Very Small-Scale Clustering and Merger Rate of Luminous Red Galaxies

We present the small-scale (0.01<r<8 h^{-1} Mpc) projected correlation function w_p(r_p) and real space correlation function xi(r) of 24520 luminous early-type galaxies from the Sloan Digital Sky Survey Luminous Red Galaxy (LRG) sample (0.16<z<0.36). ``Fiber collision'' incompleteness of the SDSS spectroscopic sample at scales smaller than 55 arcseconds prevents measurements of the correlation function for LRGs on scales smaller than ~0.3 Mpc by the usual methods. In this work, we cross-correlate the spectroscopic sample with the imaging sample, with a weighting scheme to account for the collisions, extensively tested against mock catalogs. We correct for photometric biases in the SDSS imaging of close galaxy pairs. We find that the correlation function xi(r) is surprisingly close to a r^{-2} power law over more than 4 orders of magnitude in separation r. This result is too steep at small scales to be explained in current versions of the halo model for galaxy clustering. We infer an LRG-LRG merger rate of less than or similar to 0.6 Gyr^{-1} Gpc^{-3} for this sample. This result suggests that the LRG-LRG mergers are not the main mode of mass growth for LRGs at z<0.36.