Measurements of the velocity differences (delta v's) in pairs of galaxies from large statistical samples have often been used to estimate the average masses of binary galaxies. A basic prediction of these models is that the delta v distribution ought to decline monotonically. However, some peculiar aspects of the kinematics have been uncovered, with an anomalous preference for delta v approx. equal to 72 km s(sup-1) appearing to be present in the data. The authors examine a large sample of binary galaxies with accurate redshift measurements and confirm that the distribution of delta v's appears to be non-monotonic with peaks at 0 and approx. 72 km s (exp -1). The authors suggest that the non-zero peak results from the isolation criteria employed in defining samples of binaries and that it indicates there are two populations of binary orbits contributing to the observed delta v distribution

Salpeter, Edwin E.

Schneider, Stephen E.

English

NASA Technical Reports Server

SELECTION EFFECTS AND BINARY GALAXY VELOCITY CES 
Stephen E. Schneider, University of Massachusetts 
Edwin E. Salpeter, Cornell University 
I. Introduction 
Measurements of the velocity differences (Av’s) in pairs of galaxies from large statistical 
samples have often been used to estimate the average masses of binary galaxies. A basic pre- 
diction of these models is that the Av distribution ought to decline monotonically. However, 
some peculiar aspects of the kinematics have been uncovered, with an anomalous preference 
for Av M 72 kms-l appearing to be present in the data. 
We examine a large sample of binary galaxies with accurate redshift measurements and 
confirm that the distribution of Av’s appears to be non-monotonic with peaks at 0 and -72 
kms-l. We suggest that the non-zero peak results from the isolation criteria employed in 
defining samples of binaries and that it indicates there are two populations of binary orbits 
contributing to the observed Av distribution. 
11. The Observed Form of the Av Distribution 
For a complete sample of binary galaxies with velocity vectors oriented at random to 
the line of sight, the distribution of their observed Av’s should be a monotonically declining 
function of Av. Even if there was a range of orbital velocities that actually were absent, 
the resultant distribution would only be flat over this range. Tifft (1980), however, found 
non-monotonic behavior in the Av distribution. Testing a hypothesis about possible non- 
monotonic behavior against observational data is difficult if the hypothesis is made after the 
data is collected (Newman, Haynes, and Terzian 1989), but fortunately, both the quality and 
quantity of data on binary galaxies has improved greatly since Tifft (1980) developed his 
paradigm of the peculiar non-monotonic behavior. 
Neutral hydrogen velocity-difference measurements of normal spiral galaxies made at 21 
cm are now generally accurate enough to clearly distinguish between the posited 72 kms-l 
peak and the expected zero-velocity peak. Excluding the pairs from Tifft (1980)’ we have 
collected data on 102 isolated binaries that have accurate 21 cm velocities for both members 
in the literature (Schneider and Salpeter 1990). The distribution of Av’s is shown in Fig. 
1 in the form of a frequency distribution f(Av) (i.e., the value in the first bin is doubled to 
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https://ntrs.nasa.gov/search.jsp?R=19910007614 2020-03-19T19:49:16+00:00Z
reflect its narrower range), using the same binning as suggested by Tifft (1980). 
40 
30 - 
$ 20 Fig. 1-Distribution of velocity differences among 102 binary galaxies 
measured at 21 cm. rcl 
10 
216 
0 ~//~//~///~/~//~/~~//~~ 
0 72 144 
Av (km s-') 
3 a
W 
-  
The distribution has fairly significant peaks in both the 0 kms-l and 72 kms-l bins; 
beyond 72 kms-l the numbers decline smoothly. Other largely independent samples and 
measurements of binaries and groups also show a peak in the 72 kms-l bin. Tifft (1980) 
also found peaks at higher multiples of 72 km s-l, but the evidence for any individual higher- 
velocity peaks has never been very strong. Newman, Haynes, and Terzian (1989) have shown 
that any freedom in the choice of the zero point or bin size can produce apparently significant 
but spurious periodic peaks. Similar problems with the statistics seem likely to arise if special 
selection criteria are applied to the data after it is collected; any resultant enhancements 
produced in the appearance of periodicity become uninterpretable. We do not comment 
further on the analysis papers claiming to find this periodicity (Tifft and Cocke 1989 and 
references therein) except to note that the statistical significance of these works is difficult to 
evaluate because of sample overlap, differing selection criteria, and differing binning intervals. 
111. Effects of Incompleteness 
The binaries in our sample were selected on the basis of there being no likely massive 
companions within a few times the separation of the pair. This selection criterion should 
eliminate most groups with three or more comparably massive members, but the result is 
a bias in the final sample: pairs with large angular separations (and large projected linear 
separations) tend to be excluded. The binary samples are therefore incomplete. Of the 
pairs in our sample, 90% have projected separations < 136 h-l kpc. This cutoff has some 
interesting implications for the form of the Av distribution. 
486 
The pro jected-separation cutoff will eliminate preferentially those pairs lying most nearly 
perpendicular to the line of sight. A selection procedure will influence f(Av) when the ap- 
parent separation and velocity of pairs are interdependent. For circular orbits, the largest 
projected Av’ occur when the projected separations are largest, while for eccentric orbits, 
the smaller Av’s occur near apocenter, so a projected-separation cutoff may influence f(Av). 
When a projected-separation cutoff is applied to orbits of even small eccentricity a non- 
monotonic distribution can result. In Fig. 2, the effect of different projected separation 
cutoffs is shown for circular orbits and for orbits with an eccentricity of 0.33. These are 
