments. This paper explores the dynamical and radiative consequences of the evolution of galactic-dimensioned filaments in electric space.
In the laboratory and in the Solar System, filamentary and cellular morphology is a well-known property of plasma. As the properties of the plasma state of matter is believed not to change beyond the range of our space probes, plasma at astrophysical dimensions must also be filamentary.
Additionally, transition regions have been observed that delineate the 'cells' of differing plasma types (Eastman, 1990). On an astrophysical scale, these transition regions should be observable at radio wavelengths via transition radiation signatures.
The suggestion that the universe be filamentary and cellular was generally disregarded until the 1980s, when a series of unexpected observations showed filamentary structure on the Galactic, intergalactic, and supergalactic scale. By this time, the analytical intractibility of complex filamentary geometries, intense self-fields, nonlinearities, and explicit time dependence had fostered the development of fully three-dimensional, fully electromagnetic, particle-in-cell simulations of plasmas having the dimensions of galaxies or systems of galaxies. It had been realized that the importance of applying electromagnetism and plasma physics to the problem of radiogalaxy and galaxy formation derived from the fact that the universe is largely a plasma universe.
Any imbalance in the constitutive properties of a plasma can set it in motion [if, in fact, it has not already derived from an evolving, motional state (Bohm, 1979)]. The moving plasma, i.e., charged particle flows, are currents that produce self magnetic fields, however weak. The motion of any other plasma across weak magnetic fields produces and amplifies electromotive forces, the energy of which can be transported over large distances via

ELECTRlC SPACE

91

currents that tend to flow along magnetic lines of force. These 'field-aligned
currents,' called Birkeland currents (Cummings and Dessler 1967) in plane-
tary magnetospheres, should also exist in cosmic plasma. The dissipation of the source energy from evolving or moving plasma in localized regions can then lead to pinches and condense states. Where double layers form in the pinches, strong electric fields can accelerate the charged particles to high energies, including gamma ray energies (Alfven, 1981). These should then display the characteristics of relativistic charged particle beams in laboratory surroundings, for example, the production of microwaves, synchrotron radiation, and non-linear behavior such as periodicities and 'flickering.'

2. Filamentation by Birkeland Currents
An electromotive force Jv x B . dl giving rise to electrical currents in con-
ducting media is produced wherever a relative perpendicular motion of plasma and magnetic fields exist (Akasofu, 1984; Alfven, 1986). An example of this is the (nightside) sunward-directed magnetospheric plasma that cuts the earth's dipole field lines near the equatorial plane, thereby producing a potential supply that drives currents within the auroral circuit. The discovery of these Birkeland currents in the earth's magnetosphere in 1974 (Dessler, 1984) has resulted in a drastic change in our understanding of aurora dynamics, now attributed to the filamentation of Birkeland charged-particle sheets following the earth's dipole magnetic-field lines into vortex current bundles.

3. Galactic Dimensioned Birkeland Currents
Extrapolating the size and strength of magnetospheric currents to interstellar space leads to the suggestion that confined current flows in interstellar clouds assists in their formation (Alfven, 1981).
As a natural extension of the size hierarchy in cosmic plasmas, the existence of galactic dimensioned Birkeland currents or filaments was hypothesized (Alfven & Falthammar, 1963; Peratt, 1986a).
A galactic magnetic field of the order BG = 10-9 - 1O-10T associated
with a galactic dimension of 1020 - 1021 m suggests the galactic current be of the order IG = 1017 - 1019A.
In the galactic dimensioned Birkeland current model, the width of a typical filament may be taken to be 35 kpc (~ 1021 m), separated from neighboring filaments by a similar distance. Since current filaments in laboratory plasmas generally have a width/length ratio in the range 10-3 - 10-5, a typical 35 kpc wide filament may have an overall length between 35 Mpc and 3.5 Gpc with an average length of 350 Mpc. The circuit, of course, is closed over this distance (Peratt, 1990).

