Correcting for chromatic stellar activity effects in transits with multiband photometric monitoring: application to WASP-52

The properties of inhomogeneities on the surface of active stars (i.e. dark spots and bright faculae) significantly influence the determination of the parameters of an exoplanet. The chromatic effect they have on transmission spectroscopy could affect the analysis of data from future space missions such as JWST and Ariel. To quantify and mitigate the effects of those surface phenomena, we developed a modelling approach to derive the surface distribution and properties of active regions by modelling simultaneous multi-wavelength time-series observables. By using the StarSim code, now featuring the capability to solve the inverse problem, we analysed $\sim$ 600 days of BVRI multiband photometry from TJO and STELLA telescopes exoplanet host star WASP-52. From the results, we simulated the chromatic contribution of surface phenomena on the observables of its transits. We are able to determine the relevant activity parameters of WASP-52 and reconstruct the time-evolving longitudinal map of active regions. The star shows a heterogeneous surface composed of dark spots with a mean temperature contrast of $575\pm150$ K with filling factors ranging from 3 to 14 %. We studied the chromatic effects on the depths of transits obtained at different epochs with different stellar spot distributions. For WASP-52, with peak-to-peak photometric variations of $\sim$7 % in the visible, the residual effects of dark spots on the measured transit depth, after applying the calculated corrections, are about $10^{-4}$ at 550 nm and $3\times10^{-5}$ at 6$\mu$m. We demonstrate that by using contemporaneous ground-based multiband photometry of an active star, it is possible to reconstruct the parameters and distribution of active regions over time, and thus, quantify the chromatic effects on the planetary radii measured with transit spectroscopy and mitigate them by about an order of magnitude.