Abstract
ABSTRACT A ‘proof of principle’ is presented, whereby the Ohmic and viscous heating determined by a three-dimensional (3D) MHD model of a coronal avalanche are used as the coronal heating input for a series of field-aligned, one-dimensional (1D) hydrodynamic models. Three-dimensional coronal MHD models require large computational resources. For current numerical parameters, it is difficult to model both the magnetic field evolution and the energy transport along field lines for coronal temperatures much hotter than $1\, \mathrm{MK}$, because of severe constraints on the time step from parallel thermal conduction. Using the 3D MHD heating derived from a simulation and evaluated on a single field line, the 1D models give coronal temperatures of $1\, \mathrm{MK}$ and densities $10^{14}\textrm {--}10^{15}\, \mathrm{m}^{-3}$ for a coronal loop length of $80\, \mathrm{Mm}$. While the temperatures and densities vary smoothly along the field lines, the heating function leads to strong asymmetries in the plasma flows. The magnitudes of the velocities in the 1D model are comparable with those seen in 3D reconnection jets in our earlier work. Advantages and drawbacks of this approach for coronal modelling are discussed.
Highlights
Multidimensional magnetohydrodynamic (MHD) computational models play an important role in understanding the storage and release of energy in the solar corona (Reale 2014; Pontin & Hornig 2020)
As we demonstrate in Appendix A, this is independent of the initial temperature and density: in particular, the temperature and density used in the MHD model cannot be sustained, as we discuss shortly
We have demonstrated how the output of a fully 3D MHD simulation of a coronal avalanche can be used to perform a series of field-aligned simulations, consisting of individual field lines
Summary
Multidimensional magnetohydrodynamic (MHD) computational models play an important role in understanding the storage and release of energy in the solar corona (Reale 2014; Pontin & Hornig 2020). Complex physics can be included in such models, including, for example, radiative transfer and partial ionization in the chromosphere, as well as anisotropic thermal conduction, energy particle transport, and optically thin radiation in the corona. Additional numerical packages can generate synthetic ‘observables’, such as emission line profiles and emission measure distributions Several issues limit the utility of such models, especially the needs to ensure numerical stability and to distinguish between the various physical timescales. In MHD models of low-β plasmas that do not consider energy transport, the time step must satisfy:
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