The missing chapter in Chandrasekhar's book...
...would have been about the magnetorotational instability. The transport of
specific angular momentum is a delicate problem in various astronomical objects.
The formation of stars and planets as well as the rotation of stellar interiors,
also the luminosity of galactic nuclei imply transporting angular momentum inside
out. Instabilities may provide such transport.
Cosmic rotation curves are not easily accessible to terrestrial experiments.
A close analogue is the TaylorCouette flow  a fluid between rotating
cylinders. If the rotation speed of the cylinders differs a lot, the flow
is unstable for higher than a critical Reynolds number. Chandrasekhar studied
such a flow with magnetic fields and could not find an earlier onset of
instability. He actually made an approximation valid for very low ratios
of viscosity to diffusivity (magn. Prandtl number, upper curves in the graph,
the Hartmann number is a measure of the magnetic field strength).
Now we studied MHD TaylorCouette
flows for large Prandtl numbers, and there is indeed a subcritical
excitation of Taylor vortices due to the presence of magnetic fields. The graphs for Prandtl
number = 1 and = 10 have a minimum. The magnetic Prandtl numbers in astrophysical
objects are indeed orders of magnitudes larger than those of terrestrial conducting
fluids (Hg 10^7, Ga 10^6, Na 10^5).
Other than in this experimental TaylorCouette flow, astrophysical rotation
profiles are hydrodynamically very stable. The magnetic fields will be
essential for angularmomentum transport. The TaylorCouette flow may,
however, be a chance to see the magnetorotational instability in
experiments. First projects are being started to get cosmic objects into
the laboratory!
(credits: G. Rüdiger, R. Arlt, AIP)
