Cool Stars with a Magnetic Personality

by Élodie Hébrard (York University) and Rakesh Yadav (Harvard-Smithonian CfA).

There is an invisible force active on the Sun which is due to its magnetic field. You may know that magnetic fields can be produced by electrical currents. The Sun’s plasma is a highly charged fluid. Due to the combined effect of large-scale ordered motions induced by the Sun’s rotation and the chaotic boiling of the plasma, there is an ample supply of electrical currents on the Sun to sustain the magnetic fields. This process of field generation by fluid motions is known as the Dynamo mechanism.

Magnetic fields are responsible for producing very violent events called X-ray flares on the Sun. The energy which is stored in the magnetic field as tension gets released in the form of energetic electromagnetic radiation (ultra violet and X-rays). These flares also accelerate the plasma in the nearby region, which is ejected with very high velocities away from the Sun. These are known as Coronal Mass Ejections (CMEs). The energetic radiation and the CMEs form a dangerous partnership as they can gradually erode away the atmosphere (crucial for developing life) of a closely orbiting planet. You can learn more about X-ray flares in this short video.

Lets move away from our solar system and discuss the Pale Red Dot. Stars which are substantially cooler than the Sun are usually referred to as “red dwarfs” or “low-mass stars”. Proxima Centauri is one such star. But do not be fooled by their “coolness”! Astronomers have been looking at such stars for decades now—it turns out these stars are very active. In fact, they generate many more X-ray flares and CMEs than the Sun. Due to the high levels of violent events on these stars, the planets orbiting around them might encounter much more hostile environments than the planets in our own solar system. Such high activity is due to the presence of a magnetic field which is much stronger than what our Sun can produce. The high activity also makes it rather tricky to find Earth-like planets around these stars. Hey, wait a minute, how do we know that these stars have strong magnetic fields?

The best way to measure the magnetic field of a star is to use the subtle effects it induces on the light it emits. Indeed, if a star has a magnetic field, its spectrum is affected: the different spectral lines split into several components, and each component has its own polarisation (it means that the magnetic field changes the vibrational properties of the light). This splitting effect is called the Zeeman effect. Measuring polarisation in spectral lines allows a reliable measurement of the stellar magnetic field, as explained in the short video below.

So now we know how we are able to measure a magnetic field, the next natural step is to reconstruct the map of the stellar magnetic field in order to know what it looks like: a dipolar field? a toroidal field?… To do that, we use the stellar rotation! More specifically, analysing the circular polarisation in spectral lines at different times as the star rotates, we get step by step a full 2D image of the magnetic field at the surface of the star. To carry out this exercise, astronomers use a method called Zeeman-Doppler Imaging (ZDI)—based on techniques developed for medical imaging! The following animations summarise the principles behind ZDI.

As the star rotates, an Earth-based observer sees the magnetic spot under different viewing angles, and moving at different projected velocities (upper panel). The level of circular polarisation measured in a spectral line evolves consequently (lower panel). The case of a radially oriented field (as depicted by the red arrows) is depicted here. Credit: J.-F. Donati.
Same as the previous figure, but here with the case of an azimuthally oriented field (as depicted by the red arrows) depicted. As opposed to the radial field situation the circular polarisation signature flips sign. This allows ZDI to disentangle between field orientations. Credit: J.-F. Donati.

Dark starspots (similar to sunspots) are a visible consequence of
the magnetic field activity of a star. As presented in Xavier Dumusque’s article, these spots induce distortions in the spectral line profiles (because of the Doppler effect), that induce radial velocity (RV) shift. Moreover, as the star rotates and the spot is carried across the visible disc, this distortion travels through the line profile (see figure below). Therefore, collecting data at different rotation phases allows us to unveil how the bright features are distributed on the stellar surface, exactly as for the magnetic field. In this case the method is simply called Doppler-Imaging.

As the star rotates, an Earth-based observer sees the dark starspot at different locations on the visible stellar disc (upper panel). This results in characteristic distortions in stellar spectral line profiles that induce an apparent radial velocity (RV) shift (lower panel). Such RV shifts can mimic the signal of a planet or completely hide the presence of a genuine planet. Credit: J.-F. Donati.

Instruments developed to gather simultaneously both the spectrum and its polarisation are called spectropolarimeters. The most used are ESPaDOnS atop the Mauna Kea in Hawaii, NARVAL atop the Pic-du-Midi in France, and HARPS-pol at La Silla observatory in Chile.

The telescopes hosting the three high-resolution spectropolarimeters designed for studies of stellar magnetic fields. From left to right: Canada-France-Hawaii Telescope, Maunakea, Hawaii, USA; ESO 3.6m Telescope, La Silla Observatory, Chile; Télescope Bernard Lyot, Pic-du-midi Observatory, France. Credits: J-C Cuillandre/E Hébrard/OMP.

