Thermal twin stars within a hybrid equation of state based on a nonlocal chiral quark model compatible with modern astrophysical observations

We investigate the extension to finite temperatures and neutrino chemical potentials of a recently developed nonlocal chiral quark model approach to the equation of state of neutron star matter. We consider two light quark flavors and current-current interactions in the scalar-pseudoscalar, vector, and diquark pairing channels, where the nonlocality of the currents is taken into account by a Gaussian form factor that depends on the spatial components of the 4-momentum. Within this framework, we analyze order parameters, critical temperatures, phase diagrams, equations of state, and mass-radius relations for different temperatures and neutrino chemical potentials. For parameters of the model that are constrained by recent multimessenger observations of neutron stars, we find that the mass-radius diagram for isothermal hybrid star sequences exhibits the thermal twin phenomenon for temperatures above 30 MeV.

Figure 1

Order parameters chiral condensate (solid line) and diquark pairing gap (dashed line) as functions of ${\mu }_B$ for temperatures $T=40$ and $T=80\mathrm{MeV}$ in panels (a) and (b), respectively, when ${\eta }_D=1.1$, ${\eta }_V=0.5$, and ${\mu }_{{\nu }_e}=0$.

Figure 1

Order parameters chiral condensate (solid line) and diquark pairing gap (dashed line) as functions of ${\mu }_B$ for temperatures $T=40$ and $T=80\mathrm{MeV}$ in panels (a) and (b), respectively, when ${\eta }_D=1.1$, ${\eta }_V=0.5$, and ${\mu }_{{\nu }_e}=0$.

Figure 2

Order parameters chiral condensate (solid line) and diquark pairing gap (dashed line) as functions of temperature $T$ for ${\mu }_B=850$ and ${\mu }_B=1200\mathrm{MeV}$ in panels (a) and (b), respectively, with ${\eta }_D=1.1$, ${\eta }_V=0.5$, and ${\mu }_{{\nu }_e}=0$.

Figure 3

Structure of the phase diagram at low temperatures and finite ${\mu }_B$ for different parametrizations of the model: full model with leptons (black line), version without charge or color neutrality (blue lines), and the simplest version, a model without diquarks or vector interactions (violet lines).

Figure 4

Phase diagrams for ${\eta }_D=0.9$ and (a) ${\eta }_V=0.1$, (b) ${\eta }_V=0.5$, and (c) ${\eta }_V=0.9$ with ${\mu }_{{\nu }_e}=0$.

Figure 5

Phase diagrams for ${\eta }_D=1.1$ and (a) ${\eta }_V=0.1$, (b) ${\eta }_V=0.5$, and (c) ${\eta }_V=0.9$ with ${\mu }_{{\nu }_e}=0$.

Figure 6

Phase diagram for quark matter model with ${\eta }_V=0.5$ and ${\eta }_D=1.1$ with and without neutrino trapping.

Figure 7

Mass-radius relations for pure hadronic matter EOSs (with a BPS crust). Different values of $T$ and the corresponding ${\mu }_{{\nu }_e}=2T$ are highlighted with thicker lines. In addition to the existing data points, for $T=30$, 40, and 50 MeV we added thinner lines corresponding to additional fixed values of ${\mu }_{{\nu }_e}=60$, 80, 100, 120, 140 MeV, from bottom to top.

Figure 8

(a) Hadron-quark phase transition points for finite temperature EOSs considering the relation ${\mu }_{{\nu }_e}/T=2$ and (b) ${\mu }_{{\nu }_e}/T=\alpha$, with $\alpha =2.4$ and 2.8.

Figure 9

(a) Hybrid EOSs constructed from the phase transitions shown in Fig. 8. (b) Squared speed of sound as a function of the energy density, for several T (and the related ${\mu }_{{\nu }_e}$).

Figure 10

Mass-central density relations from hybrid EOSs for different values of $T$ and ${\mu }_{{\nu }_e}$. Short-dashed lines correspond to $\mathrm{crust}+\mathrm{DD}2$ EOSs while solid lines also include QM. For all the cases, dotted lines show the unstable regions. Solid dots display the QM onsets and star (triangle) symbols indicate the ${\mathrm{M}}_{\max }$ locations for hybrid (hadronic) EOSs.

Figure 11

Mass-radius relations from hybrid EOSs for different values of $T$ and ${\mu }_{{\nu }_e}$. Short-dashed lines correspond to $\mathrm{crust}+\mathrm{DD}2$ EOSs while solid lines also include QM. For all the cases, dotted lines show the unstable regions. Solid dots display the QM onsets and star (triangle) symbols indicate the ${\mathrm{M}}_{\max }$ locations for hybrid (hadronic) EOSs.

Figure 12

Entropy per baryon vs pressure in the region of critical pressures obtained from Fig. 8, indicated by vertical lines. Dashed lines are for the hadronic (DD2) phase while solid lines are for the QM (3DNJL) phase of the present work.