The stellar obliquity, planet mass, and very low albedo of Qatar-2 from K2 Photometry

Abstract

The Qatar-2 transiting exoplanet system was recently observed by the {\it Kepler} telescope as part of {\it K2} Campaign 6. The photometric time series has one-minute time sampling and a precision of about 690~ppm, after filtering out artifacts and spurious trends. We identify dozens of starspot-crossing events, when the planet eclipsed a relatively dark region of the stellar photosphere. The observed patterns in the sequence of these events demonstrate that the planet always transits over the same range of stellar latitudes, and therefore that the stellar obliquity is less than about 10$^\circ$. We support this conclusion with two different modeling approaches: one based on explicit identification and timing of the events, and the other based on fitting the light curves with a spotted-star model. We are also able to refine the usual transit parameters and measure the stellar rotation period ($18.5 \pm 1.9$~days), corresponding to a 'gyrochronological' age of $1.4 \pm 0.3$ Gyr. Coherent flux variations with the same period as the transits are seen throughout the entire light curve. These variations are well modeled as the combined effects of ellipsoidal light variations ($17.4 \pm 2.8$~ppm) and Doppler boosting ($11.9 \pm 2.5$~ppm). The magnitudes of these effects are both consistent with a planetary mass of $2.6 \pm 0.5~ M_{\text{Jup}}$, which is in turn consistent with the mass determined by the Doppler technique. No occultations are detected, giving a 2$σ$ upper limit of $0.013$ on the planet's visual geometric albedo. The measured transit times are consistent with a constant orbital period. In particular we find no evidence for orbital decay, although we are only able to place a weak lower bound on the relevant tidal quality factor: $Q'_\star > 1.5\times 10^4$~(95\% confidence).