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.

Thermally enhanced tearing in solar current sheets: Explosive reconnection with plasmoid-trapped condensations

“…The condensations that are entrapped within the coalescing plasmoids thereby also show rapid variations of the radiative losses across their edges, much like the prominence corona transition region (PCTR), also at play for individual coronal rain blobs. Note that the precise variation of temperature, density and radiative losses is here not incorporating effects of anisotropic thermal conduction, and therefore we have extremely sharp transitions, as explained also in (Hermans & Keppens 2021).…”

Multi-Scale Variability of Coronal Loops Set by Thermal Non-Equilibrium and Instability as a Probe for Coronal Heating

“…The evolution of the condensations depends on one hand on the thermal instability regime, and in particular on the inflow velocity u = n R /k, which can lead to fragmentation effects due to strong oscillations in size, temperature and density. On the other hand, Hermans and Keppens (2021) have shown that the cooling curve chosen for the treatment of the radiative losses, and in particular the treatment at low temperatures (<20 000 K), greatly varies the growth rate of the instability and the morphology of the condensations. This theory has been applied to the formation of coronal rain and prominences in the solar context.…”

Thermal Instability in Radiation Hydrodynamics: Instability Mechanisms, Position-dependent S-curves, and Attenuation Curves

“…Testing the viability of this model will require solving the equations of radiation MHD (RMHD). Advances in understanding of the dynamics of TI in MHD have been led by the solar physics community in recent years (see reviews by Antolin & Froment 2022;Soler & Ballester 2022), especially in the context of solar prominence formation and the coronal rain phenomenon (e.g., Claes & Keppens 2019;Claes et al 2020;Hermans & Keppens 2021). Because these studies have all assumed an optically thin formalism where attenuation is neglected, we stress that the RHD framework and analysis methods presented here are equally applicable to the equations of RMHD.…”