The Influence of Numerical Resolution on Coronal Density in Hydrodynamic Models of Impulsive Heating

Abstract

The effect of the numerical spatial resolution in models of the solar corona and corona/chromosphere interface is examined for impulsive heating over a range of magnitudes using one-dimensional hydrodynamic simulations. It is demonstrated that the principal effect of inadequate resolution is on the coronal density. An underresolved loop typically has a peak density of at least a factor of two lower than a resolved loop subject to the same heating, with larger discrepancies in the decay phase. The temperature for underresolved loops is also lower indicating that lack of resolution does not "bottle up" the heat flux in the corona. Energy is conserved in the models to under 1% in all cases, indicating that this is not responsible for the low density. Instead, we argue that in underresolved loops the heat flux "jumps across" the transition region to the dense chromosphere from which it is radiated rather than heating and ablating transition region plasma. This emphasizes the point that the interaction between corona and chromosphere occurs only through the medium of the transition region. Implications for three-dimensional magnetohydrodynamic coronal models are discussed.

MHD modelling of coronal loops: injection of high-speed chromospheric flows

“…The uniformly high resolution along the z direction allows us to accurately describe both the steep transition region and the moving shock front. To determine that the resolution in the steep gradient regions was high enough (e.g., Bradshaw & Cargill 2013), we made a test at higher spatial resolution along z (dz = 0.5 × 10 6 cm) and ascertained that the results do not change except for a few details.…”

Forward Modelling of a Brightening Observed by AIA

“…In this work, the resolution was such that the smallest grid cell width was 0.12 km. Bradshaw and Cargill (2013) and others found that an inadequate resolution of the transition region primarily leads to an underestimated coronal density.…”

“…The evolution of the impulsively heated loop was simulated using the 1D hydrodynamics and radiation code HYDRAD (Bradshaw andMason, 2003a, 2003b;Bradshaw and Cargill, 2013). The loop begins in an initial idealised equilibrium where the hydrostatic equations are solved from the footpoint to the loop apex for one side and mirrored on the basis of symmetry.…”

“…Bradshaw and Cargill (2006) found significant departure from equilibrium in models of coronal loops heated by nanoflares. In this work we factor in the effects of non-equilibrium ionisation by using the established HYDRAD code (Bradshaw and Cargill, 2013) for our simulations and modelling.…”

Physics of outflows near solar active regions

“…We approximated the observed structure as a long loop and modelled it using the 1-D hydrodynamics and radiation code HYDRAD (Bradshaw and Cargill, 2013). The simulations were carried out taking into account the 15 most abundant elements in the solar atmosphere; to begin with they were considered to be in equilibrium for calculating the initial state and then not in equilibrium for the ensuing simulations.…”