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Milky Way Galaxy

The Capture of Winds by Sgr A*

The power generated as radio waves by the central Galactic black hole is several hundred times the power generated by the Sun.  When the estimated power emitted at infrared wavelengths is included, the total power is over one thousand times the power of the Sun.  This is a surprisingly low value, because Sgr A* is surrounded by many sources of gas that should enable the black hole to generate 100 million times more power than it does.  The problem is not that Sgr A* lacks fuel for generating power; rather, it is inefficient at generating electromagnetic radiation from this fuel.

Over a dozen stars within 1 parsec of Sgr A* expel strong winds from their photospheres.  It is uncertain what type of stars these are, but they have the characteristics of very massive stars.  Strong winds are typical of very high-mass stars such as OB supergiants and Wolf-Rayet stars?the latter type of star is a highly-evolved OB supergiant that has blown away about half of its mass over its lifetime.  Such stars generate enough light to drive away their outer layers as a high-velocity wind.

Light has momentum.  When light from a star's photosphere scatters with free electrons and electrons bound to atoms within the star's atmosphere, momentum is transferred from the light to the atmosphere.  This exchange of momentum is effectively an outward pressure exerted by the light on the atmosphere.  If enough radiation flows through the atmosphere, the pressure of the light on the atmosphere will exceed the force of gravity, and the atmosphere will be driven from the star as a high-velocity wind.

The force exerted by radiation on an atmosphere is weakest when the gas in the atmosphere is fully ionized.  In this state, the interaction of light with matter is through the scattering of light by free electrons; force is exerted on the ions by the electrons through a large-scale electric field that is created when the electrons start moving away from the star.  The luminosity at which the radiative pressure on a fully-ionized plasma is precisely counteracted by the gravitational force at the photosphere of a star is called the Eddington limit.  It depends on only one parameter: the mass of the star.  The Eddington limit is directly proportional to the mass of the star.  In practice, a plasma is only partially ionized, and the light scatters both with free electrons and with electrons bound to atoms.  Light exerts more pressure on a bound electron than on a free electron, so one finds that radiation drives a wind from a star at a luminosity that is somewhat less than the Eddington limit.

The Eddington limit for the Sun is 1.251038 ergs s?1 which is 31,000 times the Sun's luminosity.  The luminosity of a star rises much more rapidly with its mass than does the Eddington limit, so stars with masses above around 20 solar masses can generate power that exceeds the Eddington limit.  These are the stars that drive a steady wind from their photospheres.   As the radiation drives the wind, energy is transferred from the radiation to the wind, so although the power in the wind and the power in the radiation combined exceed the Eddington limit, the power in radiation remains close to the Eddington limit.  Over its lifetime, a stars with a radiatively-driven wind can lose half of its mass.  This large mass loss enables the massive stars orbiting Sgr A* to feed the black hole.

The Eddington limit is not limited to stars; it sets the upper limit on the amount of radiation a black hole can produce as it consumes gas.  If the gas falling into a black hole releases more radiation than the Eddington limit, then the energy in the radiation drives some of this gas from the black hole as a wind.  The energy in the radiation is converted into kinetic energy carried by the wind.  This conversion drives down the power in the radiation to a value close to the Eddington limit.  This is why the Eddington limit  is used as a benchmark for power output from a black hole?a black hole cannot be much more luminous than its Eddington limit.  Sgr A*, which is 3.6 million times more massive than the Sun, has an Eddington limit of 4.51044 ergs s?1, or 1011 times the power generated by the Sun.

Relatively little gas is needed to drive the central black hole at its Eddington limit.  If all of the gravitational potential energy release by gas falling into the black hole is converted into radiation, then the Eddington limit of 4.51044 ergs s?1 for Sgr A* is achieved for an inflow of 51023 g s?1, or 0.008 solar masses per year.  To generate a power of 1,000 times the solar luminosity requires only 21015 g s?1, or 310?11 solar masses per year.

The central black hole should be feeding on the winds of the massive stars lying within 10 arc seconds (0.4 AU) of the black hole.  The winds of these stars, which are seen through the Doppler broadening of the lines in their spectra, move with velocities ranging from 200 km s?1 to 1,000 km s?1; these velocities are sufficiently high to enable most of the wind to escape the black hole.  Through these winds, the stars lose from 10?5 solar masses per year to nearly 10?3 solar masses per year.  If the central black hole captures all of this gas, the power generated by the gas as it falls onto the black hole would just equal the Eddington limit. But the central black hole can only capture a fraction of this gas.  The amount captured depends on three parameters: the mass of the black hole, the density of the gas in the wind, and the velocity of the wind.[1]  The wind velocity is the primary factor that determines the rate at which gas from these winds flows onto Sgr A*; the higher the velocity, the lower the rate at which wind is captured by the black hole.  For the high value of 1,000 km s?1, approximately 10% of the wind is captured.   This capture rate rises dramatically for lower wind velocities.    If the wind is moving at less than the sound speed, the sound speed replaces the wind velocity in setting the rate at which the wind is captured.  Estimates are that the black hole should capture of order 10?5 solar masses per year from the winds of nearby stars.[2]   This implies that the gas falling onto the black hole is generating on order 1042 ergs s?1, and only 10?5 of this energy is being converted into observable radiation.

In most systems where gas falls onto a star or black hole, most of the gravitational potential energy of the gas is converted into radiation and into kinetic energy carried by a jet or wind.  In these systems,  the gas has some angular momentum, so it forms a rotating disk around the object towards which it is falling. The disk is called an accretion disk, because the gas in the disk drifts towards the gravitating object, eventually falling onto that object.

Under the standard theory, the accretion disk around a black hole is extremely efficient at converting gravitational potential energy into radiation.   The gas in the disk follows a nearly-circular orbit, with the inner regions of the disk rotating faster than the outer regions.  This differential rotation drives turbulence and generates magnetic field, both of which heat the accretion disk.  The effect on the disk is that gas in the disk gradually drifts inward toward the black hole; the gravitational potential energy released in this drift is converted into the kinetic energy of the disk's rotation and into the heat generated by the turbulence and the magnetic fields.  As gas drifts from the outer edge of the accretion disk to the disk's inner edge at the black hole's last stable orbit, about half of the gravitational potential energy is converted into heat.  This energy is about half of the rest mass energy of the gas.  Inside the last stable orbit, the gas of the accretion disk free-falls onto the black hole's event horizon.

Clearly the standard accretion disk theory is invalid  for Sgr A* given the amount of gas the black hole should be capturing.  This theory also run counter to the low x-ray flux:  the inner edge of a standard accretion disk that is orbiting a black hole is a strong x-ray emitter.  Sgr A*, however, is a relatively weak x-ray source.  These points of conflict with the standard accretion disk theory suggests two lines of thought: either an accretion disk does not form around the black hole, or the accretion disk that does form is very different from accretion disks found in other systems, being unable to convert heat into radiation.  Other less popular lines of thought are that most of the gas captured by the black hole is expelled in a wind before it fall far towards the black hole and that radiation from the black hole is shining in specific directions, and we are not on those paths.

[1]Bondi, H., and Hoyle, F. ?On the Mechanism of Accretion by Stars.? Monthly Notices of the Royal Astronomical Society 104 (1944): 273?282.

[2]Melia, Fulvio, and Falcke, Heino. ?The Supermassive Black Hole at the Galactic Center.? In Annual Reviews of Astronomy and Astrophysics, edited by Geoffrey Burbidge, Allan Sandage, and Frank H. Shu, vol. 39. Palo Alto, California: Annual Reviews, 2001.

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