Disk accretion flow driven by large-scale magnetic fields: Solutions with constant specific energy

We study the dynamical evolution of a stationary, axisymmetric, and perfectly conducting cold accretion disk containing a large-scale magnetic field around a Kerr black hole, trying to understand the relation between accretion and the transportation of angular momentum and energy. A one-dimensional radial momentum equation is derived near the equatorial plane, which has one intrinsic singularity at the fast critical point. We solve the radial momentum equation for solutions corresponding to an accretion flow that starts from a subsonic state at infinity, smoothly passes the fast critical point, then supersonically falls into the horizon of the black hole. The solutions always have the following features: (1) The specific energy of fluid particles remains constant but the specific angular momentum is effectively removed by the magnetic field. (2) At large radii, where the disk motion is dominantly rotational, the energy density of the magnetic field is equipartitioned with the rotational energy density of the disk. (3) Inside the fast critical point, where radial motion becomes important, the ratio of the electromagnetic energy density to the kinetic energy density drops quickly. The results indicate that: (1) disk accretion does not necessarily imply energy dissipation since magnetic fields do not have to transport or dissipate a lot of energy as they effectively transport angular momentum and (2) when resistivity is small, the large-scale magnetic field is amplified by the shearing rotation of the disk until the magnetic energy density is equipartitioned with the rotational energy density, ending up with a geometrically thick disk. This is in contrast to the evolution of small-scale magnetic fields where if the resistivity is nonzero the magnetic energy density is likely to be equipartitioned with the kinetic energy density associated with local random motions (e.g., turbulence), making a thin Keplerian disk possible