Numerical studies of gas flow in spiral galaxies

A numerical method is described which is specifically designed to treat the dynamics of an infinitesimally thin, differentially rotating, gaseous disk. The method is based on the Piecewise Parabolic Method (PPM), a higher-order extension of Godunov's method. Gravitational forces representing a linear spiral density wave in the stellar component of a galaxy are included. The calculation is Eulerian and is performed in a uniformly rotating frame of reference using plane polar coordinates. The equations are formulated in an exact perturbation form to explicitly eliminate all large, opposing terms representing force balance in the unperturbed, axisymmetric state, allowing the accurate computation of small perturbations. A series of two-dimensional hydrodynamical models is computed to test the gravitational response of a uniform, isothermal, massless gaseous disk to an imposed spiral gravitational perturbation. The parameters describing the mass distribution, rotation properties, and the spiral wave are based on the galaxy NGC 628. The solutions have shocks inside and outside corotation, depleting the region around corotation. The rate at which this region is depleted depends strongly on the strength of the imposed spiral perturbation. Potential perturbations of 10% or greater produce large radial inflows. The time needed for the gas to fall to the inner Linblad resonance in such models is only a small fraction of the Hubble time. The implied rapid evolution suggests that if galaxies exist with such large perturbations, either gas must be replenished from outside the galaxy or the perturbations must be transitory