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OCR for page 356
The Peculiar Velocity Field Predicted
from the Distribution of fR IS Garages
MICHAEL A. STRAUSS AND MARC DAVIS
Umversity of California, Berkeley
ABSTRACT
We present recent results from our full-sly redshift survey of {RAS
galaxies. After briefly describing our sample selection and observations, we
use the linear theory relation between acceleration and peculiar velocity to
make predictions of the peculiar velocity field in the Local Universe. We
compare our predictions with directly measured peculiar velocities from
the Local Supercluster spiral galaxy sample of Aaronson et al. (1982) and
the elliptical galaxy sample of Lynden-Bell e! al. (1988~. In a reference
frame at rest with respect to the Cosmic Microwave Background, there Is a
systematic bunk flow in the residuals between observations and predictions.
The Local Group itself takes part in this modon, so the bunk flow disappears
in a frame at rest with respect to the Local Group. We show with the use
of N-body techniques that this type of systematic effect is at least pardy due
to small-number statistics in the tracing of the density field. We conclude
with a discussion of the challenges facing us in the future.
The N-body results show us that we have not yet achieved an optimum
algorithm for translating from redshift space to real space; we briefly
describe several alternative procedures. We compare the coherence of the
observed and predicted peculiar velocity fields with predictions from several
cosmogonical models.
To IRAS SAMPLE
Peebles (1976) describes the velours field expected at late times in
356
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HIGH-ENERGY ASTROPHYSICS
357
linear theory; the dipole anisotropy of the galaxy distn~ution around a
given galaxy is directly proportional to the peculiar velocity of that galaxy:
., HoQ06
J [(z)x do
Or x~
(1)
where V is the peculiar velocity of the galaxy in question, Q is the cosmo-
logical density parameter, and [(x) is the fractional density perturbation
at position ~ The following year, a dipole anisotropy was discovered in
the Cosmic Microwave Background (CMB) (e.g., Lubin and Held 1986),
which was interpreted as due to a peculiar motion of the Local Group (LG)
with respect to the rest frame of the CMB of 600 km sol. It was imme-
diately realized that a measurement of the distribution of nearby galaxies
could be used in concert with equation (1), and the measured LO peculiar
velocity, to make an estimate of Q. This has been tried by many authors,
usually with the simplifying assumption that the Virgo cluster is the only
gravitating mass point (see, e.g., Davis and Peebles 1983; Huchra 1988~.
~ do better requires galaxy samples that cover a large fraction of the
sky. Pioneering work using optically selected samples of galaxies has been
done by Lahav and collaborators (Lynden-Bell et al. 1989, and references
therein). In this paper we describe a survey of galaxies observed by the
Infrared Astronomical Satellite (IRAS). We have discussed our work before
In two other conference proceedings (Strauss and Davis 1988a, 1988b; Yahil
1988), and in this paper will concentrate on new results obtained since the
writing of those articles. A much more detailed account can be found in
Strauss (1989), and in several papers in preparation.
The TRAS satellite surveyed the entire sky in four broad bands in the
far-infrared, with a resolution of approximately 1' at 60pm. Because of
the full-sly coverage and the lack of Galactic extinction in the far-infrared,
the {RAS database offers a unique opportunity to study the large-scale
distribution of galaxies. We have selected galaxy candidates hom the IRAS
Point Source Catalog (1985) using the following criteria:
1. f60/f:2 ~ 3, where fx is the flux density at wavelength A. This
discriminates effectively between stars and galaxies.
2. Ebb > 5, in a region not affected by confusion at 60pm. With
these restrictions, our sample covers 87.6% of the sky.
3. fee > 1.936 Jy.
We have obtained optical identifications and redshifts of the approx-
imately 4,500 objects meeting these criteria, thus obtaining a sample of
roughly 2,550 galaxies. The vast majority of the non-gal~es in the sample
are associated win stars and Infrared cirrus at Ebb < 10 (see Yahil 19~
for a description of how optical identifications were made at these low
latitudes). Below, we discuss some biases of the sample selection, and our
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358 AMERICAN AND SOVIET PERSPECTlYES
[RAS Galaxies f60 > 1.936 dy ,,,..
