ON THE CLUSTERING OF LY-ALPHA CLOUDS, HIGH-REDSHIFT GALAXIES, AND UNDERLYING MASS

We examine the correlation property of Ly alpha forest (along the line of sight) utilizing a hydrodynamic simulation of Ly alpha clouds in a cold dark matter universe with a cosmological constant, and compare i t to the correlation of underlying mass and galaxies. A consistent pic ture seems to emerge: the correlation strength for a given set of obje cts is positively correlated with their characteristic global density and the differences among the correlations of galaxies, Ly alpha cloud s, and mass reflect the differences in density that each trace. We fin d that the galaxies are strongly biased (nearly independent of scales) over mass by a factor of similar to 3.0, in accord with recent observ ations of high-redshift galaxies. The correlation strength of Ly alpha clouds with column densities of 10(13)-10(14) cm(-2) is comparable to that of total mass. Positive correlations with a strength of 0.1-1.0 are found for Ly alpha clouds in the velocity range 50-300 km s(-1). T he correlation is less than 0.3 at Delta v > 300 km s(-1), but here ou r simulated box is too small to give a reliable measure. Among the cor relational measures examined, an optical depth correlation function (e g. [5]) proposed here may serve as the best correlational measure. It faithfully represents the true correlation of the underlying matter, e nabling a better indication of the relationship between galaxies, Ly a lpha clouds, and underlying mass. Furthermore, it appears to be a bett er alternative to the conventional line-line correlation function, bec ause it does not require ambiguous postobservation fitting procedures such as those commonly employed in the conventional line-fitting metho ds. Neither does it depend sensitively on the observational resolution (e.g., FWHM), insofar as the clouds are resolved (i.e., the FWHM is s maller than the line width). Conveniently, it can be easily measured w ith the current observational sensitivity without being contaminated s ignificantly by the presence of noise.