Hunting Down the Cause of Solar Magnetism

Principal Investigator:
Maarit Käpylä

Aalto University, Department of Computer Science, Astroinformatics Group, Finland, and Max Planck Institute for Solar System Research, SOLSTAR group, Germany

Local Project ID:

HPC Platform used:
SuperMUC-NG of LRZ

Date published:


The research of the groups of Astroinformatics in Aalto University, Finland [1], and SOLSTAR at the Max Planck Institute for Solar System Research in Göttingen, Germany [2], focuses on understanding solar and stellar dynamos. We try to achieve this by combining highresolution, local and global numerical modelling with longterm observations. This is a challenging task: even with state of the art computational methods and resources, the stellar parameter regime remains unattainable. Therefore, we are just able to simulate “tar-stars”, namely models in which diffusivities are raised several orders of magnitude from their real values, to guarantee numerical feasibility and stability.

This work is part of the PRACE project Access-Call 20 INTERDYNS, which has been granted 57M core hours on SuperMUC-NG. Our goal is to relax some approximations, in order to simulate more realistic systems, and try to connect the results with theoretical predictions and state-of-the-art observations.

Convective turbulence, together with large scale flows, such as differential rotation (Ω-effect), plays a key role in generating and shaping the magnetic fields observed in the Sun and other stars. The most important turbulent effect is the α-effect, describing collective inductive action arising from cyclonic turbulence. The α- and Ω-effects are the two prominent generators of large scale stellar/solar magnetic fields. These turbulent effects escape observational efforts even with the largest existing and planned observational infrastructures.

In theory, these effects are parametrised by transport coefficients which collectively describe the effects of turbulence without having the need to resolve smaller scales, hence the numerical determination of these coefficients which describe them is of utmost importance.For their measurement, we employ the test-field method (TFM). In its standard form, it can be used to measure the turbulent transport coefficients in the limit where a primary magnetic background turbulence vanishes (lower resolution regime). If the background magnetic turbulence is present, i.e., in the high resolution regime, the nonlinear (NL) form of TFM is necessary. This regime is relevant for the Sun, which most likely exhibits vigorous small-scale dynamo action, generating magnetic background turbulence. Moreover, the TFM allows us to measure the full α tensor, therefore adding a considerable refinement to the standard theory, which models the α-effect merely by a scalar quantity.

Results and Methods

We use the Pencil Code [3], a highly modular code, to solve the fully compressible equations of magnetohydrodynamics (MHD). The code employs a sixth-order, central finite differences scheme for spatial discretization and a 3rd-order Runge-Kutta time-integration scheme. The chosen scheme makes the code highly scalable and adaptable. To maintain the magnetic field divergence-free, the code solves for the magnetic vector potential. The output files are written out quite often in order to restart from crashes or nodefailures.

The parallelization is implemented using MPI and allows the Code to scale up 100,000 cores. The data analysis can be performed on the fly or post-processing using Python or IDL (Interactive Data Language).

A list of disk storage, number of cores and total walltime used for the simulations described in this report are shown in Table 1. The total short term storage on SuperMUC-NG for this part of the project will be 50TB. Even though most of the simulations are still ongoing, we have already achieved interesting results.

Our new high-resolution run (A1) shows a different behaviour than an earlier low-resolution run (M0, [4]). Besides the two times higher resolution of A1, the difference between the two consists in the way heat conduction is modeled. To describe radiative heat transfer, we use in both runs the diffusion approximation. In Run M0, we prescribed a profile for the radiative heat conductivity, while in the PRACE project runs we use a Kramers-like opacity law, in which the heat conductivity depends on density and temperature. The latter, a more physically sound prescription, allows for the development of a layer which is convectively stable in the traditional sense, but in which the transport of heat is still upward-directed. This can have consequences for the properties of the flow but also for the magnetic field evolution [5]. We highlight one such difference in Figure 1.

In the meridional cuts we show the component αΦΦ for run (M0, left), versus that of our new run (A1, right). The presence of negative/positive values in the northern/southern hemisphere is crucial for obtaining the equatorward propagation of the sunspot-producing zones observed during the solar cycle. In M0, the α-effect was of the wrong sign in most of the CZ, but with the improved description of heat conduction, the region where the effect is of the correct sign has grown significantly. In the new run (A1), we now observe a reversed migration direction of the magnetic field, which shows that the changes in the α-effect profile are significant, see Figure 2.

Ongoing Research / Outlook

We presented here the first testfield measurements from our higher-resolution runs with improved heat conduction description. They indicate significant changes in the profiles of the most crucial inductive effect related to solar and stellar dynamo mechanisms, which already has important consequences for Hunting down the cause of solar magnetism understanding these dynamos. Our even higher-resolution runs (A2A4) currently undertaken will bring us into an even more turbulent regime, where magnetic background fluctuations are generated by small-scale dynamo action. To measure the turbulent effects from these runs, we will apply the novel compressible test-field method. Such analysis will allow us to study, for the first time, the interaction of small- and large-scale dynamos in a quantitative way.

References and Links

[4] Warnecke J. et al. 2018, A&A, 609, A51.
[5] Käpylä P. et al. 2019, GAFD, 113, 149183.

Research Team

Lucia Duarte2, Maarit Käpylä1,2,3 (PI), Johannes Pekkilä1, Ameya Prabhu2, Matthias Rheinhardt1, Mariangela Viviani2, Jörn Warnecke2

1Aalto University, Department of Computer Science, Astroinformatics Group, Finland
2Max Planck Institute for Solar System Research, SOLSTAR group, Germany
3Nordita, Stockholm, Sweden

Scientific Contact

Maarit J. Käpylä
Associate professor, Department of Computer Science, Aalto University &
Max Planck Research Group Leader, MPS, Göttingen
Aalto University
P.O. Box 11000 (Otakaari 1B)
FI-00076 Aalto (Finland)
e-mail: maarit.kapyla [@]


(1) This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2020 (2021)" (ISBN 978-3-9816675-4-7)

(2) This simulation project was made possible by PRACE (Partnership for Advanced Computing in Europe) allocating a computing time grant on GCS HPC system SuperMUC-NG of the Leibniz Supercomputing Centre (LRZ). GCS is a hosting member of PRACE.

Local project ID: pn98qu

May 2021

Tags: MPI for Solar System Research LRZ Astrophysics Aalto University