.! · ~ 4 ~ ~
\ `\~$ \ =¢ * ~ ~ . .~* !
~"'~'--~*';'')*'-*~'p~'-~* ~/''~"-'*
~ ~ A 2539 OBJECTS PLO ~ i Ed
`~~ ~:'~'~
360
FIGURE 1 Me distribution of galaxies in the surrey, plotted in Galactic coordinates. The
sample does not include galaxies at |b| < 5, and there are other regions at high Galactic
latitudes which are not covered due to confusion or incompleteness of the IRAS survey.
attempts to correct for them. The distribution of all galaxies in the sample
Is shown in Galactic coordinates in Figure 1. Note the strong continuity of
structures across the Galactic plane, In particular, the overdensities asso-
aated with Centaurus and the Pavo-Indus-~lescopium region (l ~ 330
appear to be physically associated. The Pisces-Perseus filament (l ~ 135 ~
and the Hydra region (l ~ 280 ~ also show continuity across the plane, as
do the underdense regions centered at 1 = 90 and 1 = 220°. Compare this
figure with the corresponding Figure la in Yahil (1988~; note how much
stronger this sense of continuity is now that we have identified galaxies in
the two strips 5 < fib; < 10 .
THE PREDICTED PECUI1AR VELOCITY f HELD
As described In detail In Strauss and Davis (1988b) and Yahi! (19~),
we have used equation (1) to predict the velocity flow field within 8,000
km -is of the Local Group. The procedure we follow is slightly modified
from that of Yahil (1988~. We first fill the missing Galactic plane strip with
random "galaxies" with number density given by an interpolation of the
density in strips with 5 < Ebb < 20, under the assumption that the continuity
across the plane descried in the last section is rear A selection function is
derived using a mammum-l~elihood estimator (Yahil 1988), which is used
to weigh the galaxies to compensate for the magnitude limit of the sample.
A value of Q is derived by requiring that equation (1) reproduce the 600
km s~: peculiar velocity of the Local Group inferred from the CMB dipole.
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HIGH-ENERGY ASTROPHYSICS
359
For an adopted value of Q = 0.7, the predicted peculiar velocity of the
Local Group is 650 lan s~i towards 1 = 250, b = +45, some 22 from
the CMB dipole direction of 1 = 270, b = +30 (Lubin and Villela 1986~.
Strauss and Davis (1988b) show that the majority of this acceleration is due
to material within 4,000 km s~t of the Local Group.1
We can go further by using equation (1) to make estimates of the
peculiar velocity of every galaxy in the sample. We restrict ourselves to
objects within 8,000 km s-i of the Local Group, because the sample
becomes prohibitively sparse at greater distances. In practice, our estimate
of the peculiar velocity of a galaxy at position x Is given by:
V( ~ HoQ0 6
41rn~
Iga axles ~
S(l z-z: D(z-z:) _ H Q° 6 /3 +W(S) (2)
Here n1 is the measured galaxy density, ¢(x~) is the value of the
selection function at distance x:, and S is a smoothing on small scales, to
be described further below. The second term corrects for the fact that the
sum is not spherically symmetric for a point displaced from the origin, and
W(S) is an additional correction applied when the source is within one
smoothing length of the edge of the sample.
The measured redshift cz. of a oalaxv may be expressed as:
, , 4~ ~ ~
cz = distance ~ (V- VEG) X,
(3)
where V and VLG are the peculiar velocity vectors of the galaxy and the
Local Group, respectively, and x is the UDut vector pointing from the Local
Group to the galaxy. We separate peculiar velocities and distances using
an iterative procedure: galaxies are initially assumed to be at their redshift
distances (V-0), and equation (2) is used to make a first estimate of the
peculiar velocity field. Distances are then updated using equation (3) and
the process is repeated until convergence. Q is kept fixed throughout this
procedure, and the value of V[,G used is that derived Mom the IRAS sample
itself on each iteration A "buffer zone" between 8,000 km s~: and 10,000
An s~i prevents galaxies from being lost from the sample if their peculiar
velocities take them beyond 8,000 An sol. The resulting peculiar velocity
field converges with a standard deviation of residuals less than 10 km s~i
after eight iterations.
