Numerical Study of Polytropes with n=1 and Differential Rotation

TL;DR

This study numerically explores the configuration space of differentially rotating polytropes with n=1, revealing diverse structures like spheroids, tori, and complex bodies, and discusses their stability implications.

Contribution

It provides a detailed numerical analysis of n=1 polytropes with differential rotation, identifying new configuration types and their dependence on rotation parameters.

Findings

Three types of configurations identified: spheroids, tori, and mixed bodies.

Exotic configurations only occur at moderate differential rotation (~sigma=2).

Many configurations exhibit large tau values, raising questions about their stability.

Abstract

The solution space of differentially rotating polytropes with n=1 has been studied numerically. The existence of three different types of configurations: from spheroids to thick tori, hockey puck-like bodies and spheroids surrounded by a torus, separate from or merging with the central body has been proved. It has been shown that the last two types appear only at moderate degrees of rotation differentiality, sigma~2. Rigid-body or weakly differential rotation, as well as strongly differential, have not led to any "exotic" types of configurations. Many calculated configurations have had extremely large values of parameter tau, which has raised the question of their stability with respect to fragmentation.