Isentropic hybrid stars in the Nambu-Jona-Lasinio model: effects of neutrino trapping

Abstract

Binary neutron star mergers and proto-neutron stars provide unique environments where dense matter is hot, lepton rich, and potentially undergoes a transition from hadronic to deconfined quark matter. We investigate the thermodynamics and stellar properties of hybrid matter under such conditions. The hadronic phase is described within a covariant density functional framework, while the quark phase is modeled using a Nambu-Jona-Lasinio (NJL) model that includes repulsive vector interactions, the axial $U_A(1)$-breaking 't Hooft determinant interaction, and two-flavor color-superconducting (2SC) pairing. The phase transition between hadronic and quark matter is constructed using a mixed-phase prescription that enforces baryon and lepton number conservation, allowing us to follow thermodynamic trajectories at fixed entropy per baryon and fixed lepton fraction. We analyze the phase structure of dense matter at finite temperature and study the composition of the hadronic, mixed, and quark phases in both neutrino-trapped and neutrino-free regimes. Our results show that neutrino trapping significantly modifies the particle composition and shifts the onset of deconfinement to higher densities. Using the resulting equations of state, we compute static stellar configurations and examine the influence of temperature and lepton content on the mass-radius relation of hybrid stars. Hot, neutrino-rich configurations are found to have larger radii and slightly higher maximum masses than their cold counterparts.

Figures (5)

• Figure S1: 3D plot of the pressure as a function of the baryon and lepton chemical potentials at fixed temperature $T=50$ MeV. The surfaces correspond to the hadronic and quark equations of state. Their intersection (black solid line) defines the phase boundary between the two phases. The blue dot–dashed line indicates the trajectory corresponding to a fixed lepton fraction $Y_{Le}=0.4$, while the red circles mark the endpoints of the mixed-phase region.
• Figure S2: The pressure as a function of baryon density for fixed lepton fraction $Y_{Le}=0.4$, different temperatures (left panel) and entropies (right panel), at fixed vector coupling $\eta_V=1$.
• Figure S3: Phase diagram in the $T$–$\varrho_B$ plane for different neutrino contents. Several isentropic trajectories are shown. The presence of trapped neutrinos shifts the onset of the hadron–quark phase transition to higher baryon densities and leads to the appearance of an extended mixed-phase region.
• Figure S4: Comparison of the composition of matter without neutrinos (left panel) and with neutrinos at fixed lepton fraction $Y_{Le}=0.4$ (right panel) and for different values of temperature.
• Figure S5: Gravitational mass–radius relations for non-rotating isentropic stars. Results are shown for entropy per baryon $S=1$ and $S=2$, with and without neutrino trapping (solid and dashed lines, respectively). For comparison, the mass–radius relation obtained from the cold baryonic equation of state is also displayed. The ellipses show 90% CL regions for PSR J0030+0451 Riley_2019Miller_2019, PSR J0740+6620 Riley_2021Miller_2021.