Consistent crust-core interpolation and its effect on non-radial neutron star oscillations

TL;DR

This paper develops a new method for matching the crust and core equations of state in neutron stars, analyzing its impact on mass-radius relations and non-radial oscillation modes, with implications for gravitational wave observations.

Contribution

It introduces a thermodynamically consistent interpolation method for crust-core EoS matching and evaluates its effects on neutron star properties and oscillation modes.

Findings

The new matching method affects neutron star radius and oscillation frequencies.

Significant differences in the $p_1$ mode frequencies are observed with different matching schemes.

The fundamental $f$-mode remains largely unaffected by the crust-core matching approach.

Abstract

To model the structure of neutron stars (NSs) theoretically,it is common to consider layers with different density regimes. Matching the equation of state (EoS) for the crust and core and obtaining a suitable description of these extreme conditions are crucial for understanding the properties of these compact objects. In this work, we construct ten different NS EoSs incorporating three distinct crust models, which are connected to the core using a thermodynamically and causally consistent formalism. For cold NSs, we propose a linear relationship between pressure and energy density in a narrow region between the crust and core, effectively establishing an interpolation function in the pressure-baryonic chemical potential plane. We then compare this EoS matching method with the classical approach, which neglects causal and thermodynamic consistency. We solve the Tolman-Oppenheimer-Volkoff equation to obtain the mass-radius relationship and compare our results with observational constraints on NSs. Furthermore, we investigate the influence of the new matching formalism on non-radial oscillation frequencies and damping times. Our findings suggest that the method used to glue the crust and core EoS impacts NS observables, such as the radius, oscillation frequencies, and damping times of non-radial modes, which may be crucial for interpreting future gravitational wave observations from neutron star mergers or isolated pulsars. The effects are particularly noticeable for low-mass NSs, regardless of the specific EoS model chosen. In particular, we find that the $p_1$ oscillation mode exhibits significant differences in frequencies among alternative matching methods, whereas the fundamental $f$-mode remains unaffected by changes in crust models or interpolation schemes.