A Cosmic Coincidence: The Power-Law Galaxy Correlation Function

We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of xi®, the galaxy two-point correlation function. Departures from a power law are mainly governed by galaxy pair counts on small scales, subject to non-linear dynamics. We assume that galaxies reside within dark matter halos and subhalos and use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal mass loss and, to a lesser degree, dynamical friction deplete the number of subhalos within larger host halos over time by ~90%, just the right amount for achieving a power-law xi® at z = 0. We find that xi® breaks from a power law at high masses, implying that only galaxies of luminosities <= Lstar should exhibit power-law clustering. We also demonstrate that xi® evolves from being far from a power law at high redshift, toward a near power law at z = 0 and deviates in the future. This is mainly caused by the evolving competition between the accretion and destruction rates of subhalos, which happen to strike just the right balance at z~0. We show that key ingredients determining the shape of xi® are the fraction of galaxies that are satellites, the relative difference in mass between the halos of isolated galaxies and halos that contain a single satellite on average, and the rareness of halos that host galaxies. These pieces are intertwined and we find no simple, universal rule for which a power-law xi® will occur. However, we do show that the physics responsible for setting the galaxy content of halos do not care about the conditions needed to achieve a power law xi® and these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of xi® for Lstar and fainter galaxy samples at low redshift is a cosmic coincidence. (Abridged)