Statistics of Satellite Galaxies Around Milky Way-Like Hosts

Abstract: We calculate the probability that a Milky-Way-like halo in the standard cosmological model has the observed number of Magellanic Clouds (MCs). The statistics of the number of MCs in the LCDM model are in good agreement with observations of a large sample of SDSS galaxies. Under the sub-halo abundance matching assumption of a relationship with small scatter between galaxy r-band luminosities and halo internal velocities v_max, we make detailed comparisons to similar measurements using SDSS DR7 data by Liu et al. (2010). Models and observational data give very similar probabilities for having zero, one, and two MC-like satellites. In both cases, Milky Way-luminosity hosts have just a \sim 10% chance of hosting two satellites similar to the Magellanic Clouds. In addition, we present a prediction for the probability for a host galaxy to have Nsats satellite galaxies as a function of the magnitudes of both the host and satellite. This probability and its scaling with host properties is significantly different from that of mass-selected objects because of scatter in the mass- luminosity relation and because of variations in the star formation efficiency with halo mass.