Classification of $g$-modes for neutron stars with a strong transition: Novel universal relation including slow stable twin stars

TL;DR

This work analyzes non-radial $g$-mode frequencies in neutron stars with strong first-order hadron-quark transitions across four twin-star categories using CSS parametrization and the relativistic Cowling approximation. It reveals category-dependent $f_g$ trends with mass and tidal deformability $\Lambda$, notably $f_g$ reaching up to $ ext{a few kHz}$ in Category II due to large $ abla\epsilon$ and transition pressures. A novel universal relation combining $f_g$, $ abla\epsilon/ abla ext{trans}$, $\Lambda$, and macroscopic stellar properties is established, achieving a high correlation and enabling inference of phase-transition parameters from multimessenger observations. These results provide a framework to distinguish slow-branch SSHS from hadronic stars via gravitational-wave asteroseismology and motivate future studies on detectability and observational strategies.

Abstract

We investigate the behavior of the non-radial gravity-pulsation discontinuity mode ($g$-mode) in hybrid compact stars with a strong first-order phase transition, which can give rise to twin-star configurations in some cases. These modes are of utmost relevance since they can be potentially excited in isolated as well as binary neutron star systems in the inspiral phase, thus allowing us to indirectly detect the presence of a deconfinement transition. In order to do this, we consider four categories of twin stars that present distinctive features in their equations of state. We employ the constant speed of sound parametrization, which accounts for a sharp phase transition between confined hadronic matter and deconfined quark matter. Then, working within the relativistic Cowling approximation to obtain the frequencies of non-radial oscillations, we find that, depending on the twin star category, the relations between $g$-mode frequencies and masses as well as tidal deformabilities display a highly distinct behavior across the diverse twin star categories that appear in the slow hadron-quark conversion regime. This distinct phenomenology provides smoking-gun evidence to clearly distinguish and further classify hybrid stars with a strong transition from purely hadronic stars using upcoming gravitational-wave data. In addition, we present for each of the categories studied the relation between the $g$-mode frequency and the normalized energy density jump. Finally, we present a novel universal relationship for the discontinuity $g$-mode able to encompass the four categories including long branches of slow stable twin stars and address its asteroseismological capability.

Figures (10)

• Figure 1: Set of EoSs, $P=P(\epsilon)$, for hybrid matter for the four categories explored in this work. We included the region of densities for the crust, i.e. the BPS EoS, and the exterior hadronic mantle, i.e. the SLy EoS. This last SLy EoS is then smoothly matched to the EoSs at higher densities where one can classify them in different categories (labeled I–IV) meaning different physics around the transition point. Additionally, the CET band is shown at low densities illustrating the agreement of our employed hybrid EoSs with this well known first-principle hadronic EoS.
• Figure 2: Results for Category I twin stars. Top panel: Mass–radius relations ($M$-$R$) for hadronic and twin stars with observational constraints from NICER (PSR J0437-4715, PSR J0740+6620, and PSR J0030+0451) and gravitational wave events (GW190425 and GW170817) for comparison. Bottom-left panel:$g$-mode frequency, $f_g$, as a function of stellar mass, $M$, where the color gradient represents the compactness ($M/R$) of the star. Bottom-right panel:$f_g$ as a function of the dimensionless tidal deformability, $\Lambda$.
• Figure 3: Results for Category II twin stars. Same legends and astrophysical constraints as that of Fig. \ref{['fig:categoryI']}.
• Figure 4: Results for Category III twin stars. Same legends and astrophysical constraints as that of Fig. \ref{['fig:categoryI']}.
• Figure 5: Results for Category IV twin stars. Same legends and astrophysical constraints as that of Fig. \ref{['fig:categoryI']}.