Structure and evolution of ultra-massive white dwarfs in general relativity

Context. Ultra-massive white dwarfs (M-star greater than or similar to 1.05 M-circle dot) are of utmost importance in view of the role they play in type Ia supernovae explosions, merger events, the existence of high-magnetic -field white dwarfs, and the physical processes in the super asymptotic giant branch phase. Aims. We aim to present the first set of constant rest-mass ultra-massive oxygen-neon white dwarf cooling tracks with masses of M-star > 1.29 M-circle dot which fully take into account the e ffects of general relativity on their structural and evolutionary properties. Methods. We computed the full evolution sequences of 1.29, 1.31, 1.33, 1.35, and 1.369 M-circle dot white dwarfs with the La Plata stellar evolution code, LPCODE. For this work, the standard equations of stellar structure and evolution have been modified to include the e ffects of general relativity. Specifically, the fully general relativistic partial di fferential equations governing the evolution of a spherically symmetric star are solved in a way so that they resemble the standard Newtonian equations of stellar structure. For comparison purposes, the same sequences have been computed for the Newtonian case. Results. According to our calculations, the evolutionary properties of the most massive white dwarfs are strongly modified by general relativity e ffects. In particular, the resulting stellar radius is markedly smaller in the general relativistic case, being up to 25% smaller than predicted by the Newtonian treatment for the more massive ones. We find that oxygen-neon white dwarfs more massive than 1.369 M-circle dot become gravitationally unstable with respect to general relativity e ffects. When core chemical distribution due to phase separation on crystallization is considered, such instability occurs at somewhat lower stellar masses, greater than or similar to 1.36 M-circle dot. In addition, cooling times for the most massive white dwarf sequences are about a factor of two smaller than in the Newtonian case at advanced stages of evolution. Finally, a sample of white dwarfs have been identified as ideal candidates to test these general relativistic e ffects. Conclusions. We conclude that the general relativity e ffects should be taken into account for an accurate assessment of the structural and evolutionary properties of the most massive white dwarfs. These new ultra-massive white dwarf models constitute a considerable improvement over those computed in the framework of the standard Newtonian theory of stellar interiors.