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Multi-Scale Coronal Heating: A New Approach to an Old Question.

Periodic Reporting for period 3 - CORONALDOLLS (Multi-Scale Coronal Heating: A New Approach to an Old Question.)

Reporting period: 2018-10-01 to 2020-03-31

One of the most remarkable properties of the Sun’s atmosphere, which, despite decades of research, is still not understood, is its thermal structure. Along with many other stars, the Sun's outer atmosphere has an extremely high temperature, rising from a surface (photosphere) temperature of 4000-6000 K, through the chromosphere and transition region to several million degrees in the outer atmosphere (corona). It has long been known that the Sun's magnetic field is responsible for the supply of energy to the atmosphere. However, how this magnetic energy is converted into thermal energy is still not understood, as models struggle to simultaneously encompass the very disparate temporal and spatial scales on which the heating has to occur.

The project aims to tackle the long-standing question of the extremely high temperatures in the Sun’s outer atmosphere (corona) by taking a comprehensive approach: forward modelling (creating synthetic observations) will be used to (i) link 3D numerical simulations of in-depth models with large scale computational experiments and (ii) provide observational diagnostics to compare models to high resolution, multi wavelength observations both qualitatively and quantitatively. This timely, multi-scale approach will achieve an innovative synergy between coronal heating and coronal seismology, where the coronal heating models will use input from, and be benchmarked against, information gained about the solar atmosphere through coronal seismology.

With this project, we aim to answer the fundamental question: Can we unambiguously identify physical heating mechanisms and determine their relative contributions, both in large-scale numerical simulations and high-resolution observations and, if so, how? In parallel, the advanced 3D computational models will provide a ‘proof of concept’ for coronal seismology, i.e. establish the robustness of the currently used simple models and how the interpretation of observed waves and oscillations in the optically thin solar atmosphere is affected by line-of-sight integration and instrument resolution.

The ultimate test for any coronal heating model would be whether (using different parameters) it could explain other hot, ‘stellar’ atmospheres. As the search for habitable exoplanets intensifies, understanding the host stars is crucial and the Sun should provide a 'benchmark' model for the study of other solar-like stars. Although we will not address stellar atmospheric heating explicitly, our multi-scale approach is a key stepping stone towards stellar heating models.
So far, we have used 3D numerical simulations and observations from different instruments and satelites to study a range of MHD wave behaviour and other dynamical processes in the solar atmosphere.

Combining 3D numerical simulations and observational data analysis, great progress has been made on establishing the true nature of observed propagating disturbances in the solar atmosphere. We showed evidence of the formation of coronal structures associated with spicules (chromospheric jets) and heating of plasma to transition region and coronal temperatures. We found that associated with the formation of spicules, the corona exhibits 1) magneto-acoustic shocks and flows and 2) transversal magnetic waves and electric currents. We also demonstrated that transverse wave induced Kelvin-Helmholtz rolls could lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations.

The team has also made progress towards its goal of gaining a deeper understanding of coronal heating on a variety of (spatial) scales. Focusing on individual heating mechanisms, driven by elementary footpoint motions, we investigated how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions.

To improve our potential to accurately model the thermodynamic evolution in 3D simulations of the solar atmosphere, we developed a new computational approach that addresses the difficulty of obtaining the correct thermodynamic interaction between the solar corona and the transition region in response to rapid heating events.

We undertook a series of studies to investigate the behaviour of MHD waves in the solar atmosphere. We showed conceptually that for some coronal structures, density gradients can evolve in a way that the wave-damping processes are inhibited. In a further study, we assessed how much energy can be converted into thermal energy by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindrical coronal structure. Follow-on work then combined observations and 3D numerical modelling to look at multi-harmonic oscillations of coronal loops. We concluded that coronal heating due to phase-mixing seemed not to provide enough energy to maintain the thermal structure of the solar corona even when multi-harmonics oscillations are included.

Using detailed 3D MHD simulations, we investigated the effects of resistivity and viscosity on the onset and growth of the Kelvin-Helmholtz Instability (KHI) in oscillating coronal loops. We found that enhancing the viscosity and resistivity acts to suppress the KHI. The formation of the instability is delayed and, in some cases, the onset is prevented completely. We also established that magnetic twist suppresses the development of the vortices associated with the instability but that the formation of the KHI in a twisted regime is accompanied by greater Ohmic dissipation.

Combining high-resolution numerical simulations and forward modelling (creating synthetic variables), we established observational signatures of resonant absorption (mode-coupling) and the associated development of KHI. We showed that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation can be obtained (a previously unexplained observed class of loop oscillations). From a further study, we established that common observational signatures included an intensity and loop width modulation at half the kink period, a fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, and overall line broadening in time.
The implementation of a jump condition which allows to correctly model the thermodynamic interactions in the solar atmosphere without having to use excessively large computational simulations is a huge step forward. We will extend this method from its current 2D implementation to 3D, which will allow us to perform detailed and realistic simulations of coronal heating mechanisms.