The Oxford-Dartmouth Thirty Degree Survey II: Clustering of Bright Lyman Break Galaxies - Strong Luminosity Dependent Bias at z=4

We present measurements of the clustering properties of bright ($L>L_{*}$) z$\sim$4 Lyman Break Galaxies (LBGs) selected from the Oxford-Dartmouth Thirty Degree Survey (ODT). We describe techniques used to select and evaluate our candidates and calculate the angular correlation function which we find best fitted by a power law, $\omega(\theta)=A_{w}\theta^{-\beta}$ with $A_{w}=15.4$ (with $\theta$ in arcseconds), using a constrained slope of $\beta=0.8$. Using a redshift distribution consistent with photometric models, we deproject this correlation function and find a comoving $r_{0}=11.4_{-1.9}^{+1.7}$ h$_{100}^{-1}$ Mpc in a $\Omega_m=0.3$ flat $\Lambda$ cosmology for $i_{AB}\leq24.5$. This corresponds to a linear bias value of $b=8.1_{-2.6}^{+2.0}$ (assuming $\sigma_{8}=0.9$). These data show a significantly larger $r_{0}$ and $b$ than previous studies at $z\sim4$. We interpret this as evidence that the brightest LBGs have a larger bias than fainter ones, indicating a strong luminosity dependence for the measured bias of an LBG sample. Comparing this against recent results in the literature at fainter (sub-$L_{*}$) limiting magnitudes, and with simple models describing the relationship between LBGs and dark matter haloes, we discuss the implications on the implied environments and nature of LBGs. It seems that the brightest LBGs (in contrast with the majority sub-$L_{*}$ population), have clustering properties, and host dark matter halo masses, that are consistent with them being progenitors of the most massive galaxies today.