Dynamical Response of White Dwarf with an Accreted Primordial Black Hole

Dark matter (DM) is an important component for the large-scale structure formation in the universe. Primordial Black Holes (PBHs) are one of the possibilities - as one type of dark matter candidate. When these PBHs fall into white dwarfs, the gravity of the PBH causes tidal heating in the WD matter along its trajectory. The hot spot triggered in the star could lead to unstable C-burning, and the subsequent explosions as Type Ia supernovae. It is unclear how the various types of white dwarf models respond to the external gravity of DM, especially when hydrodynamics instabilities are involved. By using 2-D hydrodynamic simulations, we solve the compressible hydrodynamics equations with the realistic Equation of State, to study the dynamics of the white dwarf. We examine the response of the white dwarf as the PBH moves through the center, in terms of temperature, velocity, and density. We find that the thermodynamics properties are sensitive to the PBH mass. Based on our models, we estimate the critical PBH mass to trigger Type Ia supernovae and how multi-dimensional effects, such as Kelvin-Helmholtz Instability, are involved in the heating process. Our work could shed light on the explosion trigger mechanism of Type Ia supernovae rate and help constrain the cosmic Type Ia supernova rate.