Discovery paper in Science:
Hear lead author Jerome Orosz in interview on Science Friday:
See also: System diagram and Planet artwork
Hear Interview on Science Friday with Jerome Orosz
Kepler-47 System Parameters
Table 1: A summary of the results for the photometric-dynamical model. For brevity some of the fitting parameters are not listed here. See Table S5 for a complete listing of fitting parameters.
Kepler-47 Light Curves
Fig. 1: Light curves and velocity curve data with model fits. Top: Normalized and detrended flux is plotted versus orbital phase for the primary and secondary eclipses, along with the binary star model. Middle: The radial velocities of the primary star and the best-fitting model are plotted versus the orbital phase. The expected radial velocity curve of the secondary star is shown with the dashed line. Bottom: The normalized and detrended flux near five representative transits of the inner planet and all three transits of the outer planet are shown. See Figs. S13, S14, and S15 for plots of all 18 transits of the inner planet and plots of the residuals of the various model fits.
Transit Timing Variations
Fig. 2 (below): Planetary transit time and duration variations. Left: The observed minus expected times of transit computed from a linear ephemeris are shown versus time (an “O–C” curve). The triangles show the measured deviations, and the filled circles are the predictions from the photometric-dynamical model. Four transits of the inner planet occurred in data gaps or regions of corrupted data. Top right: The O-C values of the inner planet are shown as a function of the binary phase, where the primary eclipse occurs at phase 0.0 and the secondary eclipse is at phase 0.487. Two cycles have been shown for clarity. The solid curve is the predicted deviation assuming a circular, edge-on orbit for the planet. The lateral displacement of the primary near the eclipse phases is minimal and therefore the deviation of the transit time from a linear ephemeris is near zero. The primary is maximally displaced near the quadrature phases, so transits near those phases show the most offset in time. Bottom right: The durations of the transits for the inner planet (filled circles) and the outer planet (filled squares) as a function of the orbital phase of the binary. The solid curves are the predicted durations assuming a circular, edge-on orbit for the planet. At phases near the primary eclipse, the planet and the primary star are moving in opposite directions, resulting in a narrower transit. At phases near the secondary eclipse, the planet and the primary star are moving in the same direction, resulting in a longer transit. The outer planet is moving slower than the inner planet, resulting in longer transits at the same binary phase.
Fig. 3: The time-varying insolation S received by Kepler-47 c, for different assumed eccentricities. The insolation is in units of the Solar luminosity at a distance of 1 AU (SSun = 1368 W/m2). The upper panels are for a zero eccentricity orbit and highlight the insolation variations caused by the 7.4-day orbit of the binary. The lower panels show eccentricities of e = 0.0, 0.1, 0.2, and 0.4 (colored black, green, blue, and red, respectively), and illustrate the longer time- scale variations. The dotted lines mark the limits for the inner and outer edges of the habitable zone, following the prescription in (24) for the onset of a runaway greenhouse effect and the maximum greenhouse effect.
We normally do not include actual image of the star from Kepler, but—just this once—here is what the spacecraft captures:
And below is one of the long cadence images from Kepler-47, from Quarter-9 (21-Mar-2011 00:21:34 Z),
when Kepler-47 was imaged onto row 33, column 766 of Module 18, output #3 on the focal plane.
We only downlinked 15 pixels per long cadence exposure in Q9, since the star is faint.
It is not very impressive as far as telescope images go, but it was something like
50,000 of these images taken over 1050 days that revealed the two circumbinary planets!
Credit: NASA Kepler Mission/Ames Research Center/Doug Caldwell