The influence of cosmic-rays on the magnetorotational instability

We present a linear perturbation analysis of the magnetorotational instability in the presence of the cosmic rays. Dynamical effects of the cosmic rays are considered by a fluid description and the diffusion of cosmic rays is only along the magnetic field lines. We show an enhancement in the growth rate of the unstable mode because of the existence of cosmic rays. But as the diffusion of cosmic rays increases, we see that the growth rate decreases. Thus, cosmic rays have a destabilizing role in the magnetorotational instability of the accretion discs.

💡 Research Summary

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The paper investigates how cosmic rays (CRs) influence the magnetorotational instability (MRI) that drives turbulence in astrophysical accretion discs. While MRI has long been recognized as the primary mechanism for angular‑momentum transport in ionised discs, the dynamical role of CRs—high‑energy particles whose pressure can be comparable to that of the thermal gas—has not been examined in detail. The authors adopt a two‑fluid description: the thermal gas is treated as a conventional magnetohydrodynamic (MHD) fluid, and the CR component is modelled as a separate fluid that contributes an additional isotropic pressure (p_{\rm cr}) and a diffusive energy flux (\Gamma = -\kappa_{\parallel}(\mathbf{b}!\cdot!\nabla p_{\rm cr})) directed strictly along magnetic field lines. Radiative cooling, ionisation, and CR heating are neglected, focusing solely on the dynamical coupling through pressure and diffusion.

The equilibrium configuration consists of a Keplerian disc rotating with angular velocity (\Omega \propto R^{-3/2}). The background magnetic field has vertical ((B_z)) and toroidal ((B_\phi)) components, while density, gas pressure, and CR pressure are taken as uniform. Linear perturbations are introduced in the form (\delta X \propto \exp