On the Cooling of Compact Stars in Light of the HESS J1731-347 Remnant

TL;DR

The paper tackles the cooling of compact stars in light of the HESS J1731-347 remnant by testing hadronic, hybrid, and strange-quark-star models against its mass-radius estimate and high redshifted surface temperature at an age of 2–6 kyr. It develops and applies a cohesive EOS framework (hadronic expansion around saturation density, vector MIT bag quark matter with possible density-dependent bag constant, and Maxwell phase transition) and computes cooling with diverse pairing schemes (CFL, 2SC) and envelope compositions (Fe vs He). The authors find that hadronic stars with light-element envelopes or CFL-hybrid configurations can explain the observations, while quark-only stars require strong pairing to suppress cooling; the results emphasize the pivotal role of the symmetry-energy behavior at low density and the activation/suppression of direct Urca processes in reconciling the data. These findings provide constraints on dense-matter models and guide future efforts to include heating, magnetic fields, and mixed-phase configurations in a full general-relativistic cooling treatment.

Abstract

Recent analyses on the central compact object in the HESS J1731-347 supernova remnant reported not only surprising structural properties (mass $M$ and radius $R$), but also an interesting thermal evolution. More precisely, it has been estimated that $M=0.77^{+0.20}_{-0.17}M_\odot$ and $R=10.4^{+0.86}_{-0.78}$ km (at the $1σ$ level), while a redshited surface temperature of $153^{+4}_ {-2}$ keV at an age of 2-6 kyrs has been reported. In the present work, we conduct an in-depth investigation on the possible nature (hadronic, hybrid, quark) of this compact object by attempting to not only explain its mass and radius but also the corresponding estimations for its temperature and age. In the case of hybrid stars we also examine possible effects of the symmetry energy on the activation of different neutrino emitting process, and hence on the resulting cooling curves. We found that the reported temperature and age may be compatible to hadronic stellar configurations regardless of whether pairing effects are included. In the scenario of hybrid stars, we found that the strange quark matter core has to be in a superconducting state in order to reach an agreement with the observational constraints. In addition, the hadronic phase must be soft enough so that the direct Urca process is not activated. Furthermore, we have shown that the considered cooling constraints can be reconciled within the framework of strange stars. However, quark matter has to be in a superconducting state and the quark direct Urca process needs to be blocked.

Figures (6)

• Figure 1: Mass–radius curves for each of the constructed EOSs. The black solid line corresponds to the quark EOS, the green line to the hadronic EOS, and the blue and cyan curves to the hybrid EOSs. The dots correspond to the compact star configurations listed in Table \ref{['tab:table4']}. The gray contour regions denote mass and radius measurements with respect to PSR J0740+6620 Salmi-2024, PSR J0030+0451 Miller-2019, PSR J0437-4715 Choudhury-2024, GW170817 Abbott-2018. The red contour region denotes the mass and radius measurement of the CCO in HESS J1731-347 Doroshenko-2022. The solid contours correspond to the $2\sigma$ confidence, while the dashed contours to the $1\sigma$ confidence.
• Figure 2: (a) Fermi momenta of different particle species as a function of density for the NS model. The red curve corresponds to the neutrons Fermi momentum and the green curve to the sum of the Fermi momenta for protons and electrons. (b) Evolution of the redshifted surface temperature for the NS model considering different superfluidity models. The blue region corresponds to NSs with He-envelopes and the respective green region to NSs with Fe-envelopes. The solid line denotes the case of a NS with Fe-envelope where no pairing effects were considered, while the dashed line the case of a non superfluid NS with He-envelope. The gray shaded rectangle corresponds to the estimated surface temperature and age of the HESS J1731-347.
• Figure 3: (a) Fermi momenta of different particle species as a function of density for the HS1 model. The red solid line corresponds to the Fermi momentum of neutrons, the magenta solid line to the sum of the Fermi momenta for protons and electrons, the cyan solid line to the Fermi momentum of d quarks, the blue solid line to the Fermi momentum of s quarks, the green solid line to the sum of the Fermi momenta for u quarks and electrons and the orange solid line to the difference of the Fermi momenta u quarks and electrons. The gray shaded region corresponds to the part of the star where the d-QDU is activated. (b) Evolution of the redshifted surface temperature with respect to time for the HS1 model. The blue region corresponds to a HS which suffers CFL superconductivity with $\Delta_{0_q} = 15$ MeV and has a light-element envelope, while the green region to a HS suffering the same pairing pattern and having a heavy-element envelope. The orange and the pink shaded regions correspond to HSs which suffer 2SC superconductivity. The orange (pink) region corresponds to models with an envelope of iron-like (helium-like) elements. The black solid and dashed lines describe the thermal evolution of unpaired HS models with different envelope composition. The gray shaded rectangle corresponds to the estimated surface temperature and age of the HESS J1731-347.
• Figure 4: (a) Fermi momenta versus density for HS2. The colors of the solid lines and the gray shaded region correspond to the same parameters as in Figure \ref{['fig:fig3']}a. The orange shaded region corresponds to the density area where the NDU is activated. (b) Evolution of the redshifted surface temperature with respect to time for the HS2 model. The colors of the shaded regions and the style of the curves correspond to the same cases of nucleonic envelopes and pairing types as in Figure \ref{['fig:fig3']}b.
• Figure 5: (a) Fermi momenta as a function of density for the QS model. The cyan solid line corresponds to the d quark Fermi momentum, the blue solid line to the s quark Fermi momentum, the green solid line to the sum of the u quark and electron Fermi momenta and the orange solid line to the difference between the u quarks and electrons Fermi momenta. These predictions were derived by considering the quark masses of Section \ref{['sec2']}. The gray shaded region corresponds to the density range where the d-QDU is activated which is equal to the total size of the QS. (b) Redshifted surface temperature as a function of time for the QS model, in the case where the quark masses are those of Section \ref{['sec2']} (predicting the Fermi momenta of Figure \ref{['fig:fig5']}a). (c) Redshifted surface temperature as a function of time for the QS model, considering a combination of quark masses that blocks the d-QDU process (see Appendix \ref{['app:A']}). In both panels (b,c), solid (dashed) lines denote the case of CFL (2SC) pairing. Different colors denote different envelope composition (see legend). In addition, the gray shaded rectangle corresponds to the estimated surface temperature and age of the HESS J1731-347.