This tutorial is an introduction to techniques used to characterize the atmospheres of transiting exoplanets. We intend it to be a useful guide for the undergraduate, graduate student, or postdoctoral scholar who wants to begin research in this field, but who has no prior experience with transiting exoplanets. We begin with a discussion of the properties of exoplanetary systems that allow us to measure exoplanetary spectra, and the principles that underlie transit techniques. Subsequently, we discuss the most favorable wavelengths for observing, and explain the specific techniques of secondary eclipses and eclipse mapping, phase curves, transit spectroscopy, and convolution with spectral templates. Our discussion includes factors that affect the data acquisition, and also a separate discussion of how the results are interpreted. Other important topics that we cover include statistical methods to characterize atmospheres such as stacking, and the effects of stellar activity. We conclude by projecting the future utility of large-aperture observatories such as the James Webb Space Telescope and the forthcoming generation of extremely large ground-based telescopes.
Refraction can lead to a brightening just before ingress and just after egress of a transit, as light passes through the exoplanet’s atmosphere and is refracted into our line of sight (Sidis & Sari 2010; Misra & Meadows 2014; Misra et al. 2014; Dalba 2017; Alp & Demory 2018). Refraction just outside of transit has been seen and modeled in our own solar system during transits of Venus (Pasachoff et al. 2011; García Muñoz & Mills 2012; Tanga et al. 2012). For short-period planets, the model of (Sidis & Sari 2010, hereafter S&S) implies refraction peaks typically under 100 parts per million (ppm) and comparable in duration to ingress and egress. Kepler photometry (Borucki et al. 2010) currently provides the best opportunity for detecting refraction. We search for the signature of refraction just outside of transit in Kepler photometry of 45 gas giants and firmly rule out the S&S model for four candidates.
We select Kepler Objects of Interest (KOIs) with radii at least twice that of Earth for which the S&S Equation (30) implies a peak effect greater than 10 parts per million (ppm), adjusted for Rayleigh scattering using their Equations (40)(45). We eliminate KOIs with grazing transits as well as those identified in Ford et al. (2012), Mazeh et al. (2013), and Holczer et al. (2016) as having significant transit timing variations. We also eliminate a few KOIs identified by Holczer et al. (2016) as likely planetary false positives based on the behavior of the light curves, leaving 45 planet candidates. To calculate the expected effect, we adopt the masses predicted in Chen & Kipping (2018).
We present a method to detect small atmospheric signals in Kepler’s planet candidate light curves by averaging light curves for multiple candidates with similar orbital and physical characteristics. Our statistical method allows us to measure unbiased physical properties of Kepler’s planet candidates, even for candidates whose individual signal-to-noise precludes the detection of their secondary eclipse.