Disk Accretion Flow Driven by Magnetic Fields: Solutions with Constant Specific Energy

Though it is well established that magnetic fields effectively transport angular momentum in an accretion disk, it is far from clear if magnetic fields also effectively transport or dissipate energy in the meantime. In this paper we use a simple model to study the dynamical effects of magnetic fields in an accretion disk around a Kerr black hole, trying to understand the transportation of angular momentum and energy. The model is developed from that used by Gammie (1999), where the magnetic field and the fluid velocity are assumed to have only radial and azimuthal components in a small neighborhood of the equatorial plane. Maxwell’s equations are exactly solved with the assumption that the disk plasma is perfectly conducting and the disk flow is in a stationary and axisymmetric state. Then, making use of the conservation of rest mass, energy, and angular momentum, we reduce dynamical equations to a one-dimensional radial momentum equation with radius as the only variable. The gas pressure is assumed to be zero so the radial momentum equation has only one intrinsic singularity given by the fast critical point. We then solve the radial momentum equation for solutions that start from a subsonic state at infinity, smoothly pass the fast critical point, then supersonically fall into the horizon of the black hole. We find that the solutions always have the following feature: the specific energy of fluid particles remains constant but the specific angular momentum is effectively removed by the magnetic field. This implies that a disk accretion flow driven by magnetic fields may automatically have a very low radiation efficiency since magnetic fields do not have to transport or dissipate a lot of energy as they effectively transport angular momentum. The geometry of disk is presumably to be thick since at large radii the magnetic energy is about equipartitioned with the kinetic energy of the flow. With