The Astrophysics Spectator
The Astrophysics Spectator
The simplest theory of accretion onto a black hole is for the gas to flow straight down to the black hole. If the gas has no angular momentum, falls inwards in uniform shells, and radiates only negligible energy, then its velocity and density are dependent only on the distance from the black hole. This spherically-symmetric accretion is called Bondi accretion. Theorists (or, more precisely, Bondi) solved this simple problem over half a century ago, but the solution has had little application in astrophysics; it is a beginner's exercise, a simple problem that one tackles before moving to the more physical, but difficult, problem of gas flow with angular momentum. In astrophysics the assumption that gas has no angular momentum when it falls onto a black hole is almost always bad.
All black holes candidates that we seen in our Galaxy, with the exception of Sgr A*, are found in compact binary systems. Gas in these systems flows through an unstable synchronous point, where a free body can maintain a constant distance between the star and the black hole as it orbits within the system. The gas that flows through this point carries a large angular momentum that causes the gas to form a disk around the black hole that extends from near the companion star down to the last stable orbit of the black hole.
The central Galactic black hole, Sgr A*, sees an environment that differs dramatically from the binary system environment. Sgr A* powers itself by capturing the winds of several nearby stars. These winds flows around the black hole rather than in a stream to one side of the back hole. The gas that is captured carries only a small amount of angular momentum, which, far from the black hole, permits the gas to fall nearly radially. For this reason, the gas flow far from the black hole can be described as Bondi accretion.
The basic theory for Bondi accretion is that a black hole pull a uniform, infinite gas onto itself in a steady state. Far from the black hole, the gas moves towards the black hole at much less than the sound speed; the gas is driven towards the black hole by its pressure, and not by gravity. Closer to the black hole, gas pressure and the black hole's gravitational force accelerate the gas through the sonic point, where the infall speed exceeds the sound speed. The sonic point is an event horizon for sound waves, because disturbances in the gas inside the sonic point cannot propagate away from the black hole. Inside the sonic point, both the velocity and the density of the gas rise as the gas approaches the black hole.
For fully ionize hydrogen and helium, the velocity of the gas far inside the sonic point is proportional to R?1/2, which is the relationship for a body in free fall. As the gas falls inward, its density also rises, increasing as R?3/2. Compressing a gas raises its temperature, so some of the gas's gravitational potential energy is converted into thermal energy. The temperature changes with radius as R?1, so the thermal energy rises proportionally with the kinetic energy of the gas. The gas has little time to radiate all of the thermal energy pumped into it as it falls to the black hole. Gas falls onto Sgr A* from its point of capture at 0.02 parsecs in only 15 years, and it falls from 0.2 AU to 0.1 AU, the radius of the last stable orbit, in only 1 minute. Can the gas radiate away all of its energy in these short times?
An ionized gas can generate electromagnetic energy through two principal processes: through collisions between electrons and ions (bremsstrahlung emission), and through the motion of electrons through a magnetic field (cyclotron emission). Bremsstrahlung emission can remove the energy released at the capture point in several hundred million years, which means it cools the gas by a negligible amount over the infall timescale of 15 years. This disparity in timescales grows worse as the gas falls towards the black hole. The cooling timescale is proportional to R, while the infall timescale is proportional to R3/2, so the infall timescale becomes proportionally shorter than the cooling timescale as R1/2. Bremsstrahlung is most efficient at removing energy from the gas at the capture point. Cyclotron emission can do a better job of cooling a gas, although the power radiated away depends critically on the magnetic field in the gas. As an estimate of how efficient cyclotron emission can be, one normally assumes that the magnetic field strength is at its maximum value. The maximum energy density of the magnetic field equals the thermal energy density of the gas; such a magnetic field is in equipartition with the gas, meaning that the energy is distributed equally between the magnetic field and the gas. Under this equipartition condition, cyclotron emission can cool the gas at the capture point over a timescale of several hundred million years, which is again much longer that the infall timescale. Within 1 AU of the black hole, the cyclotron cooling timescale is closer to one hundred thousand seconds, which is still long compared to the several hundred second infall timescale. Only at the last stable orbit does the cyclotron cooling timescale equal the inflow timescale. More realistically, the magnetic field should be less than the equipartition value, so the cooling timescale will be longer than these estimates.
This mismatch between the cooling and infall timescales makes Bondi accretion a horribly inefficient way of generating radiation from a black hole, which is an exceedingly useful property for explaining the emission from Sgr A*. The precise emission depends on the processes that generate and dissipate the magnetic field within the infalling gas and on how the energy is distributed among the electrons. Theorists have been able to reproduce the radio spectrum of Sgr A* from this theory with the magnetic field set to less than the equipartition value.
As long as the wind captured by the black hole can free-fall some distance onto the black hole before forming a disk, the outer regions of Sgr A* should behave as described by Bondi accretion theories. If the captured gas has negligible angular momentum, it flows directly onto the black hole's event horizon, taking all of its thermal and kinetic energy with it. However, given the long distance the gas must fall, from its point of capture 4,000 AU away from the black hole to the black hole's last stable orbit 0.1 AU away, one does not expect the flow to be radial all the way to the event horizon. Just a small amount of angular momentum will cause the gas to flow along a highly-eccentric path, much like the orbits of the stars found near the central Galactic black hole. At the periastron of the orbit followed by the gas, shock waves should form that dissipate the kinetic energy in the gas, forcing the gas into a circular orbit around the black hole. There should be a torus or disk of very hot gas orbiting the black hole. This takes us back to the original question: why don't we see radiation from the gas falling onto the black hole? Bondi accretion may explain the radio emission from the outer regions of Sgr A*, but another theory is needed to explain the absence of x-rays in the regions where angular momentum controls the flow of gas onto the black hole.
