In order to use satellite galaxies to probe the potentials of
host galaxies, one needs to *define* an appropriate sample
of host and satellite galaxies. Unlike cosmology simulators who are
blessed with full 6-dimensional phase space information, observers
are, of course, limited to 3 dimensions (RA, DEC, and redshift).
Given this limited information, then, one must base the selection
criteria on projected radii (evaluated at the redshift of the host)
and relative radial velocities, *dv*, of the candidate
hosts and satellites.
To guarantee that the dynamics of the satellites are
determined solely by their host galaxy, the hosts must be
determined to be "isolated" in some sense. That is, if another
large, bright galaxy is too close to a candidate host galaxy
to guarantee that the satellite orbits are affected solely
by the candidate host, that candidate host and its satellites are rejected
from the sample. Satellites must, necessarily, be fainter than
their host, be found within some reasonable projected radius
of the host, and have some reasonable line of sight velocity with
respect to the host.

There are a number of different selection criteria that have been used in the recent literature, and three sets of selection criteria that have been used in more than one investigation are summarized below:

Hosts must be at least 8 times brighter than any other galaxy that is within

*r*_{p}< 500 kpc and |*dv*| < 1000 km sec^{-1}. In addition, hosts must be at least 2 times brighter than any other galaxy that is within*r*_{p}< 1 Mpc and |*dv*| < 1000 km sec^{-1}. Satellites must be at least 8 times fainter than their host, must be found within*r*_{p}< 500 kpc, and must have |*dv*| < 500 km sec^{-1}. Here*h*= 0.7 has been adopted ([20], [64]).Hosts must be at least 2 times brighter than any other galaxy that falls within

*r*_{p}< 2.86 Mpc and |*dv*| < 1000 km s^{-1}. Satellites must be at least 4 times fainter than their host, must be found within*r*_{p}< 714 kpc and must have |*dv*| < 1000 km s^{-1}. Here*h*= 0.7 has been adopted ([64], [65], [66], [67]).Hosts must be at least 2.5 times brighter than any other galaxy that is within a projected radius of

*r*_{p}< 700 kpc and a relative radial velocity difference of |*dv*| < 1000 km sec^{-1}. Satellites must be at least 6.25 times fainter than their host, must be found within*r*_{p}< 500 kpc, and the host-satellite velocity difference must be |*dv*| < 500 km sec^{-1}. Here*h*= 0.7 has been adopted ([64], [68]).

Although the above criteria may seem lax or even somewhat arbitrary, in the case of the first two sets of criteria, both the Milky Way and M31 would be excluded from the sample of hosts. That is, these particular selection criteria give rise to samples of unusually isolated host galaxies. In addition, both Prada et al. [27] and Brainerd [64] adopted a number of different selection criteria in their investigations of the satellites of SDSS galaxies and concluded that there were no statistical differences between results that were obtained with different selection criteria. In other words, provided sufficiently "reasonable" criteria are adopted for selecting isolated hosts and their satellites, the results of the investigations are stable to modest differences in the details of those selection criteria.

No matter what selection criteria are adopted, however, there
will always be "interlopers" in the satellite data. Interlopers
are galaxies that are falsely identified as satellites; that is, they
pass the formal selection criteria, but they are not, in fact, dynamically
associated with the host galaxy.
The presence of interlopers will artificially inflate any measurement
of the velocity dispersion of genuine satellites, and recent
investigations of satellite dynamics
([27],
[65],
[66],
[67])
have corrected for the effects of interlopers by modeling the
distribution of host-satellite velocity differences
as the sum of a Gaussian distribution (due to the genuine
satellites) and a constant offset (due to the interlopers). Prada et al.
[27]
used numerical
simulations to show that this is a sensible way in which to correct
for the effects of interlopers. Moreover, both Brainerd & Specian
[66] and Prada et al.
[27]
have pointed out that an
accurate determination of the velocity dispersion profile,
_{v}(*r*_{p}),
for satellite galaxies depends on a proper determination of the
interloper fraction as an explicit function of the projected radius.
That is, by purely geometrical effects, the interloper fraction is
necessarily an increasing function of *r*_{p}.
An example
of fitting a "Gaussian plus offset" to the distribution of velocity
differences for late-type galaxies and early-type galaxies in the
2dFGRS is
shown in Figure 4. One can clearly see from this
figure that the velocity
dispersion of the satellites is a function of the morphology of the
host galaxy (being larger for early-type hosts than late-type
hosts), and that the interloper fraction increases with projected
radius.

The above "Gaussian plus offset" fit to the distribution of host-satellite
velocity differences accounts for the fact that the number of
interlopers is a function of projected radius, and it assumes *a
priori* that the number of interlopers at a given projected radius is
constant with |*dv*|. Recently, however, van den Bosch et al.
[69]
used simulations
of galaxy redshift surveys to investigate this and found a sharp
increase in the number of interlopers for small relative velocities.
van den Bosch et al.
[69]
note, however, that the value of
_{v} that is
determined from a simple "Gaussian
plus offset" fit is not strongly affected by the fact that the
number of interlopers varies with |*dv*|. This is because the
best-fitting value of
_{v}
is rather insensitive to the precise value of the interloper fraction.
Brainerd [67]
also finds that the number of interlopers
is larger for small values of |*dv*| than it is for large values of
| *dv*|, but that the effect is not nearly as pronounced as found
by van den Bosch et al.
[69].
Given the size
of the error bars on the distribution of host-satellite velocity
differences in the current observational samples, then, it would appear
that the simple "Gaussian plus offset" fit to the distribution of
velocity differences is more than adequate to the task of estimating
_{v}(*r*_{p}).