Constraining nuclear parameters using f-modes from glitching pulsars

Gravitational waves (GW) emanating from unstable quasi-normal modes in Neutron Stars (NS) could be accessible with the improved sensitivity of the present gravitational wave (GW) detectors or with the next-generation GW detectors and therefore employed to study the NS interior. By taking into account potential GW candidates detectable by A+ and Einstein Telescope (ET) originating from f-modes excited by glitches in isolated pulsars, we demonstrate the inverse problem of NS asteroseismology in a Bayesian formalism to constrain the nuclear parameters within a relativistic mean field (RMF) description of NS interior. We find that for a single detected GW event from the Vela pulsar in A+ and ET, with the considered RMF model, the nucleon effective mass ($m^*$) can be restricted (within $90\%$ credible interval) within $10\%$ and $5\%$, respectively. With the considered RMF model, the incompressibility ($K$) and the slope of the symmetry energy ($L$) are only loosely constrained. With a single observed event in A+ and ET, the f-mode frequency of a $1.4M_{\odot}$ ($f_{1.4M_{\odot}}$) inside a 90\% symmetric credible interval (SCI) can be confined to 100 Hz and 50 Hz, respectively. Additionally, we consider multiple GW candidates in our analysis. For detecting multiple (ten) events with A+ and ET, $m^*$ can be constrained to $3\%$ and $2\%$, respectively. All the other nuclear saturation parameters get well constrained. In particular, $K$ and $L$ can be constrained within $10\%$ and $20\%$ (< $90\%$ SCI), respectively. Within the 90\% SCI, $f_{1.4M_{\odot}}$ can be estimated within 50 Hz and 20 Hz in A+ and ET, respectively. Uncertainty of other NS properties such as radius of a $1.4M_{\odot}$ ($R_{1.4M_{\odot}}$), f-mode damping time of a $1.4M_{\odot}$ ($\tau_{1.4M_{\odot}}$) and few equations of state (EOS) properties including squared speed of sound ($c_s^2$) are also estimated.