and Cosmology

Physical space
Linear regime
Redshift space
"Squashing"
8.1 Redshift Surveys of Galaxies
Fig. 8.6. The influence of peculiar velocities on
the location of galaxies in redshift space. The
upper left panel shows the positions of galaxies
(points) in redshift space, which are in reality
located on spherical shells. Galaxies connected
by curves have the same separation from the
center of a spherically-symmetric overdensity
(such as a galaxy cluster) in real space. The
explanation for the distortion in redshift space
is given in the lower panel. On large scales,
galaxies are falling into the cluster, so that
galaxies closer to us have a peculiar velocity
directed away from us. Thus, in redshift space
they appear to be more distant than they in
fact are. The inner virialized region of the
cluster generates a “Finger of God”, shown by
the highly elongated ellipses in redshift space
directed toward the observer. Here, galaxies
from a small spatial region are spread out
in redshift space due to the large velocity
dispersion yielding large radial patterns in
corresponding wedge diagrams. In the upper
right panel, the same effect is shown for the
case where the cluster is situated close to us
(small circle in lower center)
317
Collapsed
Turnaround
Collapsing
"Finger of God"
convention of denoting the transverse separation as σ
and that along the line-of-sight in redshift space as π is
followed). Clearly visible is the oblateness of the curves
of equal correlation strength along the line-of-sight for
separations 10h −1 Mpc, for which the density field is
still linear, whereas for smaller separation the finger-ofgod
effect emerges. This oblateness at large separations
depends directly on β, due to (8.8), so that β can be determined
from this anisotropy. 2 However, one needs to
take into account the fact that galaxies are not strictly
2 In fact, one can decompose the correlation function into multipole
components, such as the monopole (which is the isotropic part of
the correlation function), quadrupole (describing the oblateness), etc.
The ratio of the quadrupole and monopole components in the linear
regime is independent of the underlying power spectrum, and depends
only on β.