Accretion Disc - Accretion Disc Physics

Accretion Disc Physics

In the 1940s, models were first derived from basic physical principles. In order to agree with observations, those models had to invoke a yet unknown mechanism for angular momentum redistribution. If matter is to fall inwards it must lose not only gravitational energy but also lose angular momentum. Since the total angular momentum of the disc is conserved, the angular momentum loss of the mass falling into the center has to be compensated by an angular momentum gain of the mass far from the center. In other words, angular momentum should be transported outwards for matter to accrete. According to the Rayleigh stability criterion,

where represents the angular velocity of a fluid element and its distance to the rotation center, an accretion disc is expected to be a laminar flow. This prevents the existence of a hydrodynamic mechanism for angular momentum transport.

On one hand, it was clear that viscous stresses would eventually cause the matter towards the center to heat up and radiate away some of its gravitational energy. On the other hand, viscosity itself was not enough to explain the transport of angular momentum to the exterior parts of the disc. Turbulence-enhanced viscosity was the mechanism thought to be responsible for such angular-momentum redistribution, although the origin of the turbulence itself was not well understood. The conventional phenomenological approach introduces an adjustable parameter describing the effective increase of viscosity due to turbulent eddies within the disc. In 1991, with the rediscovery of the magnetorotational instability (MRI), S. A. Balbus and J. F. Hawley established that a weakly magnetized disc accreting around a heavy, compact central object would be highly unstable, providing a direct mechanism for angular-momentum redistribution.