Strong correlation of the neutron star core-crust transition density with the $\sigma$-meson mass via vacuum polarization

TL;DR

This study reveals a strong correlation between neutron star core-crust transition density and the sigma-meson mass, suggesting gravitational wave data can constrain meson properties and improve understanding of neutron star crusts.

Contribution

It demonstrates that the transition density is strongly correlated with the sigma-meson mass, overshadowing uncertainties in the nuclear equation of state within the relativistic Hartree approach.

Findings

Transition density correlates strongly with sigma-meson mass.

Vacuum polarization effects significantly influence the correlation.

Implications for neutron star crust modeling and gravitational wave constraints.

Abstract

We study the neutron star core-crust transition density $\rho_t$ with the inclusion of the vacuum polarization in the dielectric function in the nonlinear relativistic Hartree approach (RHAn). It is found that the strong correlation between the $\rho_{t}$ and the scalar meson mass $m_{\sigma}$ strikingly overwhelms the uncertainty of the nuclear equation of state in the RHAn models, in contrast to the usual awareness that $\rho_{t}$ is predominantly sensitive to the isovector nuclear potential and symmetry energy. The accurate extraction of $\rho_{t}$ through the future gravitational wave measurements can thus provide a strong constraint on the longstanding uncertainty of $m_{\sigma}$, which is of significance to better infer the vacuum property. As an astrophysical implication, it suggests that the correlation between $\rho_t$ and $m_\sigma$ is very favorable to reconcile the difficulty in reproducing the large crustal moment of inertia for the pulsar glitches with the well constrained symmetry energy.