Light clusters in warm magnetized stellar matter: equation of state and thermodynamic response

Abstract

Finite-temperature equations of state (EOSs) with a controlled treatment of composition-dependent effects are becoming increasingly important for modeling proto-neutron stars and binary neutron star merger remnants, where warm matter may coexist with strong magnetic fields. At sub-saturation densities, light nuclear clusters may also emerge with sizeable abundances. For beta-equilibrated matter, with or without neutrino trapping, an interplay between magnetic fields and light-cluster formation naturally arises in determining the matter composition: charge neutrality and weak equilibrium transmit the effects of Landau quantization to the baryonic sector, modifying the equilibrium charge content; at the same time, light-cluster formation also favors the increase of the proton fraction by binding protons into nuclear clusters. In this work, we investigate this interplay within a generalized relativistic mean-field framework, in which light clusters up to alpha particles are included as explicit degrees of freedom and their in-medium dissolution is described through phenomenological binding-energy shifts. We show that the formation and subsequent dissolution of light clusters, combined with magnetic-field effects, leave characteristic signatures in the matter pressure, the isothermal squared speed of sound, and the heat capacity, leading to significant modifications of the thermodynamic stiffness of the EOS and of the heat-storage properties of warm stellar matter. Furthermore, we investigate the impact of the isovector terms of the EOS, namely its symmetry energy, on these features. These results provide microscopic insights relevant to modeling the hydrodynamic and thermal evolution of proto-neutron stars and neutron star merger remnants, while establishing a baseline for the development of more comprehensive finite-temperature EOSs for compact-star applications.