Magnetohydrodynamic Nonlinearities in Sunspot Atmospheres: Chromospheric Detections of Intermediate Shocks

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 exceptional 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 λ8542 line 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 nonlinear signatures is carried out by comparing the observationally derived slow, fast, and Alfvén shock solutions with the theoretical Rankine-Hugoniot relations. Employing over 200,000 independent measurements, we reveal that the Alfvén (intermediate) shock solution provides the closest match between theory and observations at optical depths of log₁₀τ =-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.