Time dependence in accretion onto magnetic white dwarfs

Cataclysmic variable systems containing a white dwarf with a strong magnetic field are considered. Theoretical models are presented for the temperature, density, and velocity structure of the accretion flow in the region near the surface of the white dwarf where the kinetic energy of the flow is thermalized and radiated in the form of X-rays and ultraviolet radiation. The effects of the gravitational field, heat conduction, and radiative cooling by bremsstrahlung radiation are included. The three time-dependent nonlinear differential equations for the transport of mass, momentum, and energy are numerically solved using an implicit, finite-difference method. The solution is obtained on a discrete grid of radius points, and its evolution in time is followed. At the upper boundary of the grid the matter is cool and in free fall. At the lower boundary, which is placed well inside the photosphere of the white dwarf, the mass flux is zero.