The Star Formation Rate-Density Relationship at Redshift Three
  We study the star formation rate (SFR) as a function of environment for UV selected Lyman break galaxies (LBGs) at redshift three. From deep UBVI KPNO 4-m/MOSAIC images, covering a total of 0.90 deg^2, we select 334 LBGs in slices 100 Mpc (co-moving) deep spanning the redshift range 2.9<z<3.4 based on Bayesian photometric redshifts that include the I magnitude as a prior. The slice width (100 Mpc) corresponds to the photometric redshift accuracy (\Delta_z\sim 0.15).   We used mock catalogs from the GIF2 cosmological simulations to show that this redshift resolution is sufficient to statistically differentiate the high density regions from the low density regions using $\Sigma_5$, the projected density to the 5th nearest neighbor. These mock catalogs have a redshift depth of 100 Mpc, similar to our slice width.   The large area of the MOSAIC images, 40x40 Mpc (co-moving) per field, allows us to measure the SFR from the dust-corrected UV continuum as a function of $\Sigma_5$. In contrast to low-redshift galaxies, we find that the SFR (or UV luminosity) of LBGs at z=3 shows no detectable dependence on environment over 2 orders of magnitude in density.   To test the significance of our result, we use Monte Carlo simulations (from the mock catalogs) and the same projected density estimators we applied to our data. We find that we can reject the steep z=0 SFR-density at the 5-$\sigma$ level. We conclude that the SFR-density at z=3 must be at least 3.6 times flatter than it is locally, i.e. the SFR of LBGs is significantly less dependent on environment than the SFR of local star-forming galaxies. We find that the rest-frame UV colors are also independent of environment. 
Nicolas Bouche (1), James D. Lowenthal (2) ((1) MPE, (2) Smith   College)