There are several subtleties associated with this process. In regions
that are Finalized, or even overdense by a factor of several, equation (1)
no longer holds, and this iterative procedure may cause chaos. Thus we
iWe will express distances in terms of radial velocities, as we do here, in order to bypass the
necessity of spewing the Hubble Constant.
OCR for page 360
360
AMERICAN AND SOVIET PERSPECTIVES
will never be able to properly model the "Finger of God" effect seen in the
cores of clusters. We have thus collapsed the galaxies in seven cluster cores
(Virgo, Ursa Major, Fornax, Endanus, Centaurus, Hydra, and Perseus) to a
common redshift, and have suppressed the mutual gravitational attraction
of galaxies within each cluster. Another related problem is that equation
(2) diverges at small separations. Note that because the selection function
drops sharply with distance, a pair of galaxies separated by a small amount
at a large distance from us can give each other a tremendous kick In order
to suppress this, we adopt a smoothing law, S(r) = (r/r5~3 for r ~ r5, where
r5, the smoothing length, is taken to be the mean interparticle spacing at
that distance, or 500 km s-i, whichever is larger.
The resulting velocity field is similar to that shown in Figure 10 of
Yahil (1988), and will not be reproduced here. As those figures show, the
predicted velocity field is dominated by two large mass concentrations in
Hydra-Centaurus and Perseus-Pisces. We will-compare these predictions
with the observed velocity field in the next section.
COMPARISON WllI[ THE OBSERVED PECULIAR VELOCITY DATA
Burstein (1989) reviews the current status of direct observations of the
peculiar velocity now field. In this paper, we will make comparisons of our
predictions with two data sets: the subset of the Aaronson et al. (1982)
Local Supercluster spiral galaxies with high~uality observations defined
by Faber and Burstein (19~), and the independent peculiar velocities of
individual galaxies, groups, and clusters of the Seven Samurai elliptical
galaxy sample, listed In Table 4 of Faber et al. (1989~. Figure 2 shows
the distribution of peculiar velocities in a slice through the plane of the
Local Supercluster, using the plotting technique introduced by Lynden-Bell
et al. (1988~. All galaxies in the two samples within 22.5 of the plane
are plotted, and the length of the line attached to each point is equal to
the radial peculiar velocity. Solid symbols are used for positive peculiar
velocities, and open symbols are used for negative. In the first panel of
this figure, we show the positions of the well-lmown clusters that fall in
this projection; the symbols are indicated in the figure caption. In panel
(b), the observed peculiar velocities are plotted, panel (c) shows the IRAS
predictions, and panel (d) shows the difference of (b) and (c). It is indeed
a remarkable fact that is able to reproduce the qualitative nature of the
velocity Dow field, perhaps the first direct indication that peculiar velocities
are generated by gravity, and that galaxies at least approximated trace
the mass distribution of the underlying dark matter. However, there are
some systematic differences between observations and predictions. Note,
for instance, that whereas the observed peculiar velocities (panel by to the
upper right of the Ursa Major region are large and negative, the predicted
OCR for page 361
4000
2000
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-4000
4000
2000
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-4000
HIGH-ENERGY ASTROPHYSICS
_1 1, 1 1 1 1 1 ~ 1 1 1 1 1 ' ' ' 1 1
- (a) -
~ C VUm
0
0
361
' 1 ' 1 1 1 ' ~ 1 1 1 1 1 1, 1 1 ~ 1
_ ~\\ o (b)
._ O ,/
Pa
_
Pr
- 1 1 1 1 1
1 1 1 1 ' 1 1 1 1 1 _
- ~: o 'C?
~O
;~ cs o
q,. D~o
~ oo
~ ~ ~ ~, 8 ~-
_ _ _
_ ' · _ _ ,
_ I I I I I _ ~, I,,, I,,, I,,
-4000-2000 0 2000 4000 -4000-2000 0 2000 4000
~ '.0 -w
_ 0 0
o
- 1 1 1,, 1 1,,, 1 1 -
~1
.,,,,,. ,o
~ O O
~,~!,'.0'°
:0 7~0.\ .
