Radial oscillations and stability of multiple-fluid compact stars

Abstract

I derive a system of pulsation equations for compact stars made up of an arbitrary number of perfect fluids that can be used to study radial oscillations and stability with respect to small perturbations. I assume spherical symmetry and that the only inter-fluid interactions are gravitational. My derivation is in line with Chandrasekhar's original derivation for the pulsation equation of a single-fluid compact star and keeps the contributions from the individual fluids manifest. I illustrate solutions to the system of pulsations equations with one-, two-, and three-fluid examples.

Dynamical evolution of dark matter admixed neutron stars

“…The spikes along the curves correspond to oscillation frequencies. The dotted vertical lines are the radial oscillation frequencies as computed from pulsation equations, using the methods of [43,44]. We can see that the Fourier spectrum and the dotted vertical lines line up well, which is a nontrivial check on the numerical methods developed here and in [43].…”

“…For boundary conditions and our method of solution, see [43]. Once the pulsation equations are solved for ω2 , and assuming it is positive, the radial oscillation frequency is given by ω = σ 0 (0)ω.…”

“…The single-fluid pulsation equation was derived some time ago by Chandrasekhar [54]. Its multifluid generalization [43] is reviewed in Appendix A.…”

“…Radial oscillation frequencies for dark matter admixed neutron stars have been computed from pulsation equations in [24,25,43,44]. In this subsection, we extend the tools available for their study by computing them for the first time from dynamical evolutions.…”

“…Radial oscillation frequencies may be computed by solving pulsation equations, which are derived from time dependent harmonic perturbations of static solutions, or by Fourier transforming dynamic solutions. Pulsation equations have been derived for fermion stars [54], boson stars [55][56][57][58], and for dark matter admixed neutron stars [43,59], but not for fermion-boson stars. On the other hand, as mentioned, fermion-boson stars have been dynamically evolved, from which radial os-cillation frequencies have been computed using a Fourier transform [10,15].…”