We present an analysis of the spatial distribution of gas and galaxies using new X-Shooter observations of z \sim 3 - 4 quasars .
Adding the X-Shooter data to an existing dataset of high resolution quasar spectroscopy , we use a total sample of 29 quasars alongside \sim 1 , 700 Lyman Break Galaxies ( LBGs ) in the redshift range 2 \lesssim z \lesssim 3.5 .
Analysing the Ly \alpha forest auto-correlation function using the full quasar sample , we find a clustering length of s _ { 0 } = 0.081 \pm 0.006 ~ { } h ^ { -1 } Mpc .
We then investigate the clustering and dynamics of Ly \alpha forest absorbers around z \sim 3 LBGs .
From the redshift-space cross-correlation , we find a cross-clustering length of s _ { 0 } = 0.27 \pm 0.14 ~ { } h ^ { -1 } Mpc , with power-law slope \gamma = 1.1 \pm 0.2 .
We make a first analysis of the dependence of this clustering length on absorber strength based on cuts in the sightline transmitted flux , finding a clear preference for stronger absorption features to be more strongly clustered around the galaxy population than weaker absorption features .
Further , we calculate the projected correlation function , finding a real-space clustering length of r _ { 0 } = 0.24 \pm 0.04 ~ { } h ^ { -1 } Mpc ( assuming a fixed slope \gamma = 1.1 ) .
Taking this as the underlying real-space clustering , we fit the 2D cross-correlation function with a dynamical model incorporating the infall/redshift-space distortion parameter , \beta _ { F } , and the peculiar velocity , \sqrt { \left < w _ { z } ^ { 2 } \right > } , finding \beta _ { F } = 1.02 \pm 0.22 and \sqrt { \left < w _ { z } ^ { 2 } \right > } = 240 \pm 60 km s ^ { -1 } .
This result shows a significant detection of gas infall relative to the galaxy population , whilst the measured velocity dispersion is consistent with the velocity uncertainties on the galaxy redshifts .
Finally , we evaluate the Cauchy-Schwarz inequality between the galaxy-galaxy , absorber-absorber , and galaxy-absorber correlation functions , finding a result significantly less than unity : \xi _ { ag } ^ { 2 } / ( \xi _ { gg } \xi _ { aa } ) = 0.25 \pm 0.14 .
This implies that galaxies and Ly \alpha absorbers do not linearly trace the underlying dark matter distribution in the same way .