Probing the intergalactic medium-galaxy connection toward PKS 0405-123. II.: A cross-correlation study of Lyα absorbers and galaxies at z<0.51

We present a pilot study of the clustering properties of Ly alpha absorbers with respect to known galaxies based on 112 Ly alpha absorbers and 482 galaxies identified at z < 0.5 along the sight line toward PKS 0405 - 123. The principal goal is to determine the origin of Ly alpha absorbers based on their cross-correlation amplitude with known galaxies and to investigate a possible N(H I) dependence of the cross-correlation function. The main results of our study are as follows: ( 1) The cross-correlation function xi(ga) measured using only emission-line - dominated galaxies and Ly alpha absorbers with log N(H I) >= 14 shows a comparable strength to the galaxy autocorrelation function xi(gg) on comoving, projected distance scales of less than 1 h(-1) Mpc, while there remains a lack of cross-correlation signal when using only absorption-line - dominated galaxies. This signifies a morphology-dependent xi(ga) and indicates that strong absorbers with log N( H I) >= 14 and emission-line galaxies reside in the same halo population. (2) A maximum likelihood analysis shows that Ly alpha absorbers with log N(H I) < 13.6 are consistent with being more randomly distributed with respect to known galaxies. ( 3) Finally, we find based on this single sight line that the amplitude of xi(ga) does not depend sensitively on N( H I) for strong absorbers, with log N( H I) >= 13.6.