Fundamental vibrational mode in a highly inhomogeneous star

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.