Magnetohydrodynamic Winds Driven by Line Force from the Standard Thin Disk around Supermassive Black Holes: II. A Possible Model for Ultra-fast Outflows in Radio-loud AGNs

In radio-loud active galactic nuclei (AGNs), ultra-fast outflows (UFOs) were detected at the inclination angle of ∼10°–70° away from jets. Except for the inclination angle of UFOs, the UFOs in radio-loud AGNs have similar properties to that in radio-quiet AGNs. The UFOs with such low inclination cannot be explained in the line-force mechanism. The magnetic-driving mechanism is suggested to explain the UFOs based on a self-similar solution with radiative transfer calculations. However, the energetics of self-similar solution need to be further confirmed based on numerical simulations. To understand the formation and acceleration of UFOs in radio-loud AGNs, this paper presents a model of the disk winds driven by both line force and magnetic field and implements numerical simulations. Initially, a magnetic field is set to 10 times stronger than the gas pressures at the disk surface. Simulation results imply that the disk winds driven by both line force and magnetic field could describe the properties of UFOs in radio-loud AGNs. Pure magnetohydrodynamics (MHDs) simulation is also implemented. When the initial conditions are the same, the hybrid models of magnetic fields and line force are more helpful to form UFOs than the pure MHD models. It is worth studying the case of a stronger magnetic field to confirm this result.

Far Field of a Three-Dimensional Laminar Wall Jet

We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

Larson–Penston Self-similar Gravitational Collapse

Using numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $$p=k\varrho $$ p = k ϱ , $$k>0$$ k > 0 , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.