What can we do with these measurements? First, as stellar spots plague the planet detection from radial velocity measurements, we can use the map of the spot distribution to infer the induced RV. Although new, this method holds tremendous promise in being able to filter out the stellar signal, and thus to regain the power of diagnosing the potential presence of orbiting planets. Second, if our final goal is to detect a habitable Earth-like planet around cool stars, characterising the planetary environment is of prime importance. Indeed, the reduced temperatures of cool stars move their habitable zone closer in than around Sun-like stars. Earth-like planets orbiting such stars would experience a stronger stellar magnetic pressure, exposing the planet’s atmosphere to erosion by the stellar wind and CMEs. Therefore there is an interest for estimating the stellar magnetic environment surrounding these planets. From the reconstruction of large-scale magnetic field topologies with ZDI, one can extrapolate the field outwards (see V374 Peg figure below) and ultimately it will allow a more thorough characterisation of detected planets, and a better assessment of the suitability of a planet for hosting life. Finally, the observed large-scale magnetic properties can be useful to better understand the stellar interior and the magnetic field generation.

Magnetic field lines of the active red dwarf V374 Peg, extending in space above the surface of the star. The surface magnetic field has been mapped with ZDI, serving as a basis for the extrapolation to the whole magnetosphere. The simple dipole, magnet-like structure of the field is very obvious. Field lines forming loops above the surface are shown in white, while field lines open to the interstellar medium are shown in blue. Credit: MM Jardine & J-F Donati.

So far we have discussed what we know about red dwarf stars observationally. Let’s go into some details about the latest theoretical models which try to explain why these stars have such strong magnetic fields. We will now discuss a recent supercomputer simulation which tried to mimic what happens in red dwarf stars.

In computer simulations a star is considered to be a perfect sphere of hot plasma which rotates around an axis. To model the plasma flows, we assume that it follows the Navier-Stokes equation—which basically tells us that the change in the momentum of a tiny fluid packet is proportional to the sum of various forces acting on it. The behaviour of the magnetic field is governed by Maxwell’s equations (under the so-called MHD approximation). Furthermore, there are other equations of importance which describe the energy conservation and the thermodynamical state of the fluid (temperature, pressure, etc). These equations are then solved using sophisticated numerical algorithms (codes with 10s of thousands of lines) which are run on some of the world’s largest supercomputers.

Hydra570
The HYDRA supercomputer at the Max Planck Computing and Data Facility in Garching bei München, Germany. In total there are ~83,000 cores with a main memory of 280 TB and a peak performance of about 1.7 PetaFlop/s. Credit: Max Planck Society.

If we model conditions, which are similar to those found in red dwarf stars, the simulation produces many properties similar to what we actually observe. The magnetic field resulting from this simulation is depicted in the figure below. The field lines are coming out of the visible north pole of the “star”. This is due to a large region of magnetic field with one polarity (shown with yellow shades). A similar behaviour occurs in the south pole which is not visible in the image. Along with large regions with similar polarity, there are smaller regions containing both polarities of the magnetic field (close-by yellow and blue shades), scattered almost all over the surface. These “bipolar” regions are necessary to generate twisted and stretched field lines which lead to X-ray flares and CMEs. In fact, the bipolar “active” regions on this “star” are much more numerous than what we see on the Sun. By extension, this model then predicts that the red dwarf stars should generate many more X-ray flares. The strength of the magnetic field in the image is also typically about several kiloGauss, at least ten times stronger than the Sun’s typical magnetic field.

Magnetic field simulation
Numerical simulation aimed at studying magnetic field generation in a red dwarf star. The two magnetic polarities are depicted in yellow and blue. The cyan-color pipe shows the rotation axis. Credit: Rakesh Yadav.

To sum up, this “star in a computer” is able to self-consistently produce a very strong magnetic field and predicts that these stars should be much more active than the Sun. We have made some progress in the sense that this simulated star satisfies some observational constraints. The next step is to use the predictions from this simulation and test them using more detailed observations. The Pale Red Dot project is one such step.

About the authors

Elodie Hébrard

Élodie Hébrard graduated her PhD in astrophysics in 2015 at the Institut de Recherches en Astrophysique et Planétologie of the University of Toulouse (France). She studies the use of the Zeeman-Doppler Imaging technique to characterise stellar activity and magnetic fields, ultimately designing new approaches to filter out the activity-induced  radial velocity signals that  mimic those due to planets. Élodie is now a postdoctoral fellow at the Department of Physics and Astronomy of the University of York (Canada).

Rakesh Yadav

Rakesh Yadav is a theoretical astrophysicist who uses supercomputers to understand how planets and stars produce their magnetic fields. He finished his BSc and MSc (physics) in 2011 at the Indian Institute of Technology Kanpur, India. He moved to Germany in 2012 to pursue a PhD in computational astrophysics at the Max Planck Institut für Sonnensystemforschung and the University of Göttingen. After finishing his PhD in 2015 he joined the Harvard-Smithsonian Center for Astrophysics as a Post Doctoral scientist.