Bf. Roukema et D. Vallsgabaud, ON THE EFFECTIVE SPATIAL SEPARATIONS IN THE CLUSTERING OF FAINT GALAXIES, The Astrophysical journal, 488(2), 1997, pp. 524-531
Several recent measurements have been made of the angular correlation
function w(theta, m) of faint galaxies in deep surveys (e.g., in the H
ubble Deep Field, hereafter HDF). Are the measured correlations indica
tive of the gravitational growth of primordial perturbations, or of th
e relationship between galaxies and (dark matter-dominated) galaxy hal
os? A first step in answering this question is to determine the typica
l spatial separations of galaxies whose spatial correlations, xi(r, z)
, contribute most of the angular correlation. The median spatial separ
ation of galaxy pairs contributing to a fraction p of the angular corr
elation signal in a galaxy survey is denoted by r(eff)(p) ( 3) and com
pared with the perpendicular distance, r(perpendicular to), at the med
ian redshift, z(med), of the galaxies. Over a nide range in spatial co
rrelation growth rates, epsilon, and median redshifts, r(eff)(50%) is
no more than about twice the value of r(perpendicular to), while r(eff
)(90%) is typically 4 times r(perpendicular to). Values of r(eff)(p) f
or redshift distributions representative of recent surveys indicate th
at many angular correlation measurements correspond to spatial correla
tions at comoving length scales well below 1 h(-1) Mpc. For Omega(0) =
1 and lambda(0) = 0, the correlation signal at 4'' predominant in the
Villumsen et al. (1996) estimates of w(theta, m) for faint HDF galaxi
es corresponds to r(eff)(50%)(HDF) approximate to 40 h(-1) kpc; other
cosmologies and angles up to 10'' can increase this to r(eff)(50%)(HDF
) less than or similar to 200 h(-1) kpc. The proper separations are (1
+ z) times smaller, where 1 less than or similar to z less than or si
milar to 2. These scales are small: the faint galaxy angular correlati
on measurements are at scales where halo and/or galaxy existence, let
alone interactions, may modify the spatial correlation function. These
measurements could be used to probe the radial extent of halos at hig
h redshift.