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Milky Way Galaxy

The Dark Accretion Disk of Sagittarius A*

The formation of some type of disk around the central Galactic black hole is almost inevitable.  The stellar winds captured by Sagittarius A* carry some angular momentum, which defines a periastron close to the black hole for the infalling gas.  The gas flowing into the periastron collides with the gas already there, dissipating energy and bringing the gas into a circular orbit around Sgr A*.  The gas at the periastron will constitute a disk orbiting the black hole.

Unlike the accretion disks seen around other black hole candidates, such as those found in x-ray binary systems and around the presumed massive black holes in active galactic nuclei, the hypothesized accretion disk around the central Galactic black hole is relatively dark, emitting only a fraction of the gravitational potential energy liberated by the infalling gas.  How does one explain this radiative inefficiency in an accretion disk theory?

A solution that has preoccupied the astrophysics community is for the accretion disk to carry the released gravitational potential energy to the event horizon of the black hole.[1]  This is an advective accretion disk.  As with the radiative accretion disks, the advective accretion disk is hot, but it is unable to convert its heat into radiation.  The lower capture rate of gas by Sgr A* than by the active galactic nuclei would be the cause of the advective accretion disk.

A recent alternative to the advective accretion disk uses the heat in the disk to drive a wind away from the black hole.[2]  I shall refer to this second theory as an advective wind theory, since the theory's bad-pun acronym “ADIOS” (ADiabatic Inflow-Outflow Solutions) makes me wince; some astrophysicists seem to name their theories while at the pub.

The advective disk theory for Sgr A* is a variant of the standard accretion disk theory for the flow of gas onto a black hole or a star.  The gas lies in a disk and orbits in a circle around the central object.  The rotation of the disk is differential, with the inner portions of the disk rotating at higher velocities than the outer portions.  This rotational shear drives turbulence and other processes that convert kinetic energy into thermal energy.  The loss of kinetic energy causes the gas to drift slowly inward to the central object.  As the gas drifts inward, its gravitational potential energy is converted into kinetic energy.  The difference between the radiative and the advective accretion disks is in the fate of the thermal energy generated within the disk: a radiative accretion disk converts its heat into electromagnetic radiation, but an advective accretion disk carries its heat to the central object.

The radiative accretion disk efficiently converts thermal energy into radiation of frequencies extending from the infrared to the gamma-ray bands.  This efficiency makes the radiative accretion disk an attractive theory for luminous sources, such as active galactic nuclei, but the efficiency is a big problem for Sgr A*, which emits very little radiation above the radio band. An accretion disk orbiting Sgr A* would have to trap within itself the heat it generates.  This can be done by keeping the thermal energy within the disk away from the electrons, which are responsible for most of the radiation we see from a hot gas or plasma.  The power radiated by a charged particle increases as the particle's mass decreases.  Because the electron is 2,000 times less massive than the proton, and less massive still than the nucleus of any atom, it is the most efficient particle at radiating away the energy of a gas.

The thermal energy within an accretion disk can be trapped long enough for it to be transported to the black hole if it is carried by ions and protons rather than electrons, and if the transfer of energy from ions and protons to electrons is inefficient.  This means that the temperature of the ions and protons is much higher than that of the electrons.  This idea of a two-temperature material may seem peculiar.  On Earth, high densities ensure that all the electrons and atomic nuclei at a given point within a gas or solid have the same temperature.  Collisions between electrons and atomic nuclei distributes the thermal energy equally among all particles, so that each particle has the same average kinetic energy—which temperature measures—as every other particle.  In the low-densities of space, however, different constituents of a gas or plasma are not always in thermal equilibrium.

Particles of the same mass come into thermal equilibrium with each other faster than they do with heavier or lighter particles.  This is easily understood if one thinks of how two objects collide.  In an elastic collision of two objects—where no energy is converted into heat and the two objects remain separate after the collision—if one object is in motion, and the other object is at rest, the object in motion can give all of its kinetic energy to the object at rest if both have the same mass.  The transfer of kinetic energy between objects is complete.  If the object in motion is much more massive than the object at rest, then the object in motion will knock the object at rest forward without slowing appreciably—think of a truck hitting a beach ball. For the high-mass object to lose all of its kinetic energy, it must hit many low-mass objects, which takes time.  This is precisely what happens within a gas.  The ions and protons come into equilibrium with each other before coming into equilibrium with the electrons, so the temperature of the ions can be much higher than the temperature of the electrons for timescales shorter than the timescale for transferring energy from the ions to the electrons.

