Quantifying the Impact of Starspot-Crossing Events on Retrieved Parameters from Transit Lightcurves

TL;DR

This paper investigates how starspot-crossing events (SCEs) and the Transit Light Source Effect (TLSE) bias exoplanet transit depths and planetary parameter retrievals. It employs the chromatic_fitting framework and starry to inject and recover synthetic SCEs, quantifying how well spot properties and transit depths can be constrained from single-wavelength data and how fitting compares to masking. The study finds that high-SNR SCEs tightly constrain spot longitudes but leave latitudinal and size parameters degenerate, with average transit-depth biases around 78 ppm and depth recoveries within 0.6% in many cases; for sizeable TLSE contamination, fitting SCEs improves depth recovery in most cases, while small/low-contrast spots can lead to over-correction and inflated uncertainties, especially at JWST-like precision. It further demonstrates how SCE observables can constrain the degenerate spot-parameter space and applies these ideas to Kepler-51 d with JWST data, illustrating practical priors for efficient sampling and robust interpretation of transmission spectra in the presence of stellar activity.

Abstract

Starspot-crossing events (SCEs) in exoplanet transit lightcurves are becoming increasingly common as we focus on cooler host stars and observe higher precision photometric and spectroscopic lightcurves. In this work we explore how these events affect our retrievals of transit depths, and the accuracy with which we can derive spot properties. We inject and recover synthetic SCEs in photometric lightcurves using starry. We find that for high signal-to-noise SCEs we constrain the spot longitudes tightly (>80% within 1 degree of the true value), but degeneracies complicate retrieving spot contrasts, radii and latitudes (within 17%, 19%, and 9 degrees respectively). On average the difference between injected and recovered transit depths is 0.78% or 78.3ppm. In most (80%) injections we recover the transit depth to within 0.6%. For transit depths inflated >1.3% by the Transit Light Source Effect (TLSE), fitting for a spot-crossing improves the transit depth retrieval over masking the SCE in >95% of cases. However, we find that for spots with small contrasts (<5%) and/or covering fractions (<2%), we are likely to over-correct for the TLSE, recovering a worse transit depth than simply masking. In addition, even when fitted, we find SCEs can inflate the uncertainties on recovered transit depths significantly, especially for JWST-like precisions. Finally, we determine how SCE observables can narrow the degenerate spot parameter space to provide useful priors for MCMC sampling, demonstrating this technique on a real SCE observed in Kepler-51d's lightcurve.

Figures (15)

• Figure 1: We present five samples from Section \ref{['ss:sample']} to demonstrate a range of light curve uncertainties and spot parameters. Upper: The starry stellar surface maps for each injection scenario with quadratic limb-darkening and the spot. There are slight ringing artifacts from the choice to reduce the smoothing parameter as discussed in Section \ref{['ssec:resultsspot']}. The transit chord is shown by the shaded gray region on each map. Middle: The transit light curves in each case, with injected Gaussian uncertainties. The underlying model generated by starry is shown in orange, the same transit without spot-crossing or TLSE in dotted gray, and the recovered MAP-optimized (Maximum A Posteriori) result shown in blue. Lower: The starry stellar surface maps for the MAP-optimized solution in each case.
• Figure 2: For the 1000 injected spot samples; Left: radius of the spot (in degrees), $R_{\rm{spot}}$, against the contrast between spot and quiescent photosphere. Right: the projected location of the spot centers on the surface of the star. The top half of the star is shaded as we only inject spots into one half to avoid the symmetrical degeneracy in recovery. Below $y\leq-0.8$ is also shaded as the largest spot we inject, $R_{\rm{spot}}=45\degree$, would not cross the transit chord.
• Figure 3: For the fourth spot-crossing scenario in Figure \ref{['fig:transit_models']} (SNR=11.5) we plot the log-likelihood values (colorbar) for the MAP-optimized transit and spot model for 13 different starting positions (circles). The final optimized spot locations for each starting position is indicated with an arrow. The true model is plotted with a black circle (a cross marking its centre) and the highest likelihood spot is shown with a dotted grey circle. The transit chord is marked by the shaded grey region along the star's equator ($b$=0).
• Figure 4: Recovered vs injected spot contrast, radius, latitude, longitude, and transit depth, for (a) all SCEs and (b) SCEs with SNR$\geq$4. The points marked with crosses are spots whose projections overlap with the stellar limb. Limb spots are much more difficult to fit and have intrinsically much more uncertainty. The colorbar represents the log(SNR) of each SCE.
• Figure 5: For SNR$<$4 (dashed lines) and $\geq$4 (solid lines) we show five recovered parameters: spot contrast (top left), radius (top right), latitude (middle left), longitude (middle right) and planetary radius (bottom left). On the left axis (black) we plot the percentile of the absolute difference between injected, $i$, and recovered, $r$. On the right axis (colors) we show the percentage difference from the injected value, also against percentile. Only percentiles from 50%--98% are shown here.