On the Clustering of Lyα Clouds, High-Redshift Galaxies, and Underlying Mass

We examine the correlation property of Lyα forest (along the line of sight) utilizing a hydrodynamic simulation of Lyα clouds in a cold dark matter universe with a cosmological constant, and compare it to the correlation of underlying mass and galaxies. A consistent picture seems to emerge: the correlation strength for a given set of objects is positively correlated with their characteristic global density and the differences among the correlations of galaxies, Lyα clouds, and mass reflect the differences in density that each trace. We find that the galaxies are strongly biased (nearly independent of scales) over mass by a factor of ~3.0, in accord with recent observations of high-redshift galaxies. The correlation strength of Lyα clouds with column densities of 10¹³-10¹⁴ cm^-2 is comparable to that of total mass. Positive correlations with a strength of 0.1-1.0 are found for Lyα clouds in the velocity range 50-300 km s^-1. The correlation is less than 0.3 at Δv > 300 km s^-1, but here our simulated box is too small to give a reliable measure.

Among the correlational measures examined, an optical depth correlation function (eq. [5]) proposed here may serve as the best correlational measure. It faithfully represents the true correlation of the underlying matter, enabling a better indication of the relationship between galaxies, Lyα clouds, and underlying mass. Furthermore, it appears to be a better alternative to the conventional line-line correlation function, because it does not require ambiguous postobservation fitting procedures such as those commonly employed in the conventional line-fitting methods. Neither does it depend sensitively on the observational resolution (e.g., FWHM), insofar as the clouds are resolved (i.e., the FWHM is smaller than the line width). Conveniently, it can be easily measured with the current observational sensitivity without being contaminated significantly by the presence of noise.