On the isotropy assumption and the applicability of the gasdynamical equations for collapsing systems.

Details On the isotropy assumption and the applicability of the gasdynamical equations for collapsing systems. On the isotropy assumption and the applicability of the gasdynamical equations for collapsing systems.

Nov 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...303..299h&link_type=abstract

Astronomy and Astrophysics, v.303, p.299

Astronomy and Astrophysics

Astrophysics

3

Hydrodynamics, Stars: Formation, Stellar Dynamics

Scientific paper

Rotating, isothermal collapsing protostellar and protogalactic gas systems are always being treated by use of the isotropic gasdynamical (Euler) equations; while it is standard textbook knowledge that diffusive and viscous effects can be neglected in most astrophysical plasmas with large Reynolds numbers, or in other words non-diagonal elements of the stress-energy tensor (second-order moments of the velocity distribution function) and higher order moments vanish, it is not that clear that the isotropy assumption is correct, i.e. the equality of the diagonal second-order moments. Therefore we address in this paper the question 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 realized in the static case only. This means that although collisional timescales in the gas might be very short, the collapsing system has to develop an inherent small anisotropy; the trajectory of the system in phase space is initially leading away from the isotropic path, staying continuously apart from it for a small distance. We discuss this phenomenon quantitatively by using moment equations of the Boltzmann equation and examine its consequences. It turns out that the deviation from anisotropy in most cases keeps small enough to allow for a global isotropic treatment which is consistent with expectation; applying our results to systems like cloud fluids or stellar systems, however, yields complementary results. Additionally we prove in this paper the performance of the conditions for the applicability of the gasdynamical description in a handy form and show that these conditions are usually fulfilled. We find that for a slightly Jeans unstable system in pressure equilibrium the ratio of the microscopic collision time to free-fall time has to be of order unity or smaller as has to be the Knudsen number in order to ensure the validity of gasdynamic equations.

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