# Analytic growth rate of gravitational instability in self-gravitating planar polytropes

@article{Durrive2018AnalyticGR, title={Analytic growth rate of gravitational instability in self-gravitating planar polytropes}, author={Jean-Baptiste Durrive and Mathieu Langer}, journal={Journal of Fluid Mechanics}, year={2018}, volume={859}, pages={362 - 399} }

Gravitational instability is a key process that may lead to fragmentation of gaseous structures (sheets, filaments, haloes) in astrophysics and cosmology. We introduce here a method to derive analytic expressions for the growth rate of gravitational instability in a plane stratified medium. First, the main strength of our approach is to reduce this intrinsically fourth-order eigenvalue problem to a sequence of second-order problems. Second, an interesting by-product is that the unstable part of…

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