Constraints on the magnitude of alpha in dynamo theory

Details Constraints on the magnitude of alpha in dynamo theory Constraints on the magnitude of alpha in dynamo theory

1999-03-25

arxiv.org/abs/astro-ph/9903384v2

ApJ, 534, 984, (2000)

Astronomy and Astrophysics

Astrophysics

LaTex, version in press, ApJ

Scientific paper

10.1086/308767

We consider the backreaction of the magnetic field on the magnetic dynamo coefficients and the role of boundary conditions in interpreting whether numerical evidence for suppression is dynamical. If a uniform field in a periodic box serves as the initial condition for modeling the backreaction on the turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamo coefficient $\a$, have a stringent upper limit that depends on the magnetic Reynolds number $R_M$ to a power of order -1. This is not a dynamic suppression but results just because of the imposed boundary conditions. In contrast, when mean field gradients are allowed within the simulation region, or non-periodic boundary are used, the upper limit is independent of $R_M$ and takes its kinematic value. Thus only for simulations of the latter types could a measured suppression be the result of a dynamic backreaction. This is fundamental for understanding a long-standing controversy surrounding $\alpha$ suppression. Numerical simulations which do not allow any field gradients and invoke periodic boundary conditions appear to show a strong $\alpha$ suppression (e.g. Cattaneo & Hughes 1996). Simulations of accretion discs which allow field gradients and allow free boundary conditions (Brandenburg & Donner 1997) suggest a dynamo $\alpha$ which is not suppressed by a power of $R_M$. Our results are consistent with both types of simulations.

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