Selina Kunkel | Searcharxiv

arXiv2026

The petit four of color-superconducting phases in proto-neutron star evolution

At high densities and moderate temperatures, hadronic matter is expected to undergo a first-order phase transition into a color-superconducting (CSC) state. A proto-neutron star describes the earliest evolutionary stages during the first seconds to minutes after core-collapse supernovae and therefore has the potential to assess the appearance of CSC phases at such high densities and moderate temperatures. To address this, we incorporate proto-neutron star conditions, considering neutrino-trapped and neutrino-transparent ones, into the equation of state including color-superconducting phases in a recently developed RG-consistent NJL model. Since the total baryon number of a proto-neutron star is conserved during its later evolution, tracking stellar configurations from an initial mass of the hot proto-neutron star to the final cold neutron star along isolines of baryon number allows us to investigate whether color-superconducting phases can form at any point along this trajectory. By mapping this multidimensional transition in the hot furnace of a core-collapse supernovae cooling from a neutrino-trapped birth state to a cold, neutrino-transparent final state, we reveal four distinct core evolution scenarios-our "petit four" of proto-neutron star evolution: a delayed collapse from the CSC phase to a black hole, a persistent CSC phase, a vanishing CSC phase, and a fleeting CSC phase. For our specific parameterization of the hadronic and the CSC equation of state, we find that a stable color-superconducting phase can only be sustained in the final cold neutron star for a narrow, high-mass region.

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arXiv2025

Determining the minimal mass of a proto-neutron star with chirally constrained nuclear equations of state

The minimal masses and radii of proto-neutron stars during different stages of their evolution are investigated. In our work we focus on two stages, directly after the supernova shock wave moves outwards, where neutrinos are still captured in the core and the lepton per baryon ratio is fixed to $Y_L = 0.4$, and a few seconds afterwards, when all neutrinos have left the star. All nuclear equations of state used for this purpose fulfill the binding energy constraints from chiral effective field theory for neutron matter at zero temperature. We find for the neutrino-trapped case higher minimal masses than for the case when neutrinos have left the proto-neutron star. Thermal effects, here in the form of a given constant entropy per baryon $s$, have a smaller effect on increasing the minimal mass. The minimal proto-neutron star mass for the first evolutionary stage with $Y_L = 0.4$ and $s = 1$ amounts to $M_{min} \sim 0.62M_{\odot}$ and for the stage without neutrinos and $s = 2$ to $M_{min} \sim 0.22M_{\odot}$ rather independent on the nuclear equation of state used. We also study the case related to an accretion induced collapse of a white dwarf where the initial lepton fraction is $Y_L = 0.5$ and observe large discrepancies in the results of the different tables of nuclear equations of state used. Our finding points towards a thermodynamical inconsistent treatment of the nuclear liquid-gas phase transition for nuclear equations of state in tabular form demanding a fully generalized three-dimensional Gibbs construction for a proper treatment. Finally, we demonstrate that there is a universal relation for the increase of the proto-neutron star minimal mass with the lepton fraction for all nuclear equations of state used.

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