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(r), 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(r) at z = 0. We find that xi(r) 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(r) 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(r) 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(r) 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(r) and these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of xi(r) for Lstar and fainter galaxy samples at low redshift is a cosmic coincidence. (Abridged)