The VLT LBG Redshift Survey - VI. Mapping HI in the proximity of zsim3 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.