Mathematical modeling of high-speed collision of White Dwarfs — explosion mechanism of type Ia/Iax supernovae

Type Ia supernovae are not only major sources of iron, but also «standard candles» for measuring distances in the Universe. Although these supernovae are important, their explosion mechanism is still under study. Mathematical modeling is a major (if not the only) tool for studying such astrophysical phenomena. It can be used to compile rather complex scenarios of type Ia supernova explosions. One of the scenarios is a generalized mechanism of gravitational impact, which is based on collisions of white dwarfs. The mathematical model of white dwarfs used in the paper is based on a numerical solution of the equations of gravitational hydrodynamics with an adapted stellar equation of state. The subgrid carbon burning is realized in the form of direct modeling of turbulent burning of the material. This approach makes it possible to reproduce carbon burning in a more detailed and correct way in terms of energy. To study the scenarios of a gravitational impact, we use an auxiliary one-dimensional statement of the problem of collision of white dwarfs based on an analytical solution to the problem of discontinuity breakdown in a degenerate gas. Despite the simplicity of this problem, some necessary conditions for the ignition of carbon and its further burning can be obtained in the process of its solution. Using computational experiments on a supercomputer to solve problems of type Ia supernova explosions in the full three-dimensional statement, we study in detail scenarios obtained in solving the one-dimensional problems. Two main parameters have been identified: the collision velocity and the minimum temperature of white dwarfs and an experimental relation has been obtained between these parameters and the scenarios for a type Ia/Iax supernova explosion under a gravitational impact.