Gravitational instability of finite isothermal spheres

Details Gravitational instability of finite isothermal spheres Gravitational instability of finite isothermal spheres

2001-03-11

arxiv.org/abs/astro-ph/0103159v2

A&A 381, 340 (2002)

Astronomy and Astrophysics

Astrophysics

Submitted to Astron. Astrophys

Scientific paper

10.1051/0004-6361:20011438

We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)] in the microcanonical ensemble. By studying the second variations of the free energy, we find that instability sets in precisely at the point of minimum temperature in agreement with the theorem of Katz [ Mon. Not. R. astr. Soc. 183, 765 (1978)]. The perturbation that induces instability at this point is calculated explicitly; it has not a ``core-halo'' structure contrary to what happens in the microcanonical ensemble. We also study Jeans type gravitational instability of isothermal gaseous spheres described by Navier-Stokes equations. We show analytically the equivalence between dynamical stability and thermodynamical stability and the fact that the stability of isothermal gas spheres does not depend on the viscosity. This confirms the findings of Semelin et al. [astro-ph/9908073] who used numerical methods. We also give a simpler derivation of the geometric hierarchy of scales inducing instability discovered by these authors. The density profiles that trigger these instabilities are calculated analytically; they present more and more oscillations that also follow a geometric progression. This suggests that the system will fragmentate in a series of `clumps' and that these `clumps' will themselves fragmentate in substructures. The fact that both the domain sizes leading to instability and the `clumps' sizes within a box follow a geometric progression with the same ratio suggests a fractal-like behaviour. This gives further support to the interpretation of de Vega et al. [Nature, 383, 56 (1996)].

Affiliated with

Also associated with

No associations

Rating

Gravitational instability of finite isothermal spheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gravitational instability of finite isothermal spheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gravitational instability of finite isothermal spheres will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-497861