Global structure of three distinct accretion flows and outflows around black holes through two-dimensional radiation-magnetohydrodynamic simulations
Ken Ohsuga and Shin Mineshige
- First Author’s Institution:
National Astronomical Observatory of Japan and Graduate University of Advanced Study
The authors have written a code that numerically solves the equations of radiation magnetohydrodynamics (RMHD). In other words, they solve a set of partial differential equations that describe radiation, magnetic fields, and fluid dynamics.As always, it isn’t possible to simulate reality perfectly, so a number of approximations are made. The most important is that the flow is presumed to be symmetric around the disk’s axis of rotation. This is a common and reasonable assumption and it’s important for making the problem solvable. Solving for two dimensions is a lot easier than solving for three! They further assume that the flow is symmetric across the equatorial plane. Gas that would cross the plane just bounces back. Finally, in order to solve efficiently for radiation,
they make the flux-limited diffusion approximation. Basically, the energy density of the radiation diffuses out at a rate that is limited by how quickly radiation can scatter through the gas.To capture general relativistic effects, the authors approximate the black hole’s gravity through the Paczynski-Wiita potential. This is a pretty good fit for the potential around a black hole, but it only describes a non-rotating black hole. The models can’t capture any effects due to the black hole’s spin, which are thought to be important for the formation of black hole jets.The simulation kicks off with a doughnut of material at a distance equal to 40 times the radius of the event horizon. The authors allow the flow to evolve without radiation effects for a few orbital periods before switching on radiation. Because the magnetic field describes the viscous nature of the fluid, the only free parameter that’s expected to make a qualitative difference, presuming that the gas is ideal, is the gas density.
Despite all the approximations, the simulation produces three distinct accretion flows for different choices of the density. Their models A, B, and C, shown in figure 2 of the paper (reproduced above), correspond to density parameters 1, 10-4 and 10-8 g.cm-3.In model A, the disk is geometrically thick and dominated by radiation pressure. This model closely matches the models by Abramowicz et al mentioned earlier. The flow only really accelerates towards the black hole when very close to the event horizon. Interestingly, this model drives a strong jet, powered by the intense radiation and held together by the magnetic field. This is different from other jet models that rely on black hole spin or magnetic pressure.Model B is geometrically thin and radiatively efficient, corresponding to the traditional Shakura-Sunyaev disks. The authors use their simulations to calculate the accretion efficiency (i.e. the amount of energy released per unit accreted mass). They also find that the disk is truncated at about 7 times the event horizon’s radius. Curiously, both of these numbers are quite close to theoretical predictions, but this isn’t mentioned.Finally, in model C, the gas is too sparse to radiate efficiently and puffs up, leading to very little mass being captured by the black hole. The disk-like part is about as thick as in model A, and in order to release energy, there is a strong outflow, this time powered by the magnetic field. This faint, diffuse flow is broadly similar to the flows described by Narayan and Yi.
The authors discuss their models in great detail and go on to consider them in light of a range of observational properties. They finally note some effects that their simulations cannot capture, but the fact remains that by varying just one parameter, they can produce three major modes of black hole accretion. Even though the detailed, quantitative structure doesn’t perfectly match theory, this looks like a big step in unifying our understanding of black hole accretion.