A new study has refined the universal relations describing the fundamental mode (f-mode) oscillations in neutron stars. These relations are crucial for gravitational-wave asteroseismology of neutron stars. Researchers utilized a large sample of piecewise-parametric equations of state (EOSs) to analyze the f-mode frequency and damping time within full general relativity. The work demonstrates that existing universal relations, which depend only on neutron star mass and radius, exhibit significant residuals that are strongly correlated with the overall stiffness of the EOS.

To address these residuals, the team introduced linear correction terms dependent on the characteristic radius predicted by the EOS and the slope of the mass-radius curve at intermediate masses. These corrections enhance the accuracy of the universal relations, transforming them from a single-parameter model to a three-parameter one. For instance, in the case of gravitational wave emission from a Vela-like pulsar, the signal-to-noise ratio estimation can be over/under-estimated by up to 10% with previous relations, whereas the new model provides a nearly exact prediction.

In contrast, the study found that universal relations between the f-mode and tidal deformability show minimal EOS-dependent correlations in their residuals, maintaining high EOS-insensitivity. This advancement is fundamental for the next generation of gravitational wave detectors, which will enable the detection of these signals and, consequently, the detailed study of neutron star internal structure through gravitational-wave asteroseismology.