Effect of optically thin cooling curves on condensation formation: Case study using thermal instability

Abstract

Context. Non-gravitationally induced condensations are observed in many astrophysical environments. In solar physics, common phenomena are coronal rain and prominences. These structures are formed due to energy loss by optically thin radiative emission. Instead of solving the full radiative transfer equations, precomputed cooling curves are typically used in numerical simulations. In the literature, a wide variety of cooling curves exist, and they are quite often used as unquestionable ingredients. Aims. We here determine the effect of the optically thin cooling curves on the formation and evolution of condensations. We also investigate the effect of numerical settings. This includes the resolution and the low-temperature treatment of the cooling curves, for which the optically thin approximation is not valid. Methods. We performed a case study using thermal instability as a mechanism to form in situ condensations. We compared 2D numerical simulations with different cooling curves using interacting slow magnetohydrodynamic (MHD) waves as trigger for the thermal instability. Furthermore, we discuss a bootstrap measure to investigate the far non-linear regime of thermal instability. In the appendix, we include the details of all cooling curves implemented in MPI-AMRVAC and briefly discuss a hydrodynamic variant of the slow MHD waves setup for thermal instability.Results. For all tested cooling curves, condensations are formed. The differences due to the change in cooling curve are twofold. First, the growth rate of the thermal instability is different, leading to condensations that form at different times. Second, the morphology of the formed condensation varies widely. After the condensation forms, we find fragmentation that is affected by the low-temperature treatment of the cooling curves. Condensations formed using cooling curves that vanish for temperatures lower than 20 000 K appear to be more stable against dynamical instabilities. We also show the need for high-resolution simulations. The bootstrap procedure allows us to continue the simulation into the far non-linear regime, where the condensation fragments dynamically align with the background magnetic field. The non-linear regime and fragmentation in the hydrodynamic case differ greatly from the low-beta MHD case. Conclusions. We advocate the use of modern cooling curves, based on accurate computations and current atomic parameters and solar abundances. Our bootstrap procedure can be used in future multi-dimensional simulations to study fine-structure dynamics in solar prominences.

When hot meets cold: post-flare coronal rain

“…Many other optically thin cooling curves, such as from Schure et al (2009), are also available in MPI-AMRVAC. Hermans & Keppens (2021) showed that changing the cooling curve does not truly change whether condensations happen, but only impacts the growthrate of the thermal instability and the morphology of the formed condensations.…”

Coronal rain in randomly heated arcades

“…Λ(T ) is set to be zero below 10,000 K because the plasma there is no longer fully ionized and becomes optically thick. Many optically thin cooling curves have been implemented in MPI-AMRVAC, and Hermans & Keppens (2021) studied the influence of these cooling curves on condensation formation and found that for different cooling curves, condensations may have different formation times and morphology. H is the heating term which includes the background heating and localized heating H = H bgr + H loc .…”