Coronal Cooling as a Result of Mixing by the Nonlinear Kelvin–Helmholtz Instability

Abstract

Recent observations show cool, oscillating prominence threads fading when observed in cool spectral lines and appearing in warm spectral lines. A proposed mechanism to explain the observed temperature evolution is that the threads were heated by turbulence driven by the Kelvin-Helmholtz instability that developed as a result of wave-driven shear flows on the surface of the thread. As the Kelvin-Helmholtz instability is an instability that works to mix the two fluids either side of the velocity shear layer, in the solar corona it can be expected to work by mixing the cool prominence material with that of the hot corona to form a warm boundary layer. In this paper we develop a simple phenomenological model of nonlinear Kelvin-Helmholtz mixing, using it to determine the characteristic density and temperature of the mixing layer, which for the case under study with constant pressure across the two fluids are ρ mixed = √ ρ 1 ρ 2 and T mixed = √ T 1 T 2 . One result from the model is that it provides an accurate, as determined by comparison with simulation results, determination of the kinetic energy in the mean velocity field. A consequence of this is that the magnitude of turbulence, and with it the energy that can be dissipated on fast time-scales, as driven by this instability can be determined. For the prominence-corona system, the mean temperature rise possible from turbulent heating is estimated to be less than 1% of the characteristic temperature (which is found to be T mixed = 10 5 K). These results highlight that mixing, and not heating, are likely to be the cause of the observed transition between cool to warm material in Okamoto et al. (2015). One consequence of this result is that the mixing creates a region with higher radiative loss rates on average than either of the original fluids, meaning that this instability could contribute a net loss of thermal energy from the corona, i.e. coronal cooling.

Oscillation and Evolution of Coronal Loops in a Dynamical Solar Corona

“…The evolution of the loop profile is characterized by fitting the transverse density profile with a model based on a circular cross-section and linear density profile in the inhomogeneous layer, which is satisfied exactly for the initial condition but otherwise an approximation. They therefore correspond to a value which is averaged in the azimuthal direction, whereas it is known from previous work (e.g., Barbulescu et al, 2019;Hillier and Arregui, 2019) and our Figure 1 that KHI causes density perturbations to develop which exhibit the same m = 1 symmetry as the kink mode. For example, the loop becomes extended in the direction of its displacement (e.g., Karampelas and Van Doorsselaere, 2018).…”

SolO/EUI Observations of Ubiquitous Fine-scale Bright Dots in an Emerging Flux Region: Comparison with a Bifrost MHD Simulation

“…Nonetheless, "low height" is only a conjecture because we assume that the TR is under the corona. In reality, TR could just come from the outer part of a feature (like a jet) that is cooler inside, as in Hillier & Arregui (2019).…”

How Transverse Waves Drive Turbulence in the Solar Corona

“…Not only is this initial energy unable to provide substantial heating, ref. [95] showed that if the instability forms at the boundary of a prominence, the mixing of cold, dense plasma with much hotter and more tenuous coronal plasma can cause an increase in the radiative losses and, thus, lead to enhanced cooling. This increase in the energy loss rate is much larger than the energy dissipation that could be obtained due to the relatively low wave energy content.…”

“…At the time, this was posited as evidence for wave heating in action. However, a later study by [95] argued this was not a result of energy dissipation, but was instead caused by the mixing of hot coronal plasma with a cooler prominence material. This leads to an average temperature increase in the prominence boundary, causing the transfer of emission from cooler to hotter lines.…”