The distribution of stellar mass in the low-redshift Universe

We use a complete and uniform sample of almost half a million galaxies from the Sloan Digital Sky Survey to characterize the distribution of stellar mass in the low-redshift Universe. Galaxy abundances are well determined over almost four orders of magnitude in stellar mass and are reasonably but not perfectly fit by a Schechter function with characteristic stellar mass m(*) = 6.7 x 1010 M-circle dot and with faint-end slope alpha = -1.155. For a standard cosmology and a standard stellar initial mass function, only 3.5 per cent of the baryons in the low-redshift Universe are locked up in stars. The projected autocorrelation function of stellar mass is robustly and precisely determined for r(p) < 30 h-1 Mpc. Over the range 10 h-1 kpc < r(p) < 10 h-1 Mpc, it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is xi*(r) = (r/6.1 h-1 Mpc)-1.84. Relative to the dark matter, the bias of the stellar mass distribution is approximately constant on large scales, but varies by a factor of 5 for r(p) < 1 h-1 Mpc. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance Lambda cold dark matter cosmology. Detailed comparison suggests that a fluctuation amplitude Sigma(8) similar to 0.8 is preferred to the somewhat larger value adopted in the Millennium Simulation models with which we compare our data. This comparison also suggests that observations of stellar mass autocorrelations as a function of redshift might provide a powerful test for the nature of Dark Energy.