CLUSTERING OF GALAXIES IN THE HUBBLE-DEEP-FIELD

We compute the two-point angular correlation function w(theta) for a s ample of similar to 1700 galaxies to a magnitude limit equivalent to R similar to 29.5, using a catalog derived from the Hubble Deep Field i mages. A nonzero value of w(theta) is measured down to R = 29.0. The a mplitude of w(theta) at the bright magnitude limit (R similar to 26) i s consistent with previous ground-based observations. At fainter magni tudes the clustering amplitude continues to decrease, but at a slower rate than that predicted by the power law w(1 '') proportional to 10(- 0.27R) observed for shallower samples. The observed w(theta) over the magnitude range 20 < R < 29 is consistent with linear evolution of the clustering of a galaxy population which at present has a correlation length r(0) of about 4 h(-1) Mpc, close to that of local IRAS galaxies . We also investigate the impact that magnification bias induced by we ak gravitational lensing may have on our results. Although the observe d amplitude of w(theta) can differ from the true amplitude by up to 30 %, this effect is not large enough to influence our conclusions. Final ly, by using a color-selected sample, we examine whether the expected effects of magnification bias can be used for an independent determina tion of cosmological paameters in deep images. We conclude that the am plitude of the effect can be large and in some cases even produce an u pturn of the amplitude of the correlation with limiting magnitude. How ever, we find that it is not possible to detect the effects of magnifi cation bias on w(theta) from images alone. If redshift information bec omes available, it is possible to measure the effects of magnification bias directly and thus constrain the density parameter Omega(0) and t he bias factor b.