EDP Sciences
Free access
Volume 375, Number 3, September 2001
Page(s) 1091 - 1099
Section Physical and chemical processes
DOI http://dx.doi.org/10.1051/0004-6361:20010857

A&A 375, 1091-1099 (2001)
DOI: 10.1051/0004-6361:20010857

Boyle's law and gravitational instability

M. Lombardi1 and G. Bertin2

1  Institüt für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
2  Università degli Studi di Milano, Dipartimento di Fisica, via Celoria 16, 20133 Milano, Italy

(Received 20 April 2001 / Accepted 8 June 2001 )

We have re-examined the classical problem of the macroscopic equation of state for a hydrostatic isothermal self-gravitating gas cloud bounded by an external medium at constant pressure. We have obtained analytical conditions for its equilibrium and stability without imposing any specific shape and symmetry to the cloud density distribution. The equilibrium condition can be stated in the form of an upper limit to the cloud mass; this is found to be inversely proportional to the power 3/2 of a form factor $\mu$ characterizing the shape of the cloud. In this respect, the spherical solution, associated with the maximum value of the form factor, $\mu = 1$, turns out to correspond to the shape that is most difficult to realize. Surprisingly, the condition that defines the onset of the Bonnor instability (or gravothermal catastrophe) can be cast in the form of an upper limit to the density contrast within the cloud that is independent of the cloud shape. We have then carried out a similar analysis in the two-dimensional case of infinite cylinders, without assuming axisymmetry. The results obtained in this paper generalize well-known results available for spherical or axisymmetric cylindrical isothermal clouds that have had wide astrophysical applications, especially in the study of the interstellar medium.

Key words: equation of state -- gravitation -- instabilities -- methods: analytical -- ISM: clouds

Offprint request: M. Lombardi, lombardi@astro.uni-bonn.de

© ESO 2001