2
, 1 , , , 1 ,
FIGURE 2 The velocity field of the Aaronson et al. and Faber et a1. gala~y samples in
a slice through the Local Supercluster plane, in the CMB hame. (a) Ihe positions of the
major clusters [ailing in the slice: V = V~rgo, Um = Ursa Major, C = Centaurus, Pa
= Pavo, Pe = Perseus, and Pi = Pisces. (b) The observed veloci~ field. (c) Ihe IRAS
predicted velocin~r field. (d) The dillerence between (b) and (c).
motions (panel c3 are very quiet; predicts that the pulls of the Pisces-Perseus
and Hydra-Centaurus superclusters appro~mately balance in this region.
Note also the ve~y large observed peculiar velocities towards Centaurus;
IRAS predicts motion of the same sigr~, but of smaller amplitude. In panel
(d), there is a systematic motion seen in the difference between predicted
and obsened peculiar velocities, as if there is a buLk Dow component to
the motion that IRAS does not see. We find consistent solutions for the
buLk flow using the Aaronson et al. and Faber e' al. galaxies separately as
well as together: 250 km s~i pointing towards 1 = 320, b = -35 .
In Figure 3, the same compar~son of observed and predicted peculiar
velocities is made, this time in a frame at rest with respect to the Local
OCR for page 362
362
4000
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o
-2000
-4000
4000
2000
o
-2000
-4000
AMETtICAN AND SOVIET PERSPECTIVES
_1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ 1 1 1
- (a) -
C VUm
Pa
Pi
- 1' ~ ~ 1 ~
O.,, c, ,.,,,,,,0 ,,0
- Am,, 0 i": ' 0 0
_ jets
~ ~ WeI~.t
1 1 1 1 ~ 1 IS I ~ 1 1 1 1 1, 1 1 1 1
. ° (b) -
. _ °. . ° oo _
o i,,
_ . o o. .
_ o°, - ; ,,.~"~2o'O'
he ',,.r,l° ~`
: _
t
' T ~ I ' I l, ' I 1 1 ~ I I I
_ ~-~ Dt2O _
o. O - 0 ' -. ..o
~ ~ ,, oso O O O O ~, ~
..' .` _
(d) -
. _
I , I I, l l l,, l'l l, l t l ,, l l l ' l ~
-4000-2000 0 2000 4000 -4000-2000 0 2000 4000
-
FIGIJRE 3 As in F~gure 2, but plotted in the rest hame of the Local Group.
Group. This is not a tribal change, because in order to transform the IRAS
predicted motions, we use the Local Group motion as predicted by IRAN,
while the observed LO frame peculiar velocities are merely the difference
between their redshift and observed distance. Note now in panel (d) that
the sense of an overall bunk flow to the residuals between observed and
predicted peculiar velocities has vanished, and we are left with mostly
small-scale motions that we have not modelled correctly. Thus Me Local
Group itself takes part in the bulk Dow seen in the residuals in Figure
2d. The only significant systematic effect remaining in the LO frame is a
strong infall in the direction of Hydra-Centaurus that IRAS is unable to
reproduce. This plot should be compared with Figure 7b, panel 2, of Faber
and Burste~n (1988), which shows residuals of observed peculiar velocities
after subtracting away the predictions of their Great Attractor model.
This comparison shows that there is a bunk motion within a sphere of
4,000 km s-i radius, which IRAS is not properly modelling. Moreover,
OCR for page 363
HIGH-ENER~ ~TROP~SICS
363
the Local Group also takes part in this motion; most of the deviation of
the IRAS calculated peculiar velocity for the Local Group from the value
measured from the CMB dipole can be attributed to this motion. We show
in the next section this may be explained as a purely statistical effect caused
by dilute sampling of the density field.
COMPARISON WITH N-BODY MODELS
Our iteration scheme can be tested with N-body models for which we
know the true distances of every point. We used N-body models consisting
of 262,144 particles in a box 360 Mpc on a side (Ho = 50 km s~i Mpc-~)
in an Q = 1 universe, with an initial power spectrum of perturbations
appropriate for universe dominated by Cold Dark Matter, and evolved
until the mars density contrast in a sphere of radius 16 Mpc is b-i = 0.5.