92

A. L. PERATT

4. The Large Scale Structure of the Plasma Universe
Surface currents, delineating plasma regions of different magnetization, temperature, density, and chemical composition give space a cellular struc-
ture (Alfven & Falthammar, 1963). As current-carrying sheet beams collect
into filaments, the morphology of the surface currents is filamentary. For the case of tenuous cosmic plasmas, the thermokinetic pressure is
often negligible and hence the magnetic field is force-free. Under the influence of the electromagnetic fields the charged particles drift with the velocity

v = (E x B) /E2

(1)

The overall plasma flow is inwards and matter is accumulated in the filaments which, because of their qualitative field line pattern, are called "magnetic ropes". Magnetic ropes should therefore tend to coincide with material filaments that have a higher density than the surroundings. The cosmic magnetic ropes or current filaments are not observable themselves, but the associated filaments of condensed matter can be observed by the radiation they emit and absorb.
It is because of the convection and neutralization of plasma into radiatively cooled current filaments (due to synchrotron losses) that matter in the plasma universe should often display a filamentary morphology.

5. Synchrotron Emission from Pinched Particle Beams
One of the most important processes that limit the energies attainable in particle accelerators is the radiative loss by electrons accelerated by the magnetic field of a betatron or synchrotron. This mechanism was first brought to the attention of astronomers by Alfven and Herlofson (1950); a remarkable suggestion at a time when plasma, magnetic fields, and laboratory physics were thought to have little, if anything, to do with a cosmos filled with isolated "island" universes (galaxies). Synchrotron radiation is characterized by a generation of frequencies appreciably higher than the cyclotron frequency of the electrons; a continuous spectra (for a population of electrons) whose intensity decreases with frequency beyond a critical frequency (near intensity maxima); increasing beam directivity with increasing
relativistic factor 'Y ('Y = (1 - ,8)-1/2); and polarized electromagnetic wave
vectors. Z-Pinches are among the most prolific radiators of synchrotron radiation
known. In this regard, the Bennett-pinch (Bennett 1934), or Z-pinch, as a synchrotron source has been treated by Meierovich (1984) and Newberger et. al. (1984).

ELECTRIC SPACE

93

TABLE 1. Simulation derived parameters based on the radiation properties of the double radio galaxy Cygnus A.

Parameter
Galactic current, Ia Galactic magnetic field, B(J Galactic magnetic field, B. Plasma temperature, T Plasma density, n. Electric field strength, E. Synchrotron power, POlin Radiation burst duration Total energy

Simulation Value
2.4 X 1019 A 2.5 X 10-4 G 2.0 X 10-4 G 2.0 - 32.0 keY 1.79 x 10-3 cm-3 62 mV/m 1.16 x 1037 W 1.28 X 1014 S 6.3 X 1062 J

The radiation produced from the two nearest plasma filaments in interaction replicates both the isophotal and power spectra from double radio galaxies (Figure 1). Table I delineates the basic parameters used in the interacting galactic filament simulation.
Because the highly relativistic electrons depicted in Figure 1 flow in direction outwards from the plane of the figure, the synchrotron radiation is also beamed in this direction (Johner, 1988).
The monochromatic power of quasars and double radio galaxies span a range of about 1033W - 1039W (Peratt, 1986b). For example, the "prototype" double radio galaxy Cygnus A has an estimated radio luminosity of 1.6-4.4 x 1037W. Together with the power calculated, the simulation isophotes are very close to those observed from this object (Peratt, 1986a). The upper row of Figure 1 suggests that previously apparently unrelated double radio galaxies all belong to the same species but are simply seen at different times in their evolution.
6. Confining and Interacting Forces Between Cosmic Currents
If the cosmic current is cylindrical and in a rotationless, steady-state condition, it is described by the Carlqvist Relation:
(2)
for a current of radius r = a where J-to is the permeability of free space, G is
the gravitational constant, m is the mean particle mass, N is the number
of particles per unit length, and LlWBz and LlWk are the differential beam

94

A. L. PERATT

Figure 1. (top) Synchrotron isophotes (various frequencies) of double radio galaxies, (bottom) Simulation analogs at time lOA Myr to 58.7 Myr. Time increases from left to right.

magnetic and kinetic energies, respectively (Peratt, 1992a)1. Thus, whether

or not a current or beam is gravitationally balanced, electromagnetically

balanced, or force-free, depends on the magnitude of the individual terms in

Eq.(2). Applications of the Carlqvist Relation are presented in this journal

(Verschuur, 1995).

