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arXiv · 1007.1652

Lane-Emden stars, selfgravitating disks and the Sobolev inequality

Patryk Mach·Edward Malec
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Abstract

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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Patryk Mach, Edward Malec. 2010-07-09. Lane-Emden stars, selfgravitating disks and the Sobolev inequality. https://doi.org/10.1111/j.1365-2966.2010.17764.x

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