Fundamental oscillation modes of neutron stars: validity of universal relations

Understand

We study the $f$-mode frequencies and damping times of nonrotating neutron stars (NS) in general relativity (GR) by solving the linearized perturbation equations, with the aim to establish "universal" relations that depend only weakly on the equations of state (EOS).

• Using a more comprehensive set of EOSs, we re-examine some proposed linearizations that describe the $f$-mode parameters in terms of mass and radius of the neutron star (NS), and we test a more recent proposal for expressing the $f$-mode parameters as quadratic functions of the effective compactness.
• Our extensive results for each equation of state considered allow us to study the accuracy of each proposal.
• In particular, we find that the damping time deviates quite considerably from the proposed linearization.