The Structure of Isothermal, Self‐gravitating, Stationary Gas Spheres for Softened Gravity

A theory for the structure of isothermal, self-gravitating gas spheres inpressure equilibrium in a softened gravitational field is developed. The oneparameter spline softening proposed by Hernquist & Katz (1989) is used. We showthat the addition of this extra scale parameter implies that the set ofequilibrium solutions constitute a one-parameter family, rather than the oneand only one isothermal sphere solution for Newtonian gravity. We demonstratethe perhaps somewhat surprising result that for any finite choice of softeninglength and temperature, it is possible to deposit an arbitrarily large mass ofgas in pressure equilibrium and with a non-singular density distribution insideof r_0 for any r_0 > 0. The theoretical predictions of our models are comparedwith the properties of the small, massive, quasi-isothermal gas clumps whichtypically form in numerical Tree-SPH simulations of 'passive' galaxy formationof Milky Way sized galaxies. We find reasonable agreement despite the neglectof rotational support in the models. We comment on whether the hydrodynamicalresolution in our numerical simulation of galaxy formation is sufficient, andfinally we conclude that one should be cautious, when comparing results ofnumerical simulations involving gravitational softening and hydrodynamicalsmoothing, with reality.Comment: 22 pages Latex + 12 figure