Effects of magnetic fields on the propagation of nuclear flames in magnetic white dwarfs

We investigate effects of the magnetic field on the propagation of laminar flames of nuclear reactions taking place in white dwarfs (WDs) with the mass close to the Chandrasekhar limit. We calculate the velocities of laminar flames parallel and perpendicular to uniform magnetic fields as eigenvalues of steady solutions for magnetic hydrodynamical equations. As a result, we find that even when the magnetic pressure does not dominate the entire pressure it is possible for the magnetic field to suppress the flame propagation through the thermal conduction. Above the critical magnetic field, the flame velocity decreases with increasing magnetic field strength as $v \sim B^{-1}$. In media with densities of $10^{7}, 10^{8}, \,\mathrm{and}\,10^{9} \unit{g\,cm^{-3}}$, the critical magnetic fields are orders of $\sim 10^{10}, 10^{11}, \,\mathrm{and}\,10^{12} \unit{G}$, respectively.