White dwarf-neutron star matter transition and the effect of light elements

Abstract

White dwarfs and neutron stars are unique laboratories for dense nuclear matter physics. We develop a single relativistic mean-field framework that treats both classes of compact star, and the transition between them, on the same footing: the nuclei of white-dwarf matter are solved self-consistently as Wigner-Seitz cells with the full electromagnetic interaction, while the same Lagrangian yields the uniform nuclear matter of the neutron-star interior. Within this unified description we compute light-element white dwarfs seeded by $^4$He, $^{12}$C, and $^{16}$O, following each fixed-$A$ sequence along its neutronization path and connecting it to the neutron-star branch through exact Maxwell junctions, from which the corresponding mass-radius relations are derived. The helium- and carbon-seeded white-dwarf sequences attain maximum masses of ${\sim}1.4\,M_\odot$ and ${\sim}1.0\,M_\odot$, respectively. On the neutron-star branch, the retained light-element envelope changes the predicted radii only at the percent level---by approximately $0.2~$km at $1.4\,M_\odot$, within current observational uncertainties. Providing a consistent zero-temperature equation of state from white-dwarf to neutron-star densities, this unified framework offers a natural starting point for studies of white-dwarf--neutron-star binary mergers, progenitor-star evolution, decihertz gravitational-wave sources, and related multimessenger phenomena.