We test the reliability of a method to measure the mean halo mass of absorption line systems such as damped Ly \alpha absorbers ( DLAs ) .
The method is based on measuring the ratio of the cross-correlation between DLAs and galaxies to the autocorrelation of the galaxies themselves , which is ( in linear theory ) the ratio of their bias factor \overline { b } .
We show that the ratio of the projected cross- and autocorrelation functions ( w _ { dg } ( r _ { \theta } ) / w _ { gg } ( r _ { \theta } ) ) is also the ratio of their bias factor irrespective of the galaxy distribution , provided that one uses the same galaxies for w _ { dg } ( r _ { \theta } ) and w _ { gg } ( r _ { \theta } ) .
Thus , the method requires only multi-band imaging of DLA fields , and is applicable to all redshifts .
Here , we focus on z = 3 DLAs .
We demonstrate that the cross-correlation method robustly constrains the mean DLA halo mass using smoothed particle hydrodynamics ( SPH ) cosmological simulations that resolve DLAs and galaxies in halos of mass M _ { h } \gtrsim 5.2 \times 10 ^ { 10 } M _ { \odot } .
If we use the bias formalism of Mo & White ( 2002 ) with the DLA and galaxy mass distributions of these simulations , we predict an amplitude ratio w _ { dg } / w _ { gg } of 0.771 .
Direct measurement of these correlation functions from the simulations yields w _ { dg } / w _ { gg } = \overline { b } _ { DLA } / \overline { b } _ { gal } = \hbox { $ 0.7 % 3 \pm 0.08 $ } , in excellent agreement with that prediction .
Equivalently , inverting the measured correlation ratio to infer the ( logarithmically ) averaged DLA halo mass yields \langle \log M _ { DLA } ( \hbox { M$ { } _ { \odot } $ } ) \rangle = \hbox { $ 11.13 ^ { +0.13 } _ { - % 0.13 } $ } , in excellent agreement with the true value in the simulations : \langle \log M _ { DLA } \rangle = \hbox { $ 11.16 $ } is the probability weighted mean mass of the DLA host halos in the simulations .
The cross-correlation method thus appear to yield a robust estimate of the average host halo mass even though the DLAs and the galaxies occupy a broad mass spectrum of halos , and massive halos contain multiple galaxies with DLAs .
If we consider subsets of the simulated galaxies with high star formation rates ( representing Lyman break galaxies [ LBGs ] ) , then both correlations are higher , but their ratio still implies the same DLA host mass , irrespective of the galaxy subsamples , i.e. , the cross-correlation technique is also reliable .
The inferred mean DLA halo mass , \langle \log M _ { DLA } \rangle = \hbox { $ 11.13 ^ { +0.13 } _ { -0.13 } $ } , is an upper limit since the simulations do not resolve halos less massive than \sim 10 ^ { 10.5 } M _ { \odot } .
Thus , our results imply that the correlation length between DLAs and LBGs is predicted to be , at most , \sim \hbox { $ 2.85 $ } h ^ { -1 } Mpc given that z = 3 LBGs have a correlation length of r _ { 0 } \simeq 4 h ^ { -1 } Mpc .
While the small size of current observational samples does not allow strong conclusions , future measurements of this cross-correlation can definitively distinguish models in which many DLAs reside in low mass halos from those in which DLAs are massive disks occupying only high mass halos .