Self-gravitating astrophysical mass with singular central density vibrating in fundamental mode

TL;DR

This paper compares the vibrational properties of a self-gravitating viscous liquid mass with a central density singularity to a homogeneous model, with implications for understanding stellar and gas cloud oscillations.

Contribution

It introduces a spectral analysis of fundamental vibrational modes in a singular density model, contrasting it with homogeneous models, relevant for asteroseismology.

Findings

Differences in frequency formulas between singular and homogeneous models.

Distinct lifetime characteristics of the fundamental mode in both models.

Relevance to pre-white dwarf and star-forming cloud oscillations.

Abstract

The fluid-dynamical model of a self-gravitating mass of viscous liquid with singular density at the center vibrating in fundamental mode is considered in juxtaposition with that for Kelvin fundamental mode in a homogeneous heavy mass of incompressible inviscid liquid. Particular attention is given to the difference between spectral formulae for the frequency and lifetime of $f$-mode in the singular and homogeneous models. The newly obtained results are discussed in the context of theoretical asteroseismology of pre-white dwarf stage of red giants and stellar cocoons -- spherical gas-dust clouds with dense star-forming core at the center.