# Limb darkening measurements from TESS and Kepler light curves of transiting exoplanets

**Authors:** P. F. L. Maxted  
**arXiv:** [2212.09117](https://arxiv.org/abs/2212.09117)  
**Date:** 2022-12-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2212.09117v1/

## Key points

- Inaccurate limb-darkening models can cause errors in analyzing light curves for transiting exoplanet and eclipsing binary star systems.
- P.F.L. Maxted compared predicted limb-darkening profiles to those measured from high-quality light curves of 43 FGK-type stars in transiting exoplanet systems observed by Kepler and TESS missions.
- Two parameters were used for comparison: $h^{\prime}_1 = I_{\lambda}(\frac{2}{3})$ and $h^{\prime}_2 = h^{\prime}_1 - I_{\lambda}(\frac{1}{3})$
- Most tabulations of limb-darkening data agreed well with observed values of $h^{\prime}_1$ and $h^{\prime}_2$, but there was a small but significant offset $\Delta h^{\prime}_1 \approx 0.006$ compared to observed values that could be attributed to a mean vertical magnetic field strength $\approx 100$\,G expected in photospheres of inactive solar-type stars but not accounted for by typical stellar model atmospheres.
- Accurate limb-darkening models are essential for determining accurate planetary radii from transit observations, which has implications for PLATO mission's precision measurements of planetary radii.
- More precise models that account for magnetic fields in photospheres of solar-type stars are needed.

## Summary

Inaccurate limb-darkening models can introduce significant errors in the analysis of light curves for transiting exoplanet and eclipsing binary star systems. To address this issue, P.F.L. Maxted compared limb-darkening profiles predicted by stellar atmosphere models to those measured from high-quality light curves of 43 FGK-type stars in transiting exoplanet systems observed by the Kepler and TESS missions. The comparison was done using two parameters: $h^{\prime}_1 = I_{\lambda}(\frac{2}{3})$ and $h^{\prime}_2 = h^{\prime}_1 - I_{\lambda}(\frac{1}{3})$, where $I_{\lambda}(\mu)$ is the specific intensity emitted in the direction $\mu$, the cosine of the angle between the line of sight and the surface normal vector. These parameters are straightforward to interpret and insensitive to how they are computed. Maxted found that most tabulations of limb-darkening data agreed well with observed values of $h^{\prime}_1$ and $h^{\prime}_2$. However, there was a small but significant offset $\Delta h^{\prime}_1 \approx 0.006$ compared to observed values that could be attributed to a mean vertical magnetic field strength $\approx 100$\,G expected in photospheres of inactive solar-type stars but not accounted for by typical stellar model atmospheres. These results have implications for PLATO mission's precision measurements of planetary radii as accurate limb-darkening models are essential for determining accurate planetary radii from transit observations. Therefore, these findings highlight the need for more precise models that account for magnetic fields in photospheres of solar-type stars. Overall, Maxted's study provides valuable insights into improving our understanding of limb-darkening effects on transit observations and emphasizes the importance of accurate modeling techniques when analyzing exoplanetary systems.