Journal Article

Self-gravitating discs and the Sobolev inequality

Patryk Mach and Edward Malec

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 411, issue 2, pages 1313-1316
Published in print February 2011 | ISSN: 0035-8711
Published online February 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.17764.x
Self-gravitating discs and the Sobolev inequality

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We estimate the minimal mass of self-gravitating polytropic discs using the famous Sobolev inequality. This resembles the well-known mass formula for Lane–Emden stars. For ideal gas with the polytropic index n= 3, the minimal mass is not smaller than the Jeans mass. The accuracy of the estimate is verified in a number of numerical examples. The bound works well for heavy self-gravitating discs and is less useful for light discs.

Keywords: accretion, accretion discs; gravitation; hydrodynamics

Journal Article.  2720 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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