Dynamical response to supernova-induced gas removal in spiral galaxies with dark matter halo

We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For the purpose of comparison, we also consider the homogeneous and   r ⁻¹  profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass-loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass-loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully–Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass-loss becomes larger than that before the mass-loss, suggesting that the mass-loss would most likely occur from the central disc region where the specific angular momentum is low.