Magnetic field effects on the thermonuclear combustion front of Chandrasekhar mass white dwarfs

The explosion of a type Ia supernova starts in a white dwarf as a laminar deflagration at the center of the star and soon several hydrodynamic instabilities, in particular, the Rayleigh-Taylor instability, begin to act. A cellular stationary combustion and a turbulent combustion regime are rapidly achieved by the flame and maintained up to the end of the so-called flamelet regime when the transition to detonation is believed to occur. The burning velocity at these regimes is well described by the fractal model of combustion. Using a semi-analytic approach, we describe the effect of magnetic fields on the fractalization of the front considering a white dwarf with a nearly dipolar magnetic field. We find an intrinsic asymmetry on the velocity field that may be maintained up to the free expansion phase of the remnant. Considering the strongest values inferred for a white dwarf's magnetic fields with strengths up to $10^{8}-10^{9}$ G at the surface and assuming that the field near the centre is roughly 10 times greater, asymmetries in the velocity field higher than $10-20 %$ are produced between the magnetic polar and the equatorial axis of the remnant which may be related to the asymmetries found from recent spectropolarimetric observations of very young SN Ia remnants. Dependence of the asymmetry with white dwarf composition is also analyzed.