The competition between the hydrodynamic instability from noise and magnetorotational instability in the Keplerian disks

TL;DR

This paper compares magnetorotational instability (MRI) and hydrodynamic instability growth rates in Keplerian disks, analyzing the effects of noise, magnetic fields, and viscosity on their dominance and stability.

Contribution

It introduces a detailed analysis of the competition between MRI and hydrodynamic instabilities, including the impact of noise and viscosity on their growth rates in accretion flows.

Findings

MRI active within specific magnetic field ranges

Noise induces instability in MRI inactive regions

Hydrodynamic growth rates can surpass MRI under certain conditions

Abstract

We venture for the comparison between growth rates for magnetorotational instability (MRI) and hydrodynamics instability in the presence of an extra force in the local Keplerian accretion flow. The underlying model is described by the Orr-Sommerfeld and Squire equations in the presence of rotation, magnetic field and an extra force, plausibly noise with a nonzero mean. We obtain MRI using Wentzel-Kramers-Brillouin (WKB) approximation without extra force for purely vertical magnetic field and vertical wavevector of the perturbations. Expectedly, MRI is active within a range of magnetic field, which changes depending on the perturbation wavevector magnitude. Next, to check the effect of noise on the growth rates, a quartic dispersion relation has been obtained. Among those four solutions for growth rate, the one that reduces to MRI growth rate at the limit of vanishing mean of noise in the MRI active region of the magnetic field, is mostly dominated by MRI. However, in MRI inactive region, in the presence of noise the solution turns out to be unstable, which are almost independent of the magnetic field. Another growth rate, which is almost complementary to the previous one, leads to stability at the limit of vanishing noise. The remaining two growth rates, which correspond to the hydrodynamical growth rates at the limit of the vanishing magnetic field, are completely different from the MRI growth rate. More interestingly, the latter growth rates are larger than that of the MRI. If we consider viscosity, the growth rates decrease depending on the Reynolds number.