Self-Gravitating Astrophysical Mass With Singular Central Density Vibrating in Fundamental Mode

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.

Vibrations of a diamagnetically levitated water droplet

“…Note that this result differs from that of a uniform-density self-gravitating body, σ G = [(8/3)πGρl(l − 1)/(2l + 1)] 1/2 [32]. Bastrukov has recently obtained a similar spectrum for a self-gravitating liquid droplet with radially-varying density distribution ρ(r < a) ∝ 1/r, having a singular density at the center [33].…”

Alfvén seismic vibrations of crustal solid-state plasma in quaking paramagnetic neutron star

“…Regarding the difference between node-free oscillatory behavior of solid sphere and spherical mass of an incompressible liquid it is appropriate to note that the liquid sphere is able to sustain solely spheroidal node-free vibrations of fluid velocity. The canonical example is the Kelvin fundamental mode of oscillating fluid velocity in a heavy spherical mass of incompressible homogeneous liquid restored by forces represented as gradient of pressure and gradient of potential of self-gravity [36]. In the meantime, the node-free vibrations of solid sphere restored by elastic force (represented as divergence of shear mechanical stresses) are characterized by two eigenmodes.…”

Geometric creation of quantum vorticity

“…As shown in [18], this vacuum field is stable against collapse due to self-gravitation, i.e., the equivalent Jeans length is greater than the radius of the universe. (See [27] for a model of a self-gravitating liquid mass which vibrates.) The NLKG equation is used (as opposed to the non-linear Schödinger equation), because relativistic effects are essential in this context.…”