The velocity field was smoothed with a Gaussian of width 100 lan sol.
Particles with peculiar velocities of 600 km s~t, lying in regions of local
overdensity ~ with -0.2 ~ ~ < 1.0, and with smooth local velocity field,
were chosen as Local Group candidates. "IRAS" Dw`-limited catalogues
were constructed around these Local Group candidates by selecting objects
according to the number density and selection function of the real data; no
biasing was applied in the galaxy selection, so these objects do trace the
mass of the simulation. For more details, see Gorski e! al. (1989~.
We then ran our iteration program on the N-body "IRAS" catalogue.
That is, we gave the program only the Formation on the redshift of each
particle as observed in the rest frame of the EG particle, and let it run
to predict the true distances and the peculiar velocity field of the particles
in the simulation. Q was set equal to unity for these simulations. We
emphasize that the motivation is not so much to test the Cold Dark Matter
cosmogony, but rather to test our iteration scheme of peculiar velocities in
the presence of non-linear erects and shot noise. A total of 18 realizations
were run: nine with different "Local Groups," and nine more with a single
"Local Group," but different random numbers selecting the galaxies in
the suney. In Figure 4, we show the direction for the predicted peculiar
velocity of the Local Group in each of these models. They all have been
rotated so that the true direction of the Local Group particle in each case
is 1 = 270, b = +30 . Notice that the scatter is of the order of 15-20,
comparable to the difference between the true and predicted motions of
the Local Group.
In one of these models, we selected a sample of points to match
closely the distn~ution of galaxies with observed peculiar velocities in the
samples used in the previous section. With this sample, we can make
a direct comparison of true and predicted radial peculiar velocities, and
see how these results compare with the real universe described in the
OCR for page 364
364
AMERICAN AND SOVIET PERSPECTIVES
1 ' 1
9 LG's
~ 9 Realizations of 1 LO
50
= 2.0
/\
Eli,
* _
~_
~_ * *_
*_
_
~O _
C'
._ _ _
c)
-
* ~
-50
. 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 ~1
0 1 00 200 300
Galactic Longitude
FIGURE 4 The distribution of predicted directions of the "Local Groups" in eighteen
N-body realizations of the sample. The large star is placed at 1 = 270, b = 30 .
previous section. The true peculiar velocities were perturbed by a gaussian
"error" with a standard deviation of 15% of the true distance to mimic the
observational situation. Unlike the real observations, we assume here that
the distances are measured exactly. In Figure 5, we show the results. Panel
(a) shows the distn~ution of Sue peculiar velocities in the CMB frame,
in exact analogy with Figure 2b. Panel ~) is then We predicted peculiar
velocity as given by the iteration procedure, and (c) is the difference
between the two. FinaLl~r, (d) is the difference of "observed" and predicted,
now in the L`G frame. Note the very strong bunk Dow seen in the residuals
in panel (c), with an amplitude of ~ 200 km s-l. Unlike the real universe,
however, there is still a significant bunk Dow in the LG frame residuals,
with an amplitude of ~ 100 km s~i (panel d), which simply says that the
deviation of the predicted LG motion from its true direction is at least
partly due to small-scale effects in this model.
We have done the same experiment in which we have assigned 15%
errors to the true distances of the gal~es to more closely simulate the
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HIGH-ENERGY ASTROPHYSICS
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2000
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365
I I I I I \\ 1 i1 ~ I I I I I I I I I _ I I I I I I \\ I t1 ~ I I l I I I i I 1
~(a) I I (b)
° O...o~ ~
O.,. '0 09~&o
O & 0
o
o
t `,
- 1 , 1 , 1 ~ ~ ~ ~ , ~ ,
1 1 1 1 1 1 ool.l 1 1 1 1 1 ' 1 1 1 1,
° (C)
~i1,
D O_ O - . ~
._ _ _ 0'-'. Oo ~
- _ o & o ~ o oo e °
_ o" °, ~
o
_
- 1 1 1 ~ 1 ~
1 1 1 1 1 1 !.1 `1 ~ ~ 1 1 1 1 1 1 1 1_
- , (d) -
o
O _
.0
_Oo 0"°~
.o o
~ F ~, t o. · ~
- ~o W.° ,.o
_ ~ o
_ o ·; · O
- o · . o ~-
_ , ~ ~ ~ oO ° J ~
_ ~' _
1_ 1 1 1 1 1,,, 1, 1 · 1 1 -
o° ~_ .
t ~_ _ t · `.
