Stellar butterfly diagrams – BUTTERFLY

The spatial distribution of sunspots as a function of time (butterfly diagram) gives important indications for solar dynamo models. In this project, we plan to demonstrate by advanced numerical simulations that the latitude of sunspots can also be found for distant stars using only information from stellar light curves. These curves obtained over long periods of time at high cadence give at least two indications of the magnetic activity: dark stellar spots and bright faculae modulate the intensity on the time scale of the rotation (~27 days for the sun); the eigenmodes of the acoustic oscillations are affected by the surface magnetic activity (the acoustic waves travel faster in magnetic regions)
We will model the perturbations in intensity and seismic observables for a given distribution of spots and faculae. We will solve the equations of solar oscillations with rotation considering localized velocity perturbations near the surface. We will use a massively parallel numerical approach based on a high-order hybridized discontinuous Galerkin method. We further couple the approach with boundary element methods to drastically reduce the computational cost. We will invert seismic disturbances to retrieve the position of the magnetic activity. These inversion techniques will be validated with solar observations. This interdisciplinary project is based on the collaboration between applied mathematicians and astrophysicists. From 2026, this work will be applied to the thousands of solar-type stars that will be observed by the European PLATO mission.