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Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE, Astrophysics, Earth and Planetary Astrophysics, astro-ph.EP, Astrophysics, Solar and Stellar Astrophysics, astro-ph.SR
Abstract:
The discovery of the first binary neutron star merger, GW170817, has spawned
a plethora of global numerical relativity simulations. These simulations are
often ideal (with dissipation determined by the grid) and/or axisymmetric
(invoking ad hoc mean-field dynamos). However, binary neutron star mergers
(similar to X-ray binaries and active galactic nuclei inner discs) are
characterised by large magnetic Prandtl numbers, $\rm Pm$, (the ratio of
viscosity to resistivity). $\rm Pm$ is a key parameter determining dynamo
action and dissipation but it is ill-defined (and likely of order unity) in
ideal simulations. To bridge this gap, we investigate the magnetorotational
instability (MRI) and associated dynamo at large magnetic Prandtl numbers using
fully compressible, three-dimensional, vertically stratified, isothermal
simulations of a local patch of a disc. We find that, within the bulk of the
disc ($z\lesssim2H$, where $H$ is the scale-height), the turbulent intensity
(parameterized by the stress-to-thermal-pressure ratio $\alpha$), and the
saturated magnetic field energy density, $E_\text{mag}$, produced by the MRI
dynamo, both scale as a power with Pm at moderate Pm ($4\lesssim \text{Pm}
\lesssim 32$): $E_\text{mag} \sim \text{Pm}^{0.74}$ and $\alpha \sim
\text{Pm}^{0.71}$, respectively. At larger Pm ($\gtrsim 32$) we find deviations
from power-law scaling and the onset of a plateau. Compared to our recent
unstratified study, this scaling with Pm becomes weaker further away from the
disc mid-plane, where the Parker instability dominates. We perform a thorough
spectral analysis to understand the underlying dynamics of small-scale
MRI-driven turbulence in the mid-plane and of large-scale Parker-unstable
structures in the atmosphere.
