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II. Modelling stellar magnetic fields and activity signals to better understand their generation, evolution and interactions with close-in planets
II. Modelling stellar magnetic fields and activity signals to better understand their generation, evolution and interactions with close-in planets
Understanding the processes controlling the generation and temporal evolution of the magnetic fields of low-mass stars is a fundamental prerequisite to study the activity phenomena that they induce and their interactions with close-in planets. High-resolution spectropolarimetry, where high-resolution unpolarized and circularly-/linearly-polarized spectra are simultaneously obtained, is the most reliable way to constrain the strength and geometry of the magnetic field, as well as the distribution of bright and dark features at the stellar surface. Under the action of a magnetic field, each excitation level splits into a certain number of sublevels of energy due to the Zeeman effect. The latter induces observable signatures on both unpolarized spectra (line splitting), allowing to access the disk-integrated magnetic flux density, and on circularly-polarized (resp. linearly-polarized) spectra, which depends on the projection of the magnetic field vector along (resp. orthogonally to) the line-of-sight. As a consequence, time-series of circularly-polarized Zeeman signatures allow us to access the surface distribution of the large-scale magnetic field vector. The technique used to derive the magnetic topology from polarized Zeeman signatures is called Zeeman-Doppler Imaging (ZDI; see the reviews of Donati & Landstreet 2009 and Kochukhov 2016). The magnetic topologies are the best proxies to study the underlying dynamo processes, which control the amplification and evolution of the magnetic fields, as well as the activity phenomena they induce (e.g., spot/plages, flares) and, in particular, the geometry of the stellar wind and its interaction with close-in planets. In this section, I present my main contribution to study the magnetic fields of low-mass stars and their interactions with stellar activity and close-in planets.
1. The large-scale magnetic field of Proxima Centauri
Luminosity in the X-rays vs Rossyby number for partly-convective stars (gray dots) and fully-convective red dwarfs (red dots) following the activity-rotation relationship (source: Wright et al. 2018).
Our neighbour, Proxima Centauri, is an active red dwarf. Due to its very low mass, its interior is entirely convective and, thus, is different from the Sun which harbours an external convective zone and an inner radiative zone. The magnetic fields of fully-convective red dwarfs is thought to be generated by dynamo processes as, for example, (i) these stars are magnetically-active and (ii) they activity indicators follow the same activity-rotation relationship as solar-type stars (see the left-hand figure), where the activity level increases linearly with stellar Rossby number (i.e., ratio between stellar period and turnover time of the convective granules) until reaching a saturation plateau. The current paradigm for solar-type stars is that magnetic field is amplified by a so-called αΩ-dynamo process. Starting from an almost purely poloidal field, at the solar minimum the inner solar differential rotation, strongest at the interface between the convective and radiative zones (a.k.a. the tachocline) shears the field lines until the field is mostly toroidal, at the solar maximum: it's the Ω effect. Under the effect of helical turbulence (the field lines rising with ascending convective cells get twisted by the Coriolis force), the toroidal field is progressively converted into a poloidal field of opposite polarity. However, fully-convective red dwarfs do not possess a tachocline and their ability to power dynamo processes is not yet understood, hence the need to observe their magnetic fields.
Spectropolarimetric observations of late red dwarfs have shown that (i) there is a sharp change in the magnetic properties between partly-convective stars (more massive than ~0.35 solar mass) and (ii) the magnetic properties of fully-convective M dwarfs exhibit a bimodal distribution between strong axisymmetric dipolar field, on the one hand, and less strong, more complex non-axisymmetric field on the other hand. These observations are illustrated on the right-hand figure, widely called "confusiogram". Each symbol represents a star with observed magnetic properties (using ZDI) on a rotation period-mass diagram. The size of the symbol is proportional to the magnetic strength, its color depicts the fraction of poloidal field (red standing for purely poloidal and dark blue for purely toroidal) and its shape indicates the fraction of axisymmetric field (decagons: purely axisymmetric and stars: purely non-axisymmetric). The horizontal line indicates the full-convection threshold. Source of the figure: Baptiste Klein - PhD thesis (in English). The origin of this bimodality, either attributed to bimodal dynamo regime or to a unique dynamo process oscillating between the two topologies described above, is unclear.
