Lane-Emden stars, selfgravitating disks and the Sobolev inequality

Details Lane-Emden stars, selfgravitating disks and the Sobolev inequality Lane-Emden stars, selfgravitating disks and the Sobolev inequality

2010-07-09

arxiv.org/abs/1007.1652v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

9 pages, 2 figures

Scientific paper

We estimate the minimal mass of selfgravitating polytropic disks using the famous Sobolev inequality. This bound 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 selfgravitating disks and is less useful for light disks.

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