Numerical Study of Polytropes with n = 1 and Differential Rotation

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, \(\sigma \simeq 2\). 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.