Lane-Emden stars, selfgravitating disks and the Sobolev inequality
Solar and Stellar Astrophysics
2015-05-19 v1
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.
Keywords
Cite
@article{arxiv.1007.1652,
title = {Lane-Emden stars, selfgravitating disks and the Sobolev inequality},
author = {Patryk Mach and Edward Malec},
journal= {arXiv preprint arXiv:1007.1652},
year = {2015}
}
Comments
9 pages, 2 figures