Abstract
The pressure anisotropy-driven magnetohydrodynamic (MHD) waves and instabilities are the significant sources of energy transfer in astrophysical outflows, such as solar wind, spiral arms of galaxies and accretion disks. The heat-flux corrections, rotation and anisotropic viscosity play an unavoidable role in the wave dissipation and instabilities in such systems. In this work, we have investigated the effects of heat-flux vector and Braginskii viscosity tensor on the low-frequency hydromagnetic Chew–Goldberger–Low (CGL) waves, firehose instability and gravitational instability in uniformly rotating, strongly magnetized and anisotropic heat-conducting plasmas. The Braginskii viscosity tensor is considered in the CGL fluid equations, including heat-flux corrections and uniform rotation, keeping in mind the actual physical conditions of spiral arms of galaxies and solar coronal heating. The linear dispersion properties of gravitational instability, firehose instability, slow and fast CGL wave dissipation have been analyzed in various parametric limits. The dynamical stability of the system is discussed using the Routh–Hurwitz criterion. It is found that in the transverse propagation, the growth rate of the gravitational instability is decreased due to the presence of viscosity, and it remains unaffected due to the heat-flux corrections. In the parallel propagation, the effects of viscosity and heat-flux parameters are found to decrease the threshold wavenumber and stabilize the growth rate of gravitational instability. The upper and lower bounds of wavenumbers that determine the system’s stability, instability and overstability are decreased due to the viscosity and rotation parameters. The numerical calculations of various parameters show that gravitational instability plays a vital role in the spiral arms of the galaxies. The present results have been applied to understand the influence of heat-flux vector, rotation and viscosity on the slow and fast magnetosonic modes in the solar coronal heating mechanism.
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Acknowledgements
This work was supported by Addis Ababa University SIDA project No. 51080124 and Indian Space Research Organisation (ISRO) Bangalore under ISRO-RESPOND scheme through grant No. ISRO/RES/2/427/21-22. Author ETD acknowledges Centre for Atmospheric Research (CAR), NASRDA, Nigeria for their hospitality during his stay as visiting researcher. Author RPP gratefully acknowledges Inter-University Center for Astronomy and Astrophysics (IUCAA), Pune (India), for awarding him Visiting Associateship. The authors are thankful to the anonymous reviewers for their constructive and helpful comments.
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Appendices
A Solutions of various equations given in Sect. 2
The divergence of perturbed viscosity stress tensor Eqs. (13–15) can be written as
In Eq. (19), the magnetic pressure term can be expressed as
Using Eq. (23) the pressure stress tensor term can be expressed as
where \(\partial _{x,y,x}=\partial /\partial x, \partial /\partial y,\) and \( \partial /\partial z\).
The reduced form of \(\delta p_{\perp }\) and \(\delta p_{\parallel }\) can be obtained by using Eqs. (35) and (37), and doing further simplifications one can solve for \(\delta p_{\parallel }\)
where
Using Eqs. (36) and (38) and doing further simplifications, we can solve for \(\delta p_{\perp }\) as
where
B Solutions of the equation of motion
On substituting Eqs. (72) and (73) into Eq. (19) and doing further simplification, one can get:
The \(\hat{\mathbf {x}}-\) component of equation of motion
The \(\hat{\mathbf {y}}-\) component of equation of motion
The \(\hat{\mathbf {z}}-\) component of equation of motion
After substituting the relevant perturbations and derivatives, one can obtain
C The matrix elements of the matrix \([A_{lm}]\)
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Desta, E.T., Prajapati, R.P. & Eritro, T.H. Effects of heat-flux vector and Braginskii viscosity on wave dissipation and instabilities in rotating gravitating anisotropic plasmas. Eur. Phys. J. Plus 137, 437 (2022). https://doi.org/10.1140/epjp/s13360-022-02644-4
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DOI: https://doi.org/10.1140/epjp/s13360-022-02644-4