Partnership for Advanced Computing in Europe (PRACE)

PRACE Award N.2011050755

The way to heating the solar corona: finely-resolved twisting of magnetic loops
Reale F., Orlando S., Guarrasi M., Miceli M. 2011/2012

Summary of the project

The question of what heats the solar and stellar coronae to million degrees is very important in Astrophysics and Plasma Physics. The Sun is a unique laboratory, since it is the only star that we can resolve in detail and it is also a place where one can find extreme ambient conditions. Coronal heating concerns mechanisms of magnetic energy release and confinement, with very important implications for research on energy production. At the same time its investigation is very challenging. The energy from photospheric plasma motions is carried by the magnetic field that confines plasma in a multitude of arch-like structures anchored in the photosphere, the coronal loops.
The aim of this project is to study the twisting of coronal loops with unprecedented model (ten-fold) resolution and completeness, necessary to answer reliably and for the first time important questions on coronal heating, e.g., how is reconnection distributed along and across the loop? How does it compete with kink instability? Does it reach a steady state? The results will produce high-impact scientific publications. The modelled region includes a single coronal loop, described as a straight magnetic flux tube linking two chromospheric layers. The loop model accounts for the reduction of beta and the consequent expansion of the magnetic flux tubes from the chromosphere to the corona. The plasma and magnetic field evolution is described by solving the full 3-D MHD plasma equations including gravity, ohmic and thin plasma radiative losses, thermal conduction. The thin chromosphere/corona transition region is accurately described with resolution down to ~20 km, that leads to a very small time integration step, and that has made this task prohibitive so far.
Our project is based on a single large-scale 3D-MHD simulation. We extend the initial 2D configuration to 3D by a simple 360deg rotation. Then we keep one boundary surface fixed and apply a rotation motion to the inner part of the opposite boundary, thus forcing the magnetic field lines to twist around the loop central axis. The magnetic field will be stressed and eventually become unstable, reconnecting or rearranging to less stressed configuration. The geometric domain is a cube with 768x384x384 grid cells, enclosing a loop with total length of 20000km. We follow the loop evolution for about two 360deg footpoint rotations (5000s). We use the PLUTO 3D-MHD code, with the super- time-stepping technique to optimize the demanding thermal conduction. PLUTO is already well-tested on our problem in 2D, and optimized on PRACE Tier-0 systems. In particular, since it is already tested on the BLUE-Gene/P up to 32,768 processors on a problem with very similar size, the CINECA/FERMI machine is highly suitable for the simulation we propose. The 3D simulation scales linearly with respect to the 2D well-tested ones, requiring a computing time of ~28.8Mhours on the FERMI HPC system. Using 40000 cores per step the simulation can be performed in ~1 month of continuous wall clock time, and, including the warm-up, a total of 3 months and ~30.4Mhours CPU-time.

