Shedding light on the MRI-driven dynamo in a stratified shearing box

Abstract

ABSTRACT We study the magneto-rotational instability (MRI) dynamo in a geometrically thin disc (H/R ≪ 1) using stratified zero net (vertical) flux shearing box simulations. We find that mean fields and electromotive forces (EMFs) oscillate with a primary frequency fdyn = 0.017 Ω (approximately nine orbital period), but also have higher harmonics at 3fdyn. Correspondingly, the current helicity has two frequencies 2fdyn and 4fdyn, which appear to be the beat frequencies of mean fields and EMFs, respectively, as expected from the magnetic helicity density evolution equation. Further, we adopt a novel inversion algorithm called the ‘Iterative Removal Of Sources’, to extract the turbulent dynamo coefficients in the mean-field closure using the mean magnetic fields and EMFs obtained from the shearing box simulation. We show that an α-effect (αyy) is predominantly responsible for the creation of the poloidal field from the toroidal field, while shear generates back a toroidal field from the poloidal field, indicating that an α–Ω-type dynamo is operative in MRI-driven accretion discs. We also find that both strong outflow ($\bar{v}_z$) and turbulent pumping (γz) transport mean fields away from the mid-plane. Instead of turbulent diffusivity, they are the principal sink terms in the mean magnetic energy evolution equation. We find encouraging evidence that a generative helicity flux is responsible for the effective α-effect. Finally, we point out potential limitations of horizontal (x − y) averaging in defining the ‘mean’ on the extraction of dynamo coefficients and their physical interpretations.