Stellar limb darkening plays an important role in the analysis of many astrophysical data (e.g. transiting exoplanets, eclipsing binaries, microlensing events, interferometrically measured stellar radius, Baade-Wesselink analysis of pulsating variables etc). Both stellar and galactic astrophysics as well as exoplanet science could benefit from the improvement of its understanding. Direct measurements of limb darkening can be carried out only on the Sun. To calibrate the limb darkening laws as function of stellar type, well-detached, double-lined eclipsing binaries and multi/transiting planetary systems are needed with well-measured properties – this latter requirement increases the accuracy of the calibration of the limb darkening laws.

PLATO (to be launched in 2026) is a European Space Agency M-class mission to detect and characterize primarily earth-like planets around solar-like stars in the habitable zone with 10% accuracy in planetary mass and 3% in planetary radius. Highly accurate masses and radii are needed to study the planetary interiors and habitability. Since such planets have one-year orbital periods, only two to three transits will be observed during PLATO’s long pointings. Such transiting exoplanets were not characterized with this accuracy by other missions, e.g. Kepler.

Stellar limb darkening and stellar activity are the main challenges to get the planetary radius with this accuracy from such a small number of transits of small planets. Limb darkening modifies the transit depth by a factor of two relative to the case when there is no limb darkening. Limb darkening coefficients can be determined simultaneously with the planet-to-star radius ratio if the signal-to-noise ratio (S/N) is sufficiently high, but that S/N cannot be reached here because the small number of transits and stellar activity do not allow us to increase S/N by averaging the transits.


The aim of this proposed ISSI group is to improve our understanding of stellar limb darkening to a higher accuracy that can be reached today. This will lead to a reduction in the systematic errors from the limitations in our modeling of this effect. These improvements are necessary to derive planetary radii with very high precision. Currently, there are deficits in our theoretical understanding of stellar atmospheres where the limb darkening occurs, and in how the stellar magnetic field, and other stellar activity phenomena (spots, plages, faculae, flares) play a role in this.


We plan to investigate the effects of poorly known stellar limb darkening on the derived planetary radii and the effect of stellar activity on limb darkening and also on planetary radii. This is essential in order to reach the goals of PLATO.

We aim to investigate:

  1. the gap between input stellar physics and limb darkening profiles through a uniform comparison of the different stellar atmosphere models;
  2. how stellar activity can be taken into account in the limb darkening profile calculations;
  3. what is the best way to map the limb darkening profile to different kinds of observations;
  4. what observational tests of limb darkening phenomenon can be carried out from new and existing space-based photometric data e.g. TESS & CHEOPS;
  5. which limb darkening law works best for which stellar spectral type;
  6. which is the best way of managing limb darkening in transit light curve modeling and what recommendations can we make for the development of the PLATO Exoplanet Analysis System pipeline?