Fitting functions for a disk-galaxy model with different LCDM-halo profiles

Abstract

We present an adaptation of the standard scenario of disk-galaxy formation to the concordant LCDM cosmology aimed to derive analytical expressions for the scale length and rotation speed of present-day disks that form within four different, cosmologically motivated protogalactic dark matter halo-density profiles. We invoke a standard galaxy-formation model that includes virial equilibrium of spherical dark halos, specific angular momentum conservation during gas cooling, and adiabatic halo response to the gas inflow. The mean mass-fraction and mass-to-light ratio of the central stellar disk are treated as free parameters whose values are tuned to match the zero points of the observed size-luminosity and circular speed-luminosity relations of galaxies. We supply analytical formulas for the characteristic size and rotation speed of disks built inside Einasto r^{1/6}, Hernquist, Burkert, and Navarro-Frenk-White dark matter halos. These expressions match simultaneously the observed zero points and slopes of the different correlations that can be built in the RVL space of disk galaxies from plausible values of the galaxy- and star-formation efficiencies.