Learning about Solar Magnetic Fields

through 3D global Magnetohydrodynamic simulations of solar convection and dynamo action

Currently I'm mainly working with the Solar Physics Group of the University of Montreal in 3D MHD simulations of solar convection using the EULAG-MHD code. Basically we simulate some of the Physics that are taking place in the Sun, using big computers!

I analyze the simulations outputs in order to understand the dynamics associated with the magnetic field, how this field influences the plasma flows (differential rotation, meridional circulation and turbulence) and vice-versa. These simulations are a valuable tool to help us understand the physical processes that are taking place inside our star and that we cannot measure directly through observations.

Example of simulation of solar convection The figure shows 3 snapshots of a representative EULAG-MHD simulation of solar convection. Left: temperature perturbation (-1.84 to +1.84 degrees K from dark to light); center: radial flow speed (-8.7 to +8.7 m/s from dark blue to light yellow); right: radial magnetic field (-0.013 to +0.013 tesla from green to yellow, gray is zero). All three projections are extracted in the subsurface layers (r/R=0.945). The viewpoint is 30 degrees above the equatorial plane.

Why?

Solar Magnetism as a driver of space weather

The solar magnetic field is the origin of Space Weather. It drives the solar wind and its interaction with Earth's magnetosphere causing geomagnetic storms. These storms have the ability to cripple satellites and interrupt global communications, overload power lines causing severe blackouts, induce dangerous electrical currents on ground pipelines, submit high latitude airplane travellers to high doses of radiation and even endanger the life of astronauts. For all these reasons we develop theoretical models that help us understand how the solar magnetic field evolves and try to predict the future levels of solar activity. From the point of view of other stars, stellar magnetic activity is also very important to understand the habitability conditions of exoplanets. Besides the consequences of the dangerous radiation associated with strong stellar magnetic activity, stellar winds also erode planetary atmospheres contributing to its depletion (like it happened on Mars).

If you want to learn a bit more about the Sun and its magnetic activity please check my dynamo outreach page (in portuguese). 

 

How?

Modelling the Sun in a computer

I work mainly in the field of numerical dynamo models. The modelling part consists in implementing computationaly the theoretical equations that explain the physics of magnetic fields creation, the dynamo effect. Since the Sun is made of hot plasma, Magnetohydrodynamics (MHD) paired with Thermodynamics constitute the best theoretical framework to study the origin and evolution of the magnetic field. One of the big questions that we want to answer is how can the convective zone (the highly turbulent outher layers of the Sun) create such a well organized large scale magnetic field that reverses polarity every 11 years. By doing several types of approximations to the MHD equations, we can build dynamo models in 1, 2 and 3 dimensions (depending on its application).

Different types of dynamo models

and some typical solutions for the obtained magnetic cycles

As mentioned before dynamo models can be constructed in several dimensions depending on the type of physical behaviour one wants to reproduce. I've developed models in 1D and 2D (or 2.5D) and I'm currently working with a 3D model. The first thing we aim to capture with our models is the cyclic behaviour of the Sun's magnetic field (here represented by the letter B), the so called solar cycle. Below I show some examples of how different types of models are constructed and how some of their typical solutions for the solar cycle look like...

 

Low order dynamo models

This type of model treats the dynamo mechanism as a dynamical system in one dimension (time). Usually the magnetic field, B, is represented by a differential equation that includes several coefficients that "contain" the physical structure of the star (velocity flows, diffusivity, etc). These LODM can are suited exploratory studies of simple phenomena and very long simulations. The image above show an example of a magnetic cycle obtained using a LODM, from Passos et al 2012, Sol. Phys. 279.

Kinematic Mean-field dynamos

These models solve the axisymmetric version of the induction equation in the r,theta plane (meridional slice). Usually called 2,5 D models (2 spatial dimensions + time), these type of model is by far the most popular in the literature. In this cathegory there are several types of models whose name is attributed based on its main physical mechanisms (e.g. alpha-omega, flux transport, Babcock-Leighton, etc.). These simulations can be used as predictive tools if they are driven by real data ( observational data assimilation).

3D MHD global simulations

Solving the full set of MHD equations in a 3D frameset/geometry (shell, box or wedge). The global simulations usually are done in a spherical shell (or wedge) that spans the major part of the convection zone and can include a section of the radiative zone. These simulations are computationally expensive but they can capture the very rich ecosystem of dynamical phenomena that exists between the magnetic field and the flows that are not found the other types of models.

Cosmic Rays...

Public Talk by Dr. James Cronin, Universidade do Algarve, 2007