ON THE EFFECTIVE SPATIAL SEPARATIONS IN THE CLUSTERING OF FAINT GALAXIES

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.