Open AccessThe signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
Author(s) -
Pessah Martin E.,
Chan Chikwan,
Psaltis Dimitrios
Publication year - 2006
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2006.10824.x
Subject(s) - magnetorotational instability , physics , instability , magnetohydrodynamics , reynolds stress , turbulence , mechanics , angular momentum , viscous stress tensor , classical mechanics , magnetic reynolds number , reynolds number , accretion (finance) , magnetic field , magnetohydrodynamic turbulence , shearing (physics) , astrophysics , cauchy stress tensor , thermodynamics , quantum mechanics
The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth of the instability, the mean (averaged over the disc scaleheight) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds stresses during the late times of the exponential growth of the instability is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic field. Even though we derived this property of the stress tensors for the exponential growth of the instability in incompressible flows, numerical simulations of shearing boxes show that this characteristic is qualitatively preserved under more general conditions, even during the saturated turbulent state generated by the instability.