Impact of the equation of state on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:math>- and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>- mode oscillations of neutron stars
Athul Kunjipurayil, Tianqi Zhao, Bharat Kumar, Bijay K. Agrawal, Madappa Prakash
Abstract
We investigate the impact of the neutron-star matter equation of state on the $f$- and ${p}_{1}$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and ${p}_{1}$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and ${p}_{1}$-modes and their damping times with the pressure of $\ensuremath{\beta}$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density ${\ensuremath{\rho}}_{0}$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the ${p}_{1}$-mode of $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ star is strongly correlated with the slope of the symmetry energy ${L}_{0}$ and $\ensuremath{\beta}$-equilibrated pressure at density ${\ensuremath{\rho}}_{0}$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the ${p}_{1}$-mode is better than 15% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.