I I I `1' 1-
-4000-2000 0 2000 4000 -4000-2000 0 2000 4000
FIGURE 5 The results of an N-body experiment simulating the comparison between
obsenred and predicted peculiar velocities. (a) The true peculiar veloaty field in the CMB
frame. (b) The predicted peculiar velocities for the same galaxie~ (c3 The difference
between (a) and (b3. (d) l~ne difference between obsened and predicted in the LG ~me.
Obsenations; we filld that this seriously degrades the good agreement
between "measured" and predicted pec~'liar veloci~r.
Why is it that there seems to be a missing component of granty in the
CDM model, where the pO=tS are explicitly chosen to trace the mass? In
these models, there is very little power on scales larger than the sample
(8,000 km s~~) to cause the whole sample to translate (Juszkiewicz e! al.
1989~. Our interpretation is that this effect is caused by shot noise. Imagine
a toy model in which the buLk of the modon of the region within 3,000 km
s~: is caused by a large structure at 6,000 km s~~. Because of the extremely
dilute sampling of the catalogue, the overdensity of this structure may be
traced by only a small number of points, and this number will be subject
to Poisson statisticse Thus, the inferred gravity from this structure can be
OCR for page 366
366
AMERICAN AND SOVIET PERSPECTIVES
IRAS Galaxies 1.2 1.936 Jy ~
~ art. ~*~*~*~ . * ~ 2~6 OBJECTS PLOWED
'=:*,, - At"'
360
FIGURE 6 Abe distribution of galaxies in Galactic coordinates of objects in a deeper
IRAS redshitt surveyor, in preparation. Note the appreciable overdensities associated with
the Perseus-Pisces ~ ~ 120 - 150, b ~ -30 - +30 ~ and Hydra-Centaurus (1 ~ 280 -
O a
330, b ~ 0- +45 ~ regions.
in error, affecting the predicted peculiar velocities III a systematic way.
Detailed calculations of the noise in the acceleration of galaxies relative to
the Local Group is consistent with the observed amplitude of the effect,
which must be at least partly responsible for the missing bunk motions seen
in the predicted velocity field of the real IRAS galaxies.
UNRESOLVED ISSUES, AND THE WORK AEIEAD
In the last section, we have identified shot noise as a stumbling block in
the interpretation of the comparison of our predictions with observations.
Thus we have started a deeper survey of IRAS galaxies, Dux-limited to
1.2 Jy, to rectify this situation. When the survey is completed, hopefully
in early 1991, we shall have redshifts for ~ 5,500 IRAS galaxies selected
uniformly over the sly. Figure 6 shows the distribution on the sly of
the additional objects. Because this sample goes deeper, it emphasizes
structures at distances of 3,000 - 5,000 lain sol; note in particular the strong
enhancements in the Perseus-Pisces region and the Hydra-Centaurus region.
We are in the process of using the IRAS predicted distances for the
Aaronson e! al. galaxies to construct lblly-Fisher diagrams. We hope to
make a more robust estimate of Q by finding that value that minimizes
the scatter in the TF diagram. The recent work of Dekel and Bertschinger
(1989) provides another powerful way of making comparison between TRAS
predictions and observed peculiar velocities; we will soon be able to place
OCR for page 367
HIGH-ENERGY ASTROPHYSICS
367
constraints on the relative overdensities of galaxies and dark matter
different regions of space.
ACKNOWLEDGMENTS
We thank our collaborators in this project, Amos Yahil and John
Huchra, for allowing us to use unpublished data, and for many helpful
discussions. We are grateful to Dave Burstein for sending us machine-
readable versions of me observed peculiar velocity data. MAS acknowledges
the support of an NSF Graduate Fellowship.
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Strauss, M.A 1989. Ph.D. thesis. University of California, Berkeley.
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Representative terms from entire chapter:
peculiar velocities
