On the global structure of self-gravitating discs for softened gravity

The effects of gravitational softening on the global structure of self-gravitating discs in centrifugal equilibrium are examined in relation to hydrodynamical/gravitational simulations. The one-parameter spline softening proposed by Hernquist & Katz is used. It is found that if the characteristic size of a disc, r, is comparable to or less than the gravitational softening length, epsilon, then the cross-section of the simulated disc is significantly larger than that of a no-softening (Newtonian) disc with the same mass and angular momentum. We demonstrate, furthermore, that if r less than or similar to epsilon(3/4) then the scaling relation r proportional to 3/4 holds for a given mass and specific angular momentum distribution with mass. Finally, we compare some of the theoretical results obtained in this paper and a previous one with the results of numerical Tree-SPH simulations and find qualitative agreement.