Analysis of Neutron Star f-mode Oscillations in General Relativity with Spectral Representation of Nuclear Equations of State

Abstract

We study quasi-normal f-mode oscillations in neutron star (NS) interiors within a linearized general relativistic formalism. We utilize approximately 9000 nuclear equations of state (EOSs) using spectral representation techniques, incorporating constraints on nuclear saturation properties, chiral effective field theory for pure neutron matter, and perturbative quantum chromodynamics for densities pertinent to NS cores. The median values of the f-mode frequency, ν f (damping time, τ f ) for NSs with masses ranging from 1.4 to 2.0 M ⊙ lie between 1.80 and 2.20 kHz (0.13–0.22 s) for our entire EOS set. Our study reveals a weak correlation between f-mode frequencies and individual nuclear saturation properties, prompting the necessity for more intricate methodologies to unveil multiparameter relationships. We observe a robust linear relationship between the radii and f-mode frequencies for different NS masses. Leveraging this correlation alongside NICER observations of PSR J0740+6620 and PSR J0030+0451, we establish constraints that exhibit partial and minimal overlap for observational data from Riley et al. and Miller et al., respectively, with our nucleonic EOS data set. Moreover, NICER data align closely with the radius and frequency values for a few hadron–quark hybrid EOS models. This indicates the need to consider additional exotic particles such as deconfined quarks at suprasaturation densities. We conclude that future observations of the radius or f-mode frequency for more than one NS mass, particularly at the extremes of the viable NS mass scale, would either rule out nucleon-only EOSs or provide definitive evidence in its favor.