Potential field of Proxima Centauri extrapolated from the reconstructed magnetic topology (using ZDI) at the phase of the maximum chromospheric emission
(source: Klein et al. 2021a).
Proxima Centauri is an ideal target to better understand the dynamo processes underlying fully-convective M dwarfs: Prox Cen is active (disk-integrated field of ~600 G), hosts a putative 7-yr activity cycle of unclear origin, and is a slow rotator (rotation period of ~90d), occupying thus an unpopulated part of the confusiogram above. We analysed 10 spectropolarimetric observations collected close to the stellar maximum with the HARPS-Pol spectrograph (La Silla Observatory) and detected clear Zeeman signatures, modulated throughout the stellar rotation cycle. Using ZDI, we find that Prox Cen hosts a large-scale field of 200 G, mainly dipolar but only moderately axisymmetric (see the extrapolated potential field on the left-hand side; source: Klein et al. 2021a). These observations also allow us to measure a stellar rotation period of 89.8 +/- 4.0 d. Proxima Centauri hosts a Habitable Zone planet, Proxima b, whose surface climate is expected to closely depend on the geometry of the stellar wind. The magnetic topology of Proxima Cen, published in Klein et al. 2021a, was used as an input of magneto-hydrodynamical simulations of the stellar wind by Kavanagh et al. 2021 in order to identify potential observable signatures of star-planet magnetic interactions. The planet was found to orbit in the so-called super-afvenic regime of the stellar wind, suggesting that no direct retroaction between the star and planet magnetosphere exists. Further spectropolarimetric monitoring of Proxima Centauri is highly needed to constrain the evolution of (i) the stellar magnetic properties and the confirmation of the putative magnetic cycle and (ii) the magnetic interactions between the stellar and its close-in planet. More generally, we emphasize that observing the large-scale field of a large sample of fully-convective red dwarfs in the near-infrared (with e.g. SPIRou/SPIP or CRIRES+) is the most promising way to better understand the underlying dynamo processes.
2. Investigating the magnetic field-activity relation in low-mass stars
Distribution of dark and bright inhomogeneities (colormap) at the surface of EPIC 211889233 obtained from the distortions of the unpolarized line profiles. The star is shown in flattened polar view, with the pole at the center. The solid and dash circles indicated the stellar equator and 30°/60° parallels, respectively. The ticks around the star mark the observations (in stellar phase).
The spectral contributions of the various phenomena induced by stellar activity (magnetic/brightness inhomogeneities, flares) remain obscure for stars other than the Sun. To better understand these, it is essential to observe a sample of active stars with different properties (rotation period, spectral type) simulteneously with many techniques (photometry, spectroscopy, spectropolarimetry). The stars in the continuous viewing zone of the TESS space mission are ideal targets in this venture. By combining these long-term photometric monitoring with velocimetric (HARPS/SOPHIE) and spectropolarimetric (ESPaDOnS/NARVAL/SPIRou) observations, one can hope to explore the connection between the stellar magnetic field and the activity phenomena and, thereby, better understand the dynamics of the latter and implement physically-based methods to better filter their RV contributions. In prepation for a future large-scale campaign, a few stars have been observed simultaneously with the K2 mission and with HARPS/SOPHIE and ESPaDOnS/NARVAL. I detected significant polarized Zeeman signatures in the M0 dwarf EPIC 211889233 (sweet name), which then became a prime target to prepare this large program.
I inverted the HARPS spectra into a distribution of dark inhomogeneities at the stellar surface. Doing this was not trivial as the star is rotating slowly (projected equatorial velocity of 2 km/s). As a consequence, the stellar absorption lines are not particularly broadened by the stellar rotation and mostly enclose the information of the intrinsic stellar line profile, which is unknown. When doing Doppler Imaging, we need to assume an intrinsic line profile for the stars. For rapid rotator, this assumption has no more than marginal effects on the reconstruction as the line profiles are dominated by rotation effects (see the review of Kochukhov 2016). I proposed an iterative method to overcome this limitation, fully-described in Klein et al. 2021b. The method was successfully applied to EPIC 211889233 (see left-hand figure) and the resulting map performed well at modelling the stellar activity RV signal.