In contrast to the gravitational and electromagnetic forces that deter-

mine the characteristic of an individual beam, interactions between beams

are always dominated by electromagnetic Biot-Savart forces,

J F21 = j2 X B 21d3r

(3)

for all space, where h x B21 is the Lorentz force between the field B21 induced by a current h on the current density h at current 12.2
Parallel axial currents within the filaments are long-range attractive,
while circular (helical) currents within the filaments (as the electrons gyrate along the axial magnetic field) are short-range repulsive. If the axial
currents are able to bring the filaments close enough together so that the

1When current rotation and transient phenomena are important, the Generalized B ennett Condition may be used in place of Eq.(2) (Peratt, 1992a, Chap. 2)
2The Biot-Savart force varies as r- 1 and thus dominates gravitational attraction which varies as r- 2 • 'Great Attractors', often attributed to gravitational forces between 'missing masses' display Biot-Savart, not mass attraction, characteristics.

ELECTRIC SPACE

95

Figure 2. Single frame stills of plasma in the simulation of two adjacent Birkeland fila-
= ments: wc/wp =3.0, Teo Tio=32 keY, E zo=62 mV1m. Total time elapsed: ::::: 109 yr. The
initial dimensions in frame 1 (top, lefthand corner) are: radius of filaments r jilament=17.5 kpc, distance between filaments djilaments=80 kpc. The length over which Ezo exists in the filaments is taken to be :::::10 kpc.
repulsive component of the Lorentz force becomes important, the circular currents repulse and brake, and release energy in the form of synchrotron radiation.
While a complete description of the evolution of interacting galactic currents is given elsewhere (Peratt, 1992a,b), it is useful to reproduce the evolutional sequence in this paper. Figure 2 illustrates the cross-sections of the filaments over a 109 yr period.
7. Rotation Velocities
Rotational velocities of spiral galaxies are found by measuring the doppler shift of the Ha line emitted by neutral hydrogen in the spiral arms. If the galaxy is at a cant towards earth, the emission-line in the arm moving away from earth is red-shifted while the line in the arm moving towards earth is blue-shifted. Measurements of the outer rotation curves using radio techniques indicated that these were fiat, rather than following the Keplerian law. If galaxies were gravitationally bound systems, their outer mass should follow Kepler's laws of motion and be slower than the inner mass. The fiat rotation curves of galaxies has been cited as the strongest physical evidence for the existence of dark matter. In this scenario a massive halo of dark matter has been evoked to produce the fiat rotation curves. However, the rotation curves are not really flat; they show appreciable structure representative of an instability mechanism within the arms. This instability

96

A. L. PERATT

questions the existence on any external halo of matter around galaxies that, while making the rotation curves flat, would also dampen any instability growth.

8. The Association of Neutral Hydrogen with Galactic Magnetic Fields
Neutral hydrogen distributions are characteristic of spiral galaxies but not pre-spiral galaxy forms. Because the rotation velocities of spiral galaxies are determined by the motion of neutral hydrogen, it is desirable to know the process for neutral hydrogen accumulation in late-time galaxies.
In the plasma universe model, spiral galaxies form from the interaction of current-carrying filaments at regions where electric fields exist. The individual filaments are defined by the Carlqvist Condition that specifies the relationship between gravitational and electromagnetic constraining forces (Verschuur, 1995). In this model, whether or not neutral hydrogen and other neutral gases form from hydrogenic plasma depends of the efficiency of convection of plasma into the filament.
When an electric field is present in a plasma and has a component perpendicular to a magnetic field, inward convection of the charged particles occurs. Both electrons and ions drift with velocity

v = (E X B)/B2

so that the plasma as a whole moves radially inwards. The material thus forms as magnetic ropes around magnetic flux tubes. Magnetic ropes thus contain material filaments that have a higher density than the surrounding plasma.
When a plasma is only partly ionized, the electromagnetic forces act on the non-ionized components only indirectly through the viscosity between the ionized and non-ionized constituents. For a filament, the inward radial velocity drift is
vr = Ez/Bcp

for the case of an axial electric field and azimuthal magnetic field (induced by the axial current Iz). Hence, at a large radial distance r, the rate of accumulation of matter into a filament is

-dMd t

=

27rrvrPm

=

(27rr)

2

P

Ez m /1-0 I-z

(4)

Marklund (1979) found a stationary state when the inward convections of ions and electrons toward the axis of a filament was matched by recombination and outward diffusion of the neutralized plasma (Figure 3). The