Non-radial oscillation modes in hybrid stars: consequences of a mixed phase

Abstract

We study the possibility of the existence of a deconfined quark matter in the core of neutron star (NS)s and its relation to non-radial oscillation modes in NSs and hybrid star (HS)s. We use relativistic mean field (RMF) models to describe the nuclear matter at low densities and zero temperature. The Nambu-Jona-Lasinio (NJL) model is used to describe the quark matter at high densities and zero temperature. A Gibbs construct is used to describe the hadron-quark phase transition (HQPT) at large densities. Within the model, as the density increases, a mixed phase (MP) appears at density about 2.5 times the nuclear matter saturation density (ρ0) and ends at density about 5ρ0 beyond which the pure quark matter phase appears. It turns out that a stable HS of maximum mass, M = 2.27 M⊙ with radius R = 14 km (for NL3 parameterisation of nuclear RMF model), can exist with the quark matter in the core in a MP only. HQPT in the core of maximum mass HS occurs at radial distance, rc = 0.27R where the equilibrium speed of sound shows a discontinuity. Existence of quark matter in the core enhances the non-radial oscillation frequencies in HSs compared to NSs of the same mass. This enhancement is significantly large for the g modes. Such an enhancement of the g modes is also seen for a density dependent Bayesian (DDB) parmeterisation of the nucleonic EOS. The non-radial oscillation frequencies depend on the vector coupling in the NJL model. The values of g and f mode frequencies decrease with increase the vector coupling in quark matter.