A Roche Model for Uniformly Rotating Rings
Stefan Horatschek, David Petroff
TL;DR
This paper introduces an analytical Roche model for uniformly rotating rings, providing explicit solutions in the thin ring limit and comparing them with numerical results for polytropic rings.
Contribution
It develops a new analytical Roche model for rotating rings and compares it with numerical solutions, enhancing understanding of ring structures in astrophysics.
Findings
Analytic expressions for pressure surfaces in thin rings
Agreement between analytical and numerical models in the thin ring limit
Explicit solutions even in mass-shedding scenarios
Abstract
A Roche model for describing uniformly rotating rings is presented and the results are compared with numerical solutions to the full problem for polytropic rings. In the thin ring limit, the surfaces of constant pressure including the surface of the ring itself are given in analytic terms, even in the mass-shedding case.
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