Long-term Nonlinear Behaviour of the Magnetorotational Instability in a Localised Model of an Accretion Disc

TL;DR

This paper investigates the long-term nonlinear behavior of the magnetorotational instability in a localized accretion disc model, highlighting challenges in accurately estimating angular momentum transport over extended simulations.

Contribution

It provides insights into the complexities of measuring the alpha parameter in long-duration simulations, emphasizing the influence of numerical factors.

Findings

Long-term simulations reveal variability in alpha estimates.

Numerical dissipation and computational setup significantly affect results.

Estimating alpha becomes more challenging with increased computational power.

Abstract

For more than a decade, the so-called shearing box model has been used to study the fundamental local dynamics of accretion discs. This approach has proved to be very useful because it allows high resolution and long term studies to be carried out, studies that would not be possible for a global disc. Localised disc studies have largely focused on examining the rate of enhanced transport of angular momentum, essentially a sum of the Reynolds and Maxwell stresses. The dominant radial-azimuthal component of this stress tensor is, in the classic Shakura-Sunayaev model, expressed as a constant alpha times the pressure. Previous studies have estimated alpha based on a modest number of orbital times. Here we use much longer baselines, and perform a cumulative average for alpha. Great care must be exercised when trying to extract numerical alpha values from simulations: dissipation scales, computational box aspect ratio, and even numerical algorithms all affect the result. This study suggests that estimating alpha becomes more, not less, difficult as computational power increases.