Description of the results obtained from the scientific point of view

This project investigates the heating released by magnetic reconnection of a twisted coronal loop. After tuning from extensive warm-up simulations, in our final high-resolution simulation we obtain realistic conditions for an active region loop with an appropriate assumption of switch-on diffusivity. We see that after a critical twist some parts of the loop begin to heat up with a filamentary structure similar to what is detected in real observations. The heating is produced by the dissipation of the currents produced by the twisting, which become larger than the minimum threshold for dissipation. After a while, we also see that the heating produces an expansion of the chromospheric layers upwards into the corona. This is highly expected from the typical evolution of coronal loops.
This realistic evolution is already a great achievement for us, because it shows that this approach is feasible and sound. We also obtain interesting and new constraints on where the heating is released: we see that the highest current dissipation is concentrated near the loop footpoints. Other constraints are obtained regarding the duration of the heating release: the simulation supports a discontinuous release with durations of the order of one minute, that might be in good agreement with observations.
Further analysis of the simulation results is on-going; we are focusing on the origin of the fine structure and on the details of the formation of the current sheets that release the heating.
The feasibility of this project opens new and long-term perspectives of coronal MHD modeling, complementary to other approaches that aims at describing active region boxes, instead of a box with a single loop. Our approach allows both a relatively easy control and analysis of the physical domain and results and an accurate description of the interaction between the plasma and the magnetic field in an inhomogeneous beta regime. We can isolate and highlight single physical effects. It is a proper numerical experiment. It will be certainly interesting to propose other numerical projects based on this first basic one.
For the future, we also foresee relevant applications to stellar environments, such as star-disk magnetic channels in star-forming regions. Winding of magnetic tubes is highly expected in the differential rotation between the disk and the star, and the present project is an important preliminary step. It might have a very important role in the regulation of mass accretion and coronal activity, with important implications for the planet formation and stellar evolution.
Investigating the conversion of magnetic energy into heat from reconnection processes is of great interest in the more general context of plasma physics and plasma laboratory physics and, in the long-term, for energy generation. Our simulations seem to provide some constraints on the way the energy is dissipated, because we made an operative choice of the parameters of the magnetic diffusivity that works very well. This might provide an important constraint and input for microphysics.
Our loop model requires a 3D MHD description at high spatial resolution with a computation box of more than 10,000,000 grid cells and with millions of time steps. The final simulation has required more than 5,000,000 CPU hours on FERMI, using more than 32,000 cores. Our MHD code is highly efficient on this scale of computing. This class of resources was not available before and we can therefore state that this project could not have been attacked without PRACE systems, which are therefore essential for this and the next projects.
Due to the complexity of the model, we are still in the process of analysing the results for high impact publications.

Fig. 1. Spatial distributions of the plasma density (1e9 cm^-3) at time t = 500 s (upper left panel) and t = 1940 s (upper right) and of the temperature (MK; lower left) and electric current density (A cm^-2; lower right) at time t = 1940 s in the 3D box including the twisted flux tube. The twisted magnetic field lines are also shown. The heating is switched on after t = 500 s, when the current grows above the threshold for dissipation (red) in the corona. The temperature rises to 3 MK or more in the twisted region and dense plasma evaporates from the chromosphere and fills the twisted region. The image with the current shows a very filamented structure.

Expected future work in the area

This project opens several new lines of research. It will be very interesting to study the loop evolution on a longer time scale, when the system is in a steady-state. This is important both for a comparison with observations and for the investigation of the equilibrium and statistical properties of the heating release. Additional simulations would allow 1) to constrain better the magnetic diffusivity by some exploration of the parameters space, and 2) to explore different effects, such as the kink instability expected under certain conditions and for larger winding. The same modeling can be applied to stellar environments, such as star-disk magnetic channels in star-forming regions. Winding of magnetic tubes is highly expected in the differential rotation between the disk and the star, and the present project is an important preliminary step.

Preliminary results have been presented in several international meetings:

  • F. Reale - MHD modeling of twisted coronal loops - ISSI (International Space Science Institute) working group "Coronal Heating - Using Observables to Settle the Question of Steady vs. Impulsive Heating", Bern, Switzerland, 28 February 2013;

  • S. Orlando - HPC projects in Astrophysics at INAF/OAPa: current challenges and future perspectives, PRACE-2IP WP8 Fifth Face to Face Meeting CSCS, Lugano, Switzerland, 6-8 March 2013;

  • F. Reale - Non linear processes in the solar corona - Physical Processes in Astrophysical Plasmas Inflow/outflow and stellar winds, Torino, Italy, March 12th - 14th 2013;

  • F. Reale - Toward self-consistent 3D MHD modeling of the heating of a twisted coronal loop - 6th Coronal Loop Workshop, 25-28 June 2013, LaRoche, Belgium;

  • F. Reale - News about diagnostics of hot plasma and MHD loop modeling - ISSI (International Space Science Institute) working group "Coronal Heating - Using Observables to Settle the Question of Steady vs. Impulsive Heating", Bern, Switzerland, 5 March 2014.