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We present a semi-analytic, physically motivated model for dark matter haloconcentration as a function of halo mass and redshift. The semi-analytic modelcombines an analytic model for the halo mass accretion history (MAH), based onextended Press Schechter (EPS) theory, with an empirical relation betweenconcentration and formation time obtained through fits to the results ofnumerical simulations. Because the semi-analytic model is based on EPS theory,it can be applied to wide ranges in mass, redshift and cosmology. The resultingconcentration-mass (c-M) relations are found to agree with the simulations, andbecause the model applies only to relaxed halos, they do not exhibit the upturnat high masses or high redshifts found by some recent works. We predict achange of slope in the z=0 c-M relation at a mass scale of$10^{11}\rm{M}_{\odot}$. We find that this is due to the change in thefunctional form of the halo MAH, which goes from being dominated by anexponential (for high-mass halos) to a power-law (for low-mass halos). Duringthe latter phase, the core radius remains approximately constant, and theconcentration grows due to the drop of the background density. We also analysehow the c-M relation predicted by this work affects the power produced by darkmatter annihilation, finding that at z = 0 the power is two orders of magnitudelower than that obtained from extrapolating best-fitting c-M relations. Weprovide fits to the c-M relations as well as numerical routines to computeconcentrations and MAHs.

The accretion history of dark matter halos III: A physical model for the concentration-mass relation