0.5-1 
analytic models, numerically integrated, in which we follow a Keplerian orbit, consider all 
possible orientations, and find the resultant projected separation and the line-of-sight velocity 
at equal time intervals around the entire orbit. For both eccentricities we show the complete 
sample, and then we apply more restrictive projected separation cutoffs of i, i ,  and of 
the apocenter separation; the velocities are scaled relative to the pericenter velocity of the 
orbit . 
=FA - 
; \  - - i  I \ 
- 1  I \ - 
-
\ i I  - ;  I - 
- i  I ” - 
n 
3 a 
W 
4--( 
1 . O l  : \  I I I I I I I I I I 
t 1: i l  j (a) e=O.OO 
0 0.2 0.4 0.6 0.8 1 
Fig. 2-Distribution of expected velocity differences for (a) circdar and (b) eccentric orbits, 
using a complete sample (solid line) and then applying successively narrower pro jected-separation 
cutoffs at f (long dash), (short dash), and & (dotted) of the apocenter separation. 
For non-circular orbits in general, f(Av) peaks toward Av=O in a complete sample be- 
cause the binaries spend more time at larger separations orbiting more slowly. The application 
of smaller cutoff radii makes f(Av) more and more distinctly non-monotonic as the lower ve- 
locities are removed, and this could quite reasonably contribute to a peak near 72 kms-l 
since the peak occurs at some fraction of the typical orbital velocity. 
487 
Of course, in a realistic model, a wide range of orbital parameters would be likely, which 
might “wash out” the effects seen for this simple Keplerian analysis. We therefore constructed 
a more detailed model in which we traced orbital parameters for a full population of pairs 
from the time of their formation, when they would have been expanding with the Hubble 
flow. We allowed a Gaussian distribution of angular momenta and then applied projected 
separation cutoffs to the sample at the present day. Interestingly, the only natural velocity 
scale in the model is the escape velocity of the pair on a zero-energy trajectory. Solving the 
energy-balance equation, this velocity is vest = ( i G M / t ~ ) l / ~  M 72 kms-l for M x 10l2MO. 
The pairs still expanding at present are the most widely separated and when a projected 
separation cutoff is introduced, they contribute only slightly to f(Av). On the other hand, 
the pairs that had initially small separations will presently be merging, and the major axes of 
their orbits will be made smaller still by dynamical friction. The intermediate “converging” 
pairs, which are falling back together, but which have not yet collided, prove to have the most 
interesting properties with respect to the projected-separation criterion. In Fig. 3, we show 
the effect of selection criteria on the population of converging pairs, with projected separation 
cutoffs relative to the escape separation as in Fig. 2. The non-zero peak in f(Av) occurs at 
a velocity similar to 72 kms-l for the known projected separation cutoff when the average 
pair mass is - 3 x 1011 MO. 
Fig. 3-Distribution of expected 
velocity differences for a modelled 
range of orbital parameters, using 
various projected separation cutoffs 
(relative to the escape-velocity 
separation) as in Fig. 2. 
The peak around Av = 0 in the observed distribution (Fig. 1) could be produced by 
the population of merging pairs, which would be more completely sampled because of their 
smaller major axes. A reasonable facsimile of this peak could be produced, for example, by 
I 
completely sampled e = 0.7-0.8 orbits with typical 200 km s-lrotation speeds at pericenter. 
IV. Discussion 
In summary, we see evidence of non-monotonic behavior in f( Av) for Av < 100 km s-l. 
We have constructed a fairly realistic model of binary orbits, and we find that a peak occurs in 
the population of “converging” pairs at a velocity of the order of magnitude of (GAL?H,)~/~ z
72 kms-l. We further speculate that the peak at 0 kms-l is produced merging pairs. 
We can make some predictions based on our two population model. For uniform samples 
of isolated pairs, we expect that the non-zero peak will move to larger values of Av as the 
cutoff radius is decreased or the pair mass (based on absolute magnitudes, for example) 
increases. For current samples this point is difficult to test because of another bias present 
in the data-the isolation criteria also tend to select more massive pairs at larger projected 
separations. This bias may actually help keep the non-zero peak in f( Av) from being smoothed 
out despite a range of contributing binary galaxy masses. 
We suspect, therefore, that previous dynamical estimates of binary galaxy masses are 
likely to be in error. Even if our two-population model does not prove correct, it seems clear 
that selection effects must significantly limit the range of selected orbital orientations in binary 
samples, and these effects need to be better understood. If our model is correct, only the 
merging pair population has been (approximately) completely sampled, and the characteristic 
width of its f(Av) distribution is substantially narrower than has been previously suspected; 
as a result these pairs’ masses have probably been overestimated. We conclude, though, with 
a more positive message: if there is a non-zero peak in f(Av), it may ultimately provide a 
much better tool for estimating not only the masses of converging binaries but for deciphering 
the origin and evolution of binary orbits as well. 
References 
Newman, W. I., Haynes, M. P., and Terzian, Y. 1989, A p .  J., 344, 111. 
Schneider, S. E., and Salpeter, E. E. (1990) in preparation. 
Tifft, W. G. 1980, A p .  J. ,  236, 70. 
TiEt, W. G., and Cocke, W. J. 1989, A p .  J., 336, 128. 
489 
DISCUSSION 
Miller: How bad will virial mass estimates be? Is it a 10% 
effect, a factor of two, or what? 
Schneider: The mean velocity differences will tend to be 
overestimated, but the separations underestimated. The net 
effect will tend to be overestimated masses, but based on my 
simple models, probably only by factors like two for typical cut- 
off separations. 
' 490 


Selection effects and binary galaxy velocity differences

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