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Binding energy of compact stars and their non-radial oscillations

P. Laskos-Patkos, S. Papadopoulos, Ch. C. Moustakidis

TL;DR

This work investigates whether an EOS-insensitive relation links the binding energy $E_b$ of compact stars to their non-radial oscillation frequencies, potentially observable in core-collapse events. Using a broad set of hadronic and CSS-hybrid EOSs within the relativistic Cowling approximation, it derives tight empirical relations for hadronic stars: $\frac{f_0 M^2}{\mathrm{kHz} M_\odot^2} \approx 0.27 + 29.29 \frac{E_b}{M_\odot}$ and $\frac{f_{p_1} M^2}{\mathrm{kHz} M_\odot^2} \approx 1.13 + 81.34 \frac{E_b}{M_\odot}$ with $R^2 \approx 0.99$, and similar for $1.4\,M_\odot$ stars. Hybrid EOSs with sharp phase transitions exhibit deviations up to about $30\%$, signaling sensitivity to interior composition. The results offer a framework for using multimessenger signals to constrain dense-matter physics and gravity, while highlighting the need for full General Relativity treatment and finite-temperature extensions in future work.

Abstract

In the past years, a significant effort has been made with the scope of determining correlations, involving compact star properties, that are independent of the nuclear equation of state. Such universal relations are of utmost importance as they allow for the imposition of constraints on stellar properties without directly measuring them and they may also serve as a probe of General Relativity. In the present study, we investigated the possible existence of a universal relation between the binding energy of compact stars and the frequency of their non-radial oscillations. The main motivation was related to the fact that both of the aforementioned quantities might be measured in the occurrence of a supernova explosion. Interestingly, we found that there is a empirical relation between the oscillation frequency and the binding energy for both $f$ and $p_1$ modes, assuming hadronic stellar matter. The inclusion of hybrid equations of state, incorporating sharp phase transitions, was shown to result into deviations from the aforementioned quasi-universal relation.

Binding energy of compact stars and their non-radial oscillations

TL;DR

This work investigates whether an EOS-insensitive relation links the binding energy of compact stars to their non-radial oscillation frequencies, potentially observable in core-collapse events. Using a broad set of hadronic and CSS-hybrid EOSs within the relativistic Cowling approximation, it derives tight empirical relations for hadronic stars: and with , and similar for stars. Hybrid EOSs with sharp phase transitions exhibit deviations up to about , signaling sensitivity to interior composition. The results offer a framework for using multimessenger signals to constrain dense-matter physics and gravity, while highlighting the need for full General Relativity treatment and finite-temperature extensions in future work.

Abstract

In the past years, a significant effort has been made with the scope of determining correlations, involving compact star properties, that are independent of the nuclear equation of state. Such universal relations are of utmost importance as they allow for the imposition of constraints on stellar properties without directly measuring them and they may also serve as a probe of General Relativity. In the present study, we investigated the possible existence of a universal relation between the binding energy of compact stars and the frequency of their non-radial oscillations. The main motivation was related to the fact that both of the aforementioned quantities might be measured in the occurrence of a supernova explosion. Interestingly, we found that there is a empirical relation between the oscillation frequency and the binding energy for both and modes, assuming hadronic stellar matter. The inclusion of hybrid equations of state, incorporating sharp phase transitions, was shown to result into deviations from the aforementioned quasi-universal relation.
Paper Structure (6 sections, 16 equations, 3 figures)

This paper contains 6 sections, 16 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Binding energy of compact stars
  3. Non radial stellar oscillations
  4. Equations of state
  5. Results
  6. Summary and future directions

Figures (3)

  • Figure 1: (a) Mass-radius diagrams for the hadronic EOSs employed in this study. (b) Mass-radius diagrams for the hybrid EOSs employed in this study. The number appearing in the legend indicates the difference between the energy density jump of the EOS and the critical energy density jump defined by Eq. (\ref{['eq13']}). The shaded regions (in both panels) correspond to possible constraints on the maximum mass from the observation of PSR J0348$+$0432 Antoniadis-2013, PSR J0740$+$6620 Cromatie-2020, and PSR J0952-0607 Romani-2022.
  • Figure 3: (a) The product of the $f$ mode oscillation frequency and the gravitational mass squared as a function of the binding energy appears in the top panel. The bottom panel includes the relative error ($100(y_{real}-y_{fit})/y_{fit}$) from the fitted formula. (b) Same as panel (a) but the frequency is related to the $p_1$ mode oscillations. Note that for both panels the blue dots indicate results for hadronic EOSs, while the orange (red) dots dnote results for hybrid EOS constructed with the DD2 (NL3) model.
  • Figure 4: The frequency of $f$ and $p_1$ modes as a function of the binding energy for $1.4M_\odot$ hadronic stars.