Magnetic Coriolis darkening in cool stars Charly Pinçon - Institut d’Astrophysique Spatiale, OSUPS, Observatoire de Paris with the collaboration of L. Petitdemange, R. Raynaud, L. Garcia, A. Guseva, E. Alecian, and M. Rieutord 8th TESS/15th Kepler Asteroseismic Science Consortium Workshop 15-19 July 2024, Porto, Portugal Introduction Modeling the surface brightness distribution of stars is of prime importance to interpret the large amount of available interferometric, spectropolarimetric, or photometric observations. Beyond stellar physics, this is also a prerequisite to characterize exoplanets or our Galaxy. Stellar rotation is known to be a key physical ingredient in this regard. In rapidly rotating, hot massive stars with a stably stratified radiative envelope, the centrifugal flattening can make the poles hotter and brighter than the equator; this so-called gravity darkening is today well constrained (e.g., von Zeipel 1924, Bouchaud et al. 2020). In contrast, for low-mass cool stars, the picture remains uncertain as it requires one to model the MHD turbulence that develops in their convective envelopes. In this poster, we present the results by Raynaud et al. (2018) and Pinçon et al. (2024) who studied the effect of the Coriolis force on the surface luminosity distribution of thick convective envelopes, as well as the effect of potential dynamo magnetic fields. MHD simulations - MagIC and Parody codes: solve anelastic MHD Navier-Stokes equations. - Rotating convective envelopes in [ ri , ro ]. - Parametric study: about 100 simulations. - Density contrast between 20 – 400. - Entropy jump to force convection. - Stress-free and insulating boundaries. - Thick shell: representative of a 0.35 ∼ Msun dwarf or a PMS star Fig. 3: Spherical representation of the mean luminosity distribution (measured by the Nusselt number Nu) for the nonmagnetized model and the most magnetized dynamo model (i.e., the highest value of Pm) represented in Fig. 1. Radial velocity fluctuations Results Rosurf > 1 → Turbulent homogeneization of the surface. Rosurf < 1 →Complex interplay between rotation and self-sustained magnetic fields. - Rotation-constrained turbulence can generate a strong equatorial jet (Fig. 2) : Radial heat flux inhibited, dark equatorial band (Fig. 1). - With magnetic dynamo, Pm ↗ → B ↗ : Lorentz force quenches the equatorial jet (Fig. 2) and the luminosity profile flattens (Fig. 1). In conclusion, in rapidly-rotating cool stars, an equatorial darkening may occur, whose contrast depends on the rotation rate and the magnetic field intensity (see Fig. 3). Fig. 1: Surface heat flux (measured by the Nusselt number Nu) as a function of the colatitude, and for different values of the magnetic Prandtl number Pm. These profiles are mean values computed over azimuth and time. N.B: The parameters of the models are Ek=3 10-4, Pr=1, Ra~ 107, Nρ=6. Fig. 2: Same as in Fig.1 but for the mean profile of the azimuthal velocity (inside the rotating frame of rotation rate Ω). Fig. 4: Schematic transit of an exoplanet occulting a star with an equatorial jet dimmer than the rest of its photosphere. The bottom plot shows the occultation light curve (black line), the differential flux measured for the six times shown above (points), as well as the transit signal that would be observed for a uniform limb- darkened star (gray). Surface Rossby number Magnetic Prandtl number Prospects Such a magnetic Coriolis darkening can have an impact on not only the stellar luminosity estimate, but also on planet transit retrievals, in the same way as limb and gravity darkening effects. These predictions will have to be tested in the future, either in a direct way through high resolution interferometry or indirectly through misaligned transits (Fig.4).