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 t he characteristic size of a disc, r, is comparable to or less than the gravitational softening length, epsilon, then the cross-section of th e simulated disc is significantly larger than that of a no-softening ( Newtonian) disc with the same mass and angular momentum. We demonstrat e, furthermore, that if r less than or similar to epsilon(3/4) then th e scaling relation r proportional to 3/4 holds for a given mass and sp ecific angular momentum distribution with mass. Finally, we compare so me of the theoretical results obtained in this paper and a previous on e with the results of numerical Tree-SPH simulations and find qualitat ive agreement.