The Structure of Isothermal, SelfGravitating, Stationary Gas Spheres for Softened Gravity
Abstract
A theory for the structure of isothermal, selfgravitating gas spheres in pressure equilibrium is developed for softened gravity, assuming an ideal gas equation of state. The oneparameter spline softening proposed by Hernquist & Katz is used. We show that the addition of this extra scale parameter implies that the set of equilibrium solutions constitute a oneparameter family, rather than the one and only one isothermal sphere solution for Newtonian gravity, and we develop a number of approximate, analytical or semianalytical solutions. For softened gravity, the structure of isothermal spheres is, in general, very different from the Newtonian isothermal sphere. For example, for any finite choice of softening length ε and temperature T, it is possible to deposit an arbitrarily large mass of gas in pressure equilibrium and with a nonsingular density distribution inside of r_{0} for any r_{0} > 0. Furthermore, it is sometimes claimed that the size of the smallscale, selfgravitating gas structures formed in dissipative TreeSPH simulations is simply of the order the gravitational softening length. We demonstrate, that this claim, in general, is not correct. The main purpose of the paper is to compare the theoretical predictions of our models with the properties of the small, massive, quasiisothermal gas clumps (r ~ 1 kpc, M ~ 10^{10} M_{☉}, and T ~= 10^{4} K) which form in numerical TreeSPH simulations of the formation of Milky Waysized galaxies when effects of stellar feedback processes are not included. We find reasonable agreement, despite the neglect of effects of rotational support in the models presented in this paper. We comment on whether the hydrodynamical resolution is sufficient in our numerical simulations of galaxy formation involving highly supersonic, radiative shocks, and we give a necessary condition, in the form of a simple test, that the hydrodynamical resolution in any such simulations is sufficient. Finally, we conclude that one should be cautious, when comparing results of numerical simulations, involving gratitational softening and hydrodynamical smoothing, with reality.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1998
 DOI:
 10.1086/305739
 arXiv:
 arXiv:astroph/9610085
 Bibcode:
 1998ApJ...500..610S
 Keywords:

 GALAXIES: KINEMATICS AND DYNAMICS;
 GALAXIES: STRUCTURE;
 METHODS: NUMERICAL;
 Galaxies: Kinematics and Dynamics;
 Galaxies: Structure;
 Methods: Numerical;
 Astrophysics
 EPrint:
 22 pages Latex + 12 figures