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 × 10¹⁰M_solar and with faint-end slope α = -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 < 30h^-1Mpc. Over the range 10h^-1kpc < r_p < 10h^-1Mpc, it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is ξ*(r) = (r/6.1h^-1Mpc)^-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 < 1h^-1Mpc. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance Λcold dark matter 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.