Constraining Nuclear Parameters Using Gravitational Waves from f-mode Oscillations in Neutron Stars

Gravitational waves (GWs) emanating from unstable quasi-normal modes in neutron stars (NSs) could be accessible with the improved sensitivity of the current GW detectors or with the next-generation GW detectors and, therefore, can be employed to study the NS interior. Assuming f -mode excitation in isolated pulsars with typical energy of pulsar glitches and considering potential f -mode GW candidates for A+ (upgraded LIGO detectors operating at fifth observing run design sensitivity) and Einstein Telescope (ET), we demonstrate the inverse problem of NS asteroseismology within a Bayesian formalism to constrain the nuclear parameters and NS equation of state (EOS). We describe the NS interior within relativistic mean-field formalism. Taking the example of glitching pulsars, we find that for a single event in A+ and ET, among the nuclear parameters, the nucleon effective mass ( m *) within 90% credible interval can be restricted within 10% and 5%, respectively. At the same time, the incompressibility ( K ) and the slope of the symmetry energy ( L ) are only loosely constrained. Considering multiple (10) events in A+ and ET, all the nuclear parameters are well constrained, especially m *, which can be constrained to 3% and 2% in A+ and ET, respectively. Uncertainty in the observables of a 1.4 M _⊙ NS such as radius ( ${R}_{1.4{M}_{\odot }}$ ), f -mode frequency ( ${f}_{1.4{M}_{\odot }}$ ), damping time ( ${\tau }_{1.4{M}_{\odot }}$ ), and a few EOS properties including squared speed of sound ( c _s ^2 ) are also estimated.