Designing new Stellar Activity Metrics for use with Exoplanet Transmission Spectra Obtained with both Current and Future Missions

All exoplanet host stars are unique and have the capacity to exhibit stellar activity in the form of spots and faculae to differing extents and in a highly temporally variable way. It is therefore reasonable to expect that we are seeing, and will continue to see widespread stellar contamination of differing degrees throughout both current and future observations of exoplanets in transmission. Furthermore, as this contamination is potentially varying on an epoch-to-epoch basis, using a one-size-fits-all analytical approach is unwise and implausible even for a single exoplanetary system. 

For transmission spectra obtained with both current and future instruments, the majority of the information pertaining to the extent of stellar contamination is contained within the shortest wavelength datapoints in the optical regime. As such, good coverage in both the optical and the infrared is essential for conducting accurate combined star-planet retrieval analyses. Unfortunately from the stellar-perspective, the optical regime is usually less prioritised by instrumentation with respect to the infrared, where the bulk of the planetary information lies. As such the optical region tends to have a lower resolution and the datapoints themselves frequently have larger error bars leading a retrieval to assign a lower priority to them during the fitting process. Conducting retrievals on the optical data alone is also not suggested as they require the planetary information contained within the infrared to act as an anchor point in order to perform optimally. Stellar contamination is capable of introducing significant biases in the retrieved planetary parameters if not corrected for so it is paramount that we fully understand the extent of stellar contamination within our observations. In order to achieve this, we need to leverage the information content of the shortest wavelengths to the fullest extent alongside that of the infrared, both so that we can perform complete star-planet analyses of current observations with JWST and in preparation for future exoplanet-dedicated missions e.g. Twinkle and Ariel that will open up the possibility for population studies on an unprecedented scale. 

With this rationale in mind, we introduce two new, complementary metrics, the Stellar Activity Distance (SAD) metric and the Stellar Activity Temporal (SAT) metric which are designed to indicate the extent of stellar contamination at the time of observation in a highly interpretable way. These metrics are intended to aid in the assessment of different retrieval models, alongside existing model comparison tools e.g. the Bayes Factor and activity indicators e.g. log(R′ HK), the uses of which are already well-cemented within the literature, to give a bigger picture context of the host stars stellar activity level, both during an individual observation and over subsequent visits. 

Briefly, the SAD is a chi-squared inspired, goodness-of-fit metric that focuses solely on wavelengths bluewards of 1µm. At first order the SAD seeks to determine whether any slopes in the optical data can be sufficiently reproduced by a Rayleigh scattering slope from atmospheric hazes alone, or whether or not an additional departure from Rayleigh scattering due to stellar contamination is required. This departure can be either in the form of strengthening the positive bluewards slope as is expected for a spot-dominated activity regime or nullifying/reversing the slope in the case of a faculae-dominated regime. The SAD complements the Bayes Factor as although both tools are founded on a similar ideology, they differ in that the SAD focuses solely on the fit in the optical regime, whereas the Bayes Factor indicates which model is preferred by the entire observed spectrum. In contrast, the SAT is designed to assess the repeatability, or lack thereof, of observations from subsequent visits to the same exoplanetary system. As such the SAT requires that the system has been observed at at least two different epochs with the same instrument. By taking the pairwise differences between each datapoint and computing the average we can quantify the differences between multiple observations both in ppm, or as a percentage difference with respect to the planets weighted average transit depth in the IR allowing for comparability between systems. The use of both of these metrics for WASP-6b, a planet orbiting a well-known active host star, are shown in Fig. 1 below.

Figure 1. Left – The Stellar Activity Distance metric (SAD) calculation for a single dataset combining visits with HST STIS grisms G430L and G750L for WASP-6b. The best fit retrieved spectra for two retrieval instances are plotted with the retrieval model accounting for stellar contamination shown in orange and the retrieval model neglecting this shown in cyan. The SAD is calculated as the average distance of the baseline model from the observation divided by the average distance of the stellar contamination model and here shows a strong preference for the inclusion of stellar activity for these observations of WASP-6b. Right – The Stellar Activity Temporal metric (SAT) calculated for the same planet for two G430L visits taken at different epochs. The two observations, shown in purple and cyan, appear to increasingly diverge as a function of decreasing wavelength. The orange dashed line represents the weighted average transit depth for WASP-6b calculated from the HST WFC3 observation in the IR. Adapted from Saba et al. (2024)

 

In this presentation I will introduce these metrics and show their application to both current observations with HST STIS (Saba et al. 2024) and future observations with Ariel, where they will enable us to extract as much information about the host star and its activity level from the optical FGS photometers as possible. I hope to demonstrate that, alongside other traditional activity indicators, these metrics may be used to give us a better understanding of which exoplanetary systems require follow-up observations through large, ground-based, stellar-focused surveys in order to adequately characterise the host star before we can accurately include their planets within our studies of comparative exoplanetology

REFERENCES
Saba, A., Thompson, A., Hou Yip, K., et al. 2024, arXiv:2404.15505. doi:10.48550/arXiv.2404.15505