Quasi-global galactic magnetorotational instability with Braginskii viscosity

Abstract

We present a global‐in‐radius linear analysis of the axisymmetric magnetorotational instability (MRI) in a collisional magnetized plasma with Braginskii viscosity. For a galactic angular velocity profile Ω we obtain analytic solutions for three magnetic field orientations: purely azimuthal, purely vertical and slightly pitched (almost azimuthal). In the first two cases the Braginskii viscosity damps otherwise neutrally stable modes, and reduces the growth rate of the MRI, respectively. In the final case the Braginskii viscosity makes the MRI up to 22 times faster than its inviscid counterpart, even for asymptotically small pitch angles. We investigate the transition between the Lorentz‐force‐dominated and the Braginskii viscosity‐dominated regimes in terms of a parameter ΩνnormalB/B2 where νB is the viscous coefficient and B the Alfvén speed. In the limits where the parameter is respectively small and large, we recover the inviscid MRI and the magnetoviscous instability. We obtain asymptotic expressions for the approach to these limits, and find that the Braginskii viscosity can magnify the effects of azimuthal hoop tension (the growth rate becomes complex) by over an order of magnitude. We discuss the relevance of our results to the local approximation, galaxies and other magnetized astrophysical plasmas. Our results should prove useful for benchmarking codes in global geometries.

Magnetorotational Instability: Nonmodal Growth and the Relationship of Global Modes to the Shearing Box

“…Very similar conclusions about the importance of transient effects would almost certainly hold in a more general model. In any case, many previous studies (e.g., Pessah & Psaltis 2005;Rosin & Mestel 2012;Mamatsashvili et al 2013) have shown that MRI growth is generally weakly affected by the introduction of more complex physical models, probably because the MRI itself is so virulent an instability.…”

“…Firstly, it is straightforward to extend the shearing wave equations to much more complicated domains and physical models. For example, strong magnetic fields, compressibility, stratification, or more complex diffusion operators (e.g., Pessah & Psaltis 2005;Heinemann & Papaloizou 2009;Salhi et al 2012;Rosin & Mestel 2012) could easily be accounted for in the shearing wave equations 6 . Secondly, the approach elucidates the connection between previous results that illustrate the quality of WKB methods for axisymmetric modes, and our results, which show the accuracy of the shearing wave equations over moderate time-scales.…”

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

“…More thorough discussion and detailed derivations can be found in Q02; Sharma et al. (2003), Balbus (2004), Rosin & Mestel (2012), Heinemann & Quataert (2014), Quataert et al. (2015), as well in appendix A, where we derive properties of the KMRI in a mixed-vertical–azimuthal field.…”

“…As well as extensions to the original linear analyses using either fully kinetic treatments (Sharma et al. 2003; Heinemann & Quataert 2014; Quataert, Heinemann & Spitkovsky 2015) or fluid models (Ferraro 2007; Rosin & Mestel 2012), various works have explored turbulent transport in the fully nonlinear regime, generally finding behaviour that bears a strong similarity to that seen in standard resistive MHD. Sharma et al.…”

“…This kinetic MRI (KMRI) has seen subsequent theoretical attention. As well as extensions to the original linear analyses using either fully kinetic treatments (Sharma et al 2003;Heinemann & Quataert 2014;Quataert, Heinemann & Spitkovsky 2015) or fluid models (Ferraro 2007;Rosin & Mestel 2012), various works have explored turbulent transport in the fully nonlinear regime, generally finding behaviour that bears a strong similarity to that seen in standard resistive MHD. Sharma et al (2006) (hereafter S06) was the first to study MRI turbulence in this regime using a kinetically motivated fluid closure, an approach that has been followed in a variety of works since (e.g.…”