There are many strange objects that can be found in the universe. The image shows a pair of stars that are orbiting around their common centre of mass. The blue star at the left is filling its Roche lobe, and matter is therefore streaming over towards the compact object at the right. Because the matter has too much angular momentum it cannot fall directly onto the compact object. Instead it forms an accretion disc surrounding the compact object. (This image was taken from A Wormhole in the Cosmos.) If the compact object is a white dwarf, then we will call the binary a cataclysmic variable, while if the compact object is a neutron star or a black hole, we will call the system an X-ray binary. Since the neutron star and the black hole are much more compact than a white dwarf the innermost part of the accretion disc will be much hotter in the X-ray binary, and therefore it will emit large amounts of X-rays, hence its name. The cataclysmic variable on the other hand is mostly emitting in the blue and ultraviolet parts of the spectrum. One can also find accretion discs around protostars (newborn stars that are not fully developed yet) and around the supermassive black holes that one finds in the centres of galaxies. It is also possible that they play a role during a gamma-ray burst.
The matter in an accretion disc is in general on a Keplerian orbit around the accreting object, that is it is held in place by the balance between gravity and the centrifugal force. If this was all there was, nothing would ever happen in an accretion disc, the matter would just go on revolving around the accreting star for ever, but there will always be some viscosity in the disc. The effect of the viscosity is to take away some angular momentum from each gas element and hand it over to a gas element further out. The first gas element will then move a bit closer to the accreting object, as its new angular momentum corresponds to a smaller orbit. Repeating this process many times the gas element will eventually fall down, be accreted on, the central object. In the process the accretion disc is heated by the released potential energy, which it radiates away. In many cases the heating is so efficient that the gas becomes ionised and we get a plasma. In the X-ray binaries the gas is even heated to several million degrees.
The question is then where the viscosity comes from. The usual friction that one would expect to have between the atoms in the gas is insufficient to drive the accretion. There must therefore be some way of amplifying the viscosity. Typically viscosity is amplified by turbulence, but then why is the disc turbulent? Although a lot of effort had been put into understanding the physics of accretion discs since the beginning of the 70s, there was no satisfactory explanation of where the turbulence would come from until 1991, when Steve Balbus and John Hawley showed that the accretion disc becomes unstable if there is a weak magnetic field in the disc. Numerical simulations a couple of years later showed that this instability leads to that the disc becomes turbulent. We get a form of magnetohydrodynamic turbulence. The magnetic field derives its energy from the rotation of the accretion disc, and puts this energy into the turbulence. The turbulence in its turn is heating the accretion disc, but it is also re-generating the magnetic field, which was needed to derive the energy in the first place.
The sad thing is that it is not possible to test these models of how an accretion disc becomes turbulent. The turbulence occurs on length scales that are so short that in general we cannot observe them, and surprisingly the turbulence does not have much influence on the observable properties of the accretion disc. Only by studying discs that change over is it possible to test our ideas of how the turbulence works and how it affects the disc. Fortunately there is one kind of cataclysmic variables, dwarf novae, that undergo outbursts about once a month, and by studying how the disc changes during the outbursts it is possible to measure how the turbulence affects the disc.
However the magnetic field may manifest itself in another way too. Quite often one observes that there are jets shooting out from the centres of galaxies and from protostars. It may seem that these systems do not have much in common, but in both cases there is a central mass that is surrounded by an accretion disc, and somehow all the matter in the disc is not falling down onto the central mass, but instead some of the disc material is re-directed into two jets streaming out perpendicularly to the disc. So far we do not understand in detail how these jets are formed, but most models assume that a magnetic field is transferring energy from the disc to the jet material. Furthermore the magnetic field is shaping the outflow into a thin jet and holding the gas stream together over immense distances. In some galaxies the jets extend far outside of the observable galaxies.
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