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 characterise 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 10^10 M_sun and with faint-end slope \alpha = -1.155. For a standard cosmology and a standard stellar Initial Mass Function, only 3.5% 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 Mpc/h. Over the range 10 kpc/kpc < r_p < 10 Mpc/h it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is \xi*(r) = (r/6.1 Mpc/h)^{-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 five for r_p < 1 Mpc/h. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance LCDM cosmology. Detailed comparison suggests that a fluctuation amplitude \sigma_8 ~ 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.