One can see this in a shock wave moving through a cold gas.  Because the ions are heavier than the electrons, they carry more kinetic energy than the electrons before passing through a shock wave, as measured by an observer moving with the shock wave.  After passing through the shock wave, the ions will have a much higher temperature than the electrons, because the ions passing through the shock come into equilibrium with each other before coming into equilibrium with the electrons.  The ions come into thermal equilibrium with the electrons far downstream from the shock.

A similar segregation of energy between ions and electrons is hypothesized for an advective accretion disk.  The accretion disk would then be dim if the disk can transport the thermal energy of the ions and protons to the central object before the electrons can come into equilibrium with the ions.  In a sense, the advective disk theory applied to Sgr A* is similar to the Bondi accretion theory in that both require the gas to fall onto the black hole before the ions lose their thermal energy; the difference between the theories is that Bondi accretion tries to outrun the emission of radiation by electrons, and the advective accretion disk tries to outrun the transfer of energy from ions and protons to electrons.

The advective accretion disk theory relies on the central object being a black hole; if general relativity were wrong, and the supermassive object at the center of our Galaxy were a variety of supermassive neutron star, for instance, then all the energy carried by the accreting gas would accumulate at the surface of the central object, from where it would  be released into space.  For advective accretion to explain the observations, the energy carried by the accretion disk must be trapped by the central object, which could only happen if the gas falls onto an event horizon.

The absence of radiation, of course, is not evidence that the central object is a black hole, and that general relativity is the correct description of gravity when gravitational fields are strong.  The event horizon of a black hole is not the only place to dispose of the accretion disk's heat; it can be expelled in a wind.  In this theory, the thermal energy of the gas is converted into the kinetic energy of a wind flowing away from Sgr A*.

In some sense, the motion of gas in a wind theory for Sgr A* resembles the motion of a comet on a hyperbolic orbit around the Sun.  Comets that are gravitationally unbound follow hyperbolic orbits, falling nearly radially and at a constant speed towards the Sun when far away, accelerating to higher speeds as the gravitational potential energy is converted into kinetic energy, arching around the sun at its perihelion, which is set by the comet's angular momentum, and flying away forever from the Sun, converting kinetic energy back into gravitational potential energy, until the comet drops back to its original speed far from the Sun.  The comet remains unbound from the Sun as long as orbital energy is not lost.  The gas falling onto Sgr A* in the advective theories resembles the comet in that, without a significant radiative loss of energy, it remains gravitationally unbound.  The thermal energy within the gas is available to accelerate the gas permanently away from Sgr A*.

This is the basis of the advective wind theory for Sgr A*.  In this theory, as in the advective accretion disk theory, gas flows in a disk toward the central black hole. Gravitational potential energy is converted into kinetic and thermal energy, with only an insignificant amount of the thermal energy radiated away from the system.  But the thermal energy is not trapped within the disk in this theory, as it is in the advective theory; the thermal energy drives a wind from the surface of the disk along the axis of rotation. As gas flows from the disk, it expands and accelerates, and the thermal energy within the gas is converted into kinetic energy.  Because little energy is radiated away from the disk, and because most of the gas in the disk is eventually driven away in the wind, virtually all of the thermal energy of the disk is converted into kinetic energy, and then into gravitational energy. In this theory, only a miniscule fraction of the gas captured by Sgr A* falls to the event horizon, which accounts for the low x-ray emission of Sgr A*.  In effect, the liberation of gravitational potential energy within the accretion disk is only temporary when the disk drives a wind.

These are the current ideas theorists are exploring to explain the quiescence of Sgr A*.  There is room for other ideas.  If the advances in understanding Sgr A* follow the historical pattern, the theory astrophysicists finally settle on will be far more complex than the simple theories outlined on this page.  With luck, however, one of the early, simple theories will capture the essence of what really is happening at Sgr A*.

[1]Narayan, Ramesh, and Yi, Insu.  “Advection-Dominated Accretion: Underfed Black Holes and Neuron Stars.”  The Astrophysical Journal 452 (20 October 1995): 710–735.

[2]Blandford, Roger D., and Begelman, Mitchell C.  “On the Fate of Gas Accreting at a Low Rate on to a Black Hole.” Monthly Notices of the Royal Astronomical Society 303 (1999): L1–L5.

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