Fundamental vibrational mode in a highly inhomogeneous star

TL;DR

This paper investigates the fundamental vibrational mode in highly inhomogeneous stars with singular density profiles, comparing it to uniform models, and discusses implications for asteroseismology of pre-white dwarf stars.

Contribution

It introduces a new analysis of the eigenfrequency problem for inhomogeneous stars with singular density, contrasting it with classical uniform models, and explores astrophysical applications.

Findings

Derived spectral equations for inhomogeneous star models.

Identified differences in frequency and lifetime of f-modes.

Discussed relevance to pre-white dwarf star asteroseismology.

Abstract

The eigenfrequency problem of fundamental vibrational mode in a highly inhomogeneous star, modeled by self-gravitating mass of viscous liquid with singular density at the center, is considered in juxtaposition with that for Kelvin fundamental mode in the liquid star model with uniform density. Particular attention is given to the difference between spectral equations for the frequency and lifetime of f-mode in the singular and homogeneous star models. The newly obtained results are discussed in the context of theoretical asteroseismology of pre-white dwarf stars and stellar cocoons -- spherical gas-dust clouds with dense star-forming core at the center.