ON THE ISOTROPY ASSUMPTION AND THE APPLICABILITY OF THE GASDYNAMICAL EQUATIONS FOR COLLAPSING SYSTEMS

Rotating, isothermal collapsing protostellar and protogalactic gas sys tems are always being treated by use of the isotropic gasdynamical (Eu ler) equations; while it is standard textbook knowledge that diffusive and viscous effects can be neglected in most astrophysical plasmas wi th large Reynolds numbers, or in other words non-diagonal elements of the stress-energy tensor (second-order moments of the velocity distrib ution function) and higher order moments vanish, it is not that clear that the isotropy assumption is correct, i.e. the equality of the diag onal second-order moments. Therefore we address in this paper the ques tion whether a collapsing gas cloud remains always strictly isotropic. Analytically the velocity field of an isothermal collapsing rotating gas cloud is computed and it is shown that strict isotropy can be real ized in the static case only. This means that although collisional tim escales in the gas might be very short, the collapsing system has to d evelop an inherent small anisotropy; the trajectory of the system in p hase space is initially leading away from the isotropic path, staying continuously apart from it for a small distance. We discuss this pheno menon quantitatively by using moment equations of the Boltzmann equati on and examine its consequences. It turns out that the deviation from anisotropy in most cases keeps small enough to allow for a global isot ropic treatment which is consistent with expectation; applying our res ults to systems like cloud fluids or stellar systems, however, yields complementary results. Additionally we prove in this paper the perform ance of the conditions for the applicability of the gasdynamical descr iption in a handy form and show that these conditions are usually fulf illed. We find that for a slightly Jeans unstable system in pressure e quilibrium the ratio of the microscopic collision time to free-fall ti me has to be of order unity or smaller as has to be the Knudsen number in order to ensure the validity of gasdynamic equations.