In this paper, we revisit the governing equations for linear magnetohydrodynamic (MHD) waves and instabilities existing within a magnetized, plane-parallel, self-gravitating slab. Our approach allows for fully non-uniformly magnetized slabs, which de
viate from isothermal conditions, such that the well-known Alfven and slow continuous spectra enter the description. We generalize modern MHD textbook treatments, by showing how self-gravity enters the MHD wave equation, beyond the frequently adopted Cowling approximation. This clarifies how Jeans instability generalizes from hydro to magnetohydrodynamic conditions without assuming the usual Jeans swindle approach. Our main contribution lies in reformulating the completely general governing wave equations in a number of mathematically equivalent forms, ranging from a coupled Sturm-Liouville formulation, to a Hamiltonian formulation linked to coupled harmonic oscillators, up to a convenient matrix differential form. The latter allows us to derive analytically the eigenfunctions of a magnetized, self-gravitating thin slab. In addition, as an example we give the exact closed form dispersion relations for the hydrodynamical p- and Jeans-unstable modes, with the latter demonstrating how the Cowling approximation modifies due to a proper treatment of self-gravity. The various reformulations of the MHD wave equation open up new avenues for future MHD spectral studies of instabilities as relevant for cosmic filament formation, which can e.g. use modern formal solution strategies tailored to solve coupled Sturm-Liouville or harmonic oscillator problems.
The formation of shocks within the solar atmosphere remains one of the few observable signatures of energy dissipation arising from the plethora of magnetohydrodynamic waves generated close to the solar surface. Active region observations offer excep
tional views of wave behavior and its impact on the surrounding atmosphere. The stratified plasma gradients present in the lower solar atmosphere allow for the potential formation of many theorized shock phenomena. In this study, using chromospheric Ca II 854.2nm spectropolarimetric data of a large sunspot, we examine fluctuations in the plasma parameters in the aftermath of powerful shock events that demonstrate polarimetric reversals during their evolution. Modern inversion techniques are employed to uncover perturbations in the temperatures, line-of-sight velocities, and vector magnetic fields occurring across a range of optical depths synonymous with the shock formation. Classification of these non-linear signatures is carried out by comparing the observationally-derived slow, fast, and Alfven shock solutions to the theoretical Rankine-Hugoniot relations. Employing over 200,000 independent measurements, we reveal that the Alfven (intermediate) shock solution provides the closest match between theory and observations at optical depths of log(tau) = -4, consistent with a geometric height at the boundary between the upper photosphere and lower chromosphere. This work uncovers first-time evidence of the manifestation of chromospheric intermediate shocks in sunspot umbrae, providing a new method for the potential thermalization of wave energy in a range of magnetic structures, including pores, magnetic flux ropes, and magnetic bright points.
Solar prominences are subject to all kinds of perturbations during their lifetime, and frequently demonstrate oscillations. The study of prominence oscillations provides an alternative way to investigate their internal magnetic and thermal structures
as the oscillation characteristics depend on their interplay with the solar corona. Prominence oscillations can be classified into longitudinal and transverse types. We perform three-dimensional ideal magnetohydrodynamic simulations of prominence oscillations along a magnetic flux rope, with the aim to compare the oscillation periods with those predicted by various simplified models and to examine the restoring force. We find that the longitudinal oscillation has a period of about 49 minutes, which is in accordance with the pendulum model where the field-ligned component of gravity serves as the restoring force. In contrast, the horizontal transverse oscillation has a period of about 10 minutes and the vertical transverse oscillation has a period of about 14 minutes, and both of them can be nicely fitted with a two-dimensional slab model. We also find that the magnetic tension force dominates most of the time in transverse oscillations, except for the first minute when magnetic pressure overwhelms.
We investigate how night side cooling and surface friction impact surface temperatures and large scale circulation for tidally locked Earth-like planets. For each scenario, we vary the orbital period between $P_{rot}=1-100$~days and capture changes i
n climate states. We find drastic changes in climate states for different surface friction scenarios. For very efficient surface friction ($t_{s,fric}=$ 0.1 days), the simulations for short rotation periods ($P_{rot} leq$ 10 days) show predominantly standing extra tropical Rossby waves. These waves lead to climate states with two high latitude westerly jets and unperturbed meridional direct circulation. In most other scenarios, simulations with short rotation periods exhibit instead dominance by standing tropical Rossby waves. Such climate states have a single equatorial westerly jet, which disrupts direct circulation. Experiments with weak surface friction ($t_{s,fric}=~10 -100$ days) show decoupling between surface temperatures and circulation, which leads to strong cooling of the night side. The experiment with $t_{s,fric}= 100$ days assumes climate states with easterly flow (retrograde rotation) for medium and slow planetary rotations $P_{rot}= 12 - 100$~days. We show that an increase of night side cooling efficiency by one order of magnitude compared to the nominal model leads to a cooling of the night side surface temperatures by 80-100~K. The day side surface temperatures only drop by 25~K at the same time. The increase in thermal forcing suppresses the formation of extra tropical Rossby waves on small planets ($R_P=1 R_{Earth}$) in the short rotation period regime ($P_{rot} leq$ 10 days).
We present numerical simulations in 3D settings where coronal rain phenomena take place in a magnetic configuration of a quadrupolar arcade system. Our simulation is a magnetohydrodynamic simulation including anisotropic thermal conduction, optically
thin radiative losses, and parametrised heating as main thermodynamical features to construct a realistic arcade configuration from chromospheric to coronal heights. The plasma evaporation from chromospheric and transition region heights eventually causes localised runaway condensation events and we witness the formation of plasma blobs due to thermal instability, that evolve dynamically in the heated arcade part and move gradually downwards due to interchange type dynamics. Unlike earlier 2.5D simulations, in this case there is no large scale prominence formation observed, but a continuous coronal rain develops which shows clear indications of Rayleigh-Taylor or interchange instability, that causes the denser plasma located above the transition region to fall down, as the system moves towards a more stable state. Linear stability analysis is used in the non-linear regime for gaining insight and giving a prediction of the systems evolution. After the plasma blobs descend through interchange, they follow the magnetic field topology more closely in the lower coronal regions, where they are guided by the magnetic dips.
We simulate time-dependent particle acceleration in the blast wave of a young supernova remnant (SNR), using a Monte Carlo approach for the diffusion and acceleration of the particles, coupled to an MHD code. We calculate the distribution function of
the cosmic rays concurrently with the hydrodynamic evolution of the SNR, and compare the results with those obtained using simple steady-state models. The surrounding medium into which the supernova remnant evolves turns out to be of great influence on the maximum energy to which particles are accelerated. In particular, a shock going through a $rho propto r^{-2}$ density profile causes acceleration to typically much higher energies than a shock going through a medium with a homogeneous density profile. We find systematic differences between steady-state analytical models and our time-dependent calculation in terms of spectral slope, maximum energy, and the shape of the cut-off of the particle spectrum at the highest energies. We also find that, provided that the magnetic field at the reverse shock is sufficiently strong to confine particles, cosmic rays can be easily re-accelerated at the reverse shock.
