A Lagrangian construction of rotating stars

TL;DR

This paper introduces a new Lagrangian-based numerical method for constructing axisymmetric rotating star models, demonstrating its accuracy through tests and a white dwarf cooling simulation.

Contribution

It presents a novel Lagrangian formulation and a root-finding scheme for modeling rotating stars, enabling detailed equilibrium and evolution studies.

Findings

Successfully constructed rotating star models with the method.

Achieved high accuracy compared to Eulerian codes.

Demonstrated applicability with a white dwarf cooling simulation.

Abstract

We present a new formulation for numerically obtaining axisymmetric equilibrium structures of rotating stars in two spatial dimensions. With a view to apply it to the secular evolution of rotating stars, we base it on the Lagrangian description, i.e., we solve the force-balance equations to find the spatial positions of fluid elements endowed individually with a mass, specific entropy and angular momentum. The system of nonlinear equations obtained by finite-differencing the basic equations are solved with the W4 method, which is a new multi-dimensional root-finding scheme of our own devising. We augment it with a remapping scheme to avoid distortions of the Lagrangian coordinates. In this first one of a series of papers, we will give a detailed description of these methods initially. We then present the results of some test calculations, which include the construction of both rapidly rotating barotropic and baroclinic equilibrium states. We gauge their accuracies quantitatively with some diagnostic quantities as well as via comparisons with the counterparts obtained with an Eulerian code. For a demonstrative purpose, we apply the code to a toy-model cooling calculation of a rotating white dwarf.