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).
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We have obtained the first time-resolved, disk-integrated observations of Earth’s poles with the Deep Impact spacecraft as part of the EPOXI mission of opportunity. These data mimic what we will see when we point next-generation space telescopes at nearby exoplanets. We use principal component analysis (PCA) and rotational light curve inversion to characterize color inhomogeneities and map their spatial distribution from these unusual vantage points, as a complement to the equatorial views presented by Cowan et al. in 2009. We also perform the same PCA on a suite of simulated rotational multi-band light curves from NASA’s Virtual Planetary Laboratory three-dimensional spectral Earth model. This numerical experiment allows us to understand what sorts of surface features PCA can robustly identify. We find that the EPOXI polar observations have similar broadband colors as the equatorial Earth, but with 20%-30% greater apparent albedo. This is because the polar observations are most sensitive to mid-latitudes, which tend to be more cloudy than the equatorial latitudes emphasized by the original EPOXI Earth observations.
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When Earth-mass extrasolar planets first become detectable, one challenge will be to determine which of these worlds harbor liquid water, a widely used criterion for habitability. Some of the first observations of these planets will consist of disc-averaged, time-resolved broadband photometry. To simulate such data, the Deep Impact spacecraft obtained light curves of Earth at seven wavebands spanning 300-1000 nm as part of the EPOXI mission of opportunity. In this paper, we analyze disc-integrated light curves, treating Earth as if it were an exoplanet, to determine if we can detect the presence of oceans and continents. We present two observations each spanning 1 day, taken at gibbous phases of 57° and 77°, respectively. As expected, the time-averaged spectrum of Earth is blue at short wavelengths due to Rayleigh scattering, and gray redward of 600 nm due to reflective clouds. The rotation of the planet leads to diurnal albedo variations of 15%-30%, with the largest relative changes occurring at the reddest wavelengths. To characterize these variations in an unbiased manner, we carry out a principal component analysis of the multi-band light curves; this analysis reveals that 98% of the diurnal color changes of Earth are due to only two dominant eigencolors. We use the time variations of these two eigencolors to construct longitudinal maps of the Earth, treating it as a non-uniform Lambert sphere. We find that the spectral and spatial distributions of the eigencolors correspond to cloud-free continents and oceans despite the fact that our observations were taken on days with typical cloud cover. We also find that the near-infrared wavebands are particularly useful in distinguishing between land and water. Based on this experiment, we conclude that it should be possible to infer the existence of water oceans on exoplanets with time-resolved broadband observations taken by a large space-based coronagraphic telescope.
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