Using cosmological hydrodynamic simulations we measure the mean transmitted flux in the Ly \alpha forest for quasar sightlines that pass near a foreground quasar .
We find that the trend of absorption with pixel-quasar separation distance can be fitted using a simple power law form including the usual correlation function parameters r _ { 0 } and \gamma so that ( \left < F ( r ) \right > = \sum \exp ( - \tau _ { eff } ( 1 + ( \frac { r } { r _ { 0 } } ) ^ { - \gamma } ) ) ) .
From the simulations we find the relation between r _ { 0 } and quasar mass and formulate this as a way to estimate quasar host dark matter halo masses , quantifying uncertainties due to cosmological and IGM parameters , and redshift errors .
With this method , we examine data for \sim 3000 quasars from the Sloan Digital Sky Survey ( SDSS ) Data Release 3 , assuming that the effect of ionizing radiation from quasars ( the so-called transverse proximity effect ) is unimportant ( no evidence for it is seen in the data . )
We find that the best fit host halo mass for SDSS quasars with mean redshift z = 3 and absolute G band magnitude -27.5 is \log _ { 10 } { M / { M _ { \odot } } } = 12.48 ^ { +0.53 } _ { -0.89 } .
We also use the Lyman-Break Galaxy ( LBG ) and Ly \alpha forest data of Adelberger et al in a similar fashion to constrain the halo mass of LBGs to be \log _ { 10 } { M / { M _ { \odot } } } = 11.13 ^ { +0.39 } _ { -0.55 } , a factor of \sim 20 lower than the bright quasars .
In addition , we study the redshift distortions of the Ly \alpha forest around quasars , using the simulations .
We use the quadrupole to monopole ratio of the quasar-Ly \alpha forest correlation function as a measure of the squashing effect .
We find that this does not have a measurable dependence on halo mass , but may be useful for constraining cosmic geometry .