A cosmic coincidence: The power-law galaxy correlation function

Abstract

We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of ξ(r), the galaxy two-point correlation function. While ξ(r) at large scales is set by primordial fluctuations, departures from a power law are governed by galaxy pair counts at small scales, subject to nonlinear dynamics. We assume that galaxies reside within dark matter halos and subhalos. Therefore, the shape of the correlation function at small scales depends on the amount of halo substructure. We use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal mass loss and, to a lesser extent, dynamical friction dramatically deplete the number of subhalos within larger host halos over time, resulting in a 90% reduction by z = 0 compared to the number of distinct mergers that occur during the assembly of a host halo. We show that these nonlinear processes resulting in this depletion are essential for achieving a power law ξ(r). We investigate how the shape of ξ(r) depends on subhalo mass (or luminosity) and redshift. We find that ξ(r) breaks from a power law at high masses, implying that only galaxies of luminosities ≲ L * should exhibit power-law clustering. Moreover, we demonstrate that ξ(r) evolves from being far from a power law at high redshift, toward a near power-law shape at z = 0. We argue that ξ(r) will once again evolve away from a power law in the future. This is in large part caused by the evolving competition between the accretion and destruction rates of subhalos over time, which happen to strike just the right balance at z 0. We then investigate the conditions required for ξ(r) to be a power law in a general context. We use the halo model, along with simple parameterizations of the halo occupation distribution, to probe galaxy occupation at various masses and redshifts. We show that the key ingredients determining the shape of ξ(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 ξ(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 ξ(r) and that these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of ξ(r) for L * and fainter galaxy samples at low redshift is a cosmic coincidence. © 2011. The American Astronomical Society. All rights reserved.