How numerical treatments of the transition region modify energy flux into the solar corona

TL;DR

This paper investigates how different numerical treatments of the solar transition region affect energy flux into the corona, revealing that modifications significantly alter wave dynamics and energy injection rates, with implications for modeling solar atmospheric heating.

Contribution

It quantifies the impact of thermodynamic modifications on energy flux and wave properties in solar atmospheric models, highlighting frequency-dependent effects.

Findings

Thermodynamic treatments significantly alter Alfvén wave travel times.

Energy injection rates into the corona are affected by resolution and treatment.

Modification effects are frequency dependent, complicating comparisons of drivers.

Abstract

The large temperature gradients in the solar transition region present a significant challenge to large scale numerical modelling of the Sun's atmosphere. In response, a variety of techniques have been developed which modify the thermodynamics of the system. This sacrifices accuracy in the transition region in favour of accurately tracking the coronal response to heating events. Invariably, the modification leads to an artificial broadening of the transition region. Meanwhile, many contemporary models of the solar atmosphere rely on tracking energy flux from the lower atmosphere, through the transition region and into the corona. In this article, we quantify how the thermodynamic modifications affect the rate of energy injection into the corona. We consider a series of one-dimensional models of atmospheric loops with different numerical resolutions and treatments of the thermodynamics. Then, using Alfv\'en waves as a proxy, we consider how energy injection rates are modified in each case. We find that the thermodynamic treatment and the numerical resolution significantly modify Alfv\'en travel times, the eigenfrequencies and eigenmodes of the system, and the rate at which energy is injected into the corona. Alarmingly, we find that the modification of the energy flux is frequency dependent, meaning that it may be difficult to compare the effects of different velocity drivers on coronal heating if they are imposed below an under-resolved transition region, even if the sophisticated thermodynamic adaptations are implemented.