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 lowredshift 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× 10 10M⊙ and with faint-end slope α = −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 rp < 30h Mpc. Over the range 10hkpc < rp < 10h Mpc it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is ξ(r) = (r/6.1hMpc). 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 rp < 1h Mpc. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance ΛCDM cosmology. Detailed comparison suggests that a fluctuation amplitude σ8 ∼ 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.