Magnetorotational instability

Small magnetic fields in rotating fluids provide under certain conditions to ensure that the rotation is unstable and matter falls to the center. This phenomenon is called magneto rotational instability (MRI, Magnetic rotational instability ) designates or after its discoverer also Balbus -Hawley instability. The instability makes in astrophysical accretion disks, inter alia, for the formation of stars and black holes, but can also be observed in the laboratory. It follows from the basic equations of magnetohydrodynamics ( MHD).

Importance

Both of star formation, as well as in the formation of black holes, matter accumulates in an accretion disk and rotates around the center, in which the star formed. The matter in this case flows and laminar due to the third Kepler's law with decreasing outward speed. Must remain Since the state of lowest energy is the all mass accumulates in the center on the other hand, the angular momentum of the entire system get, this means that a large proportion of the mass moves inward, through a small part of the outside after far moved, is compensated. Possible approaches generated by viscosity turbulence not prove to be enough to cause the star formation efficiency.

Steven A. Balbus and John F. Hawley showed in 1991 by analyzing the equations of magnetohydrodynamics that small magnetic fields lead to instabilities in the rotating disks. This means that the angular momentum is transferred from inside to outside and that the inner layers of matter can thus fall into the center, so that mass accumulates there.

Phenomenon

The MRI is caused by shearing of the magnetic field in the plasma. Shear occurs as the magnetic field following the plasma and the inner layers to move faster than the outer ( differential rotation ). In such a sheared surface of the magnetic element acts as a spring which brakes the inner layer, it thereby increases the benefit of the outer layers of angular momentum and brings the inner layer has a lower orbit. This can accrete mass towards the center of gravity. The MRI is the cause for the high accretion rate and thus for the high luminosity, which is on different objects (eg AGN, quasars, microquasars ) were observed.

Theory

From the linear stability analysis of the MHD equations with differential rotation we obtain the dispersion relation:

And denote the frequency and the wave vector of the disorder, the Alfvén velocity, the speed of sound, the Epizykelfrequenz and the rotational frequency of the disc.

Instability occurs when imaginary is. Then we obtain the wave equation of a fault exponential growth. It turns out that the slow branch of the magneto- sonic wave for sufficiently weak magnetic fields become unstable, ie disturbances grow exponentially. The growth characteristic time of a fault is of the order of magnitude of the local period of rotation.

Research

The effect was already described in 1959 by Evgeny Velikhov and 1960 by Subrahmanyan Chandrasekhar in connection with stability considerations of Couette flows, hence the name Velikhov - Chandrasekhar instability.

Steven A. Balbus and John F. Hawley applied the effect to astrophysical systems such differentially rotating accretion disks. They showed the effectiveness of MRI in the angular momentum transport in theory and in simulations. So you provided the physical basis of the designed in 1973 by Nikolai I. Shakura and Rashid Sunyaev model of the standard disk ( see the accretion disk ).

Current research looks, for example, the interaction of the MRI with radiation MRI in resistive, the transition from optically thick to optically thin disks and the formation of jets from accretion disks.