The VLT LBG Redshift Survey - VI. Mapping HI in the proximity of   $z\sim3$ LBGs with X-Shooter
  We present an analysis of the spatial distribution of gas and galaxies using new X-Shooter observations of $z\sim3-4$ quasars. Adding the X-Shooter data to an existing dataset of high resolution quasar spectroscopy, we use a total sample of 29 quasars alongside $\sim1700$ Lyman Break Galaxies in the redshift range $2<z<3.5$. Analysing the Ly$\alpha$ forest auto-correlation function using the full quasar sample, we find $s_0=0.081\pm0.006h^{-1}$Mpc. We then investigate the clustering and dynamics of Ly$\alpha$ forest absorbers around $z\sim3$ LBGs. From the redshift-space cross-correlation, we find $s_0=0.27\pm0.14h^{-1}$Mpc, with power-law slope $\gamma=1.1\pm0.2$. 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 $r_0=0.24\pm0.04h^{-1}$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 parameter and the peculiar velocity, finding $\beta_{\rm F}=1.02\pm0.22$ and $240\pm60$ km s$^{-1}$ respectively. 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. We evaluate the Cauchy-Schwarz inequality between the galaxy-galaxy, absorber-absorber, and galaxy-absorber correlation functions, finding a result significantly less than unity: $\xi_{\rm ag}^2/(\xi_{\rm gg}\xi_{\rm aa})=0.25\pm0.14$, implying that galaxies and Ly$\alpha$ absorbers do not linearly trace the underlying dark matter distribution in the same way. 
R. M. Bielby (Durham), T. Shanks (Durham), N. H. M. Crighton   (Swinburne), C. G. Bornancini (IATE, OAC), L. Infante (PUC), ...
astro-ph.GA