Flattened-polar views of the distributions of the radial, azimuthal and meridional components of the large-scale magnetic field vector at the surface of EPIC 211889233.
Using ZDI, I inverted the cirularly-polarized Zeeman signatures into a distribution of large-scale magnetic vector at the surface of EPIC 211889233 (see figure above). The next step of this study is then to study the correlation between the magnetic topology, the brightness distribution and the activity curves (photometric, RV, etc). This work is still ongoing and will be published in Klein et al. 2022b, in prep.
3. Searching for star-planet magnetic interactions in AU Microscopii
Illustration of star-planet magnetic interaction with a tilted stellar magnetic dipole (source: Fischer & Saur 2019).
Close-in planets around active stars are expected to interact strongly with their host star. On the one hand, these planets with receive an intense irradiation and their atmosphere will likely be hghly affected by stellar flares and corronal mass ejections. On the other hand, if the planets orbits within the Alfvèn surface of the star, i.e., the region where the stellar magnetic field lines are still closed and the wind particle's velocity in subsonic, the planets can back react on their host. As the planet moves on its orbit, it will interact with the closed stellar field lines, thereby exciting so-called Afvèn waves that will propagate towards the star. When reaching the star, such waves are expected to locally heat the stellar atmosphere (especially the chromosphère), inducing potentially-visible hot spots and triggering flares. More information on the theory of Star-planet magnetic interactions can be found, for instance, in Cuntz et al. 2000, Strugarek et al. 2019 and Fischer & Saur 2019. The search for such signatures proved to be difficult as, despite many tentative detection, only one recent "unambigous" detection has been recently reported for the well-known hot Jupiter HD 189733 b.
Once again, AU Mic is under the spotlight! In Klein et al. 2021b, not only have we analysed the stellar RV, but also its magnetic topology using ZDI. The resulting large-scale magnetic field geometry was used as an input of 3D magnetohydrodynamical simulations of the stellar wind (see Kavanagh et al. 2021, which I co-authored). The main results of this study was that, under realistic assumptions of the stellar mass loss rate, the orbit of both close-in planets will likely be in the sub-afvènic regime of the stellar wind, meaning that direct connections between the star and planet magnetospheres could exit and induce observational signatures notably in radio wavelengths. This is illustrated in the right-hand figure picturing the orbits of AU Mic b and c (black cirles) and the computed ALfvèn surface (white solid line). The color map depits the wind radial velocity (source: Kavanagh et al. 2021).
Having this in mind, I analysed the spectra collected as part of the intensive monitoring of AU Mic with HARPS, whose velocimetric analysis is described in the Section 2 of the RV planet search page. I focused my analysis on a few well-known lines forming in the stellar chromosphere, namely Ca II H&K, Hβ, He I D3, Na I D1&D2 and Hα. The emergence of magnetic field lines out of the stellar photosphere (i.e., stellar surface) locally heats the chromosphere. As a result, these non-resonnant lines appear in emission and their emission flux varies depending on the amount of magnetic regions at the stellar surface. Due to their sensitivity to magnetic fields, these lines are primary probes of star-planet magnetic interections. I thus searched for potential modulations at the orbital period of AU Mic b (or c) and at the synodic period between the star's rotation and the planet orbital periods.
Interestingly, it seems that we can see a strong modulation of the emission flux in these lines closed to the orbital period of AU Mic b (8.33d vs 8.46d). This emission is strongest for the He I line, as shown on the left-hand figure. To create this figure, I fitting a simple sine-wave to each velocity bin of the He I line profile. Brighter regions correspond to periods that are most likely found in the time-series (the brighter, the more likely), in the velocity-period space. When we compute the associated emitted power, we obtain something of the order of 10^(20) W, corresponding with the values measured for hot Jupiters. This value is typically 2 to 5 orders of magnitude large than what is predicted by theoretical models (depending on the assumptions) and the light difference between the observed period and the orbital period of AU Mic b remains hard to explain. As a consequence, we cannot firmly claim that we observe an observational signature of a star-planet interaction and we caution that further observations are needed. In particular, we would need spectropoalrimetric observations in order to simultaneously monitor the temporal variation of the emission flux and its correlation with the magnetic field topology. These results are currently submitted to MNRAS (Klein et al. 2022, submitted).
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