BYU Physics and Astronomy

We measure the mass and radius of the star and planet in the TrES-2 system using 2.7 years of observations by the Kepler spacecraft. The light curve shows evidence for ellipsoidal variations and Doppler beaming on a period consistent with the orbital period of the planet with amplitudes of 2.79(-0.62)(+0.44) and 3.44(-0.37)(+0.32) parts per million (ppm), respectively, and a difference between the dayside and the nightside planetary flux of 3.41(-0.82)(+0.55) ppm. We present an asteroseismic analysis of solar-like oscillations on TrES-2A which we use to calculate the stellar mass of 0.94 +/- 0.05 M-circle dot and radius of 0.95 +/- 0.02 R-circle dot. Using these stellar parameters, a transit model fit and the phase-curve variations, we determine the planetary radius of 1.162(-0.024)(+0.020) R-Jup and derive a mass for TrES-2b from the photometry of 1.44 +/- 0.21 M-Jup. The ratio of the ellipsoidal variation to the Doppler beaming amplitudes agrees to better than 2 sigma with theoretical predications, while our measured planet mass and radius agree within 2s of previously published values based on spectroscopic radial velocity measurements. We measure a geometric albedo of 0.0136(-0.0033)(+0.0022) and an occultation (secondary eclipse) depth of 6.5(-1.8)(+1.7) ppm which we combined with the day/night planetary flux ratio to model the atmosphere of TrES-2b. We find that an atmosphere model that contains a temperature inversion is strongly preferred. We hypothesize that the Kepler bandpass probes a significantly greater atmospheric depth on the night side relative to the day side.

We discuss the discovery and characterization of the circumbinary planet Kepler-38b. The stellar binary is single-lined, with a period of 18.8 days, and consists of a moderately evolved main-sequence star (M-A = 0.949+/-0.059 M-circle dot and R-A = 1.757+/-0.034 R-circle dot) paired with a low-mass star (M-B = 0.249+/-0.010 M-circle dot and R-B = 0.2724+/-0.0053 R-circle dot) in a mildly eccentric (e = 0.103) orbit. A total of eight transits due to a circumbinary planet crossing the primary star were identified in the Kepler light curve (using Kepler Quarters 1-11), from which a planetary period of 105.595+/-0.053 days can be established. A photometric dynamical model fit to the radial velocity curve and Kepler light curve yields a planetary radius of 4.35+/-0.11 R-circle plus, or equivalently 1.12+/-0.03 R-Nep. Since the planet is not sufficiently massive to observably alter the orbit of the binary from Keplerian motion, we can only place an upper limit on the mass of the planet of 122 M-circle dot(7.11 M-Nep or equivalently 0.384 M-Jup) at 95% confidence. This upper limit should decrease as more Kepler data become available.

We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, 18 transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet's orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical "habitable zone," where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems.

Transit timing variations provide a powerful tool for confirming and characterizing transiting planets, as well as detecting non-transiting planets. We report the results of an updated transit timing variation (TTV) analysis for 1481 planet candidates based on transit times measured during the first sixteen months of Kepler observations. We present 39 strong TTV candidates based on long-term trends (2.8% of suitable data sets). We present another 136 weaker TTV candidates (9.8% of suitable data sets) based on the excess scatter of TTV measurements about a linear ephemeris. We anticipate that several of these planet candidates could be confirmed and perhaps characterized with more detailed TTV analyses using publicly available Kepler observations. For many others, Kepler has observed a long-term TTV trend, but an extended Kepler mission will be required to characterize the system via TTVs. We find that the occurrence rate of planet candidates that show TTVs is significantly increased (similar to 68%) for planet candidates transiting stars with multiple transiting planet candidates when compared to planet candidates transiting stars with a single transiting planet candidate.

We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of the planets, which we studied through numerical integrations of initial conditions that are consistent with observations of the system, are chaotic with a Lyapunov time of only similar to 10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29: 34 resonance with the nearby first-order 6: 7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for similar to 4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large-scale orbital instabilities on the timescale of our integrations (similar to 200 million years). Restricting the orbits to this long-lived region allows a refinement of estimates of the masses and radii of the planets. We find that the long-lived region consists of the initial conditions that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.

We report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around solar-type (GK) stars. These results are based on the 1235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 R-circle plus. For each of the 156,000 target stars, we assess the detectability of planets as a function of planet radius, R-p, and orbital period, P, using a measure of the detection efficiency for each star. We also correct for the geometric probability of transit, R-star/a. We consider first Kepler target stars within the "solar subset" having T-eff = 4100-6100 K, log g = 4.0-4.9, and Kepler magnitude Kp < 15 mag, i.e., bright, main-sequence GK stars. We include only those stars having photometric noise low enough to permit detection of planets down to 2 R-circle plus. We count planets in small domains of R-p and P and divide by the included target stars to calculate planet occurrence in each domain. The resulting occurrence of planets varies by more than three orders of magnitude in the radius-orbital period plane and increases substantially down to the smallest radius (2 R-circle plus) and out to the longest orbital period (50 days, similar to 0.25 AU) in our study. For P < 50 days, the distribution of planet radii is given by a power law, df/d log R = k(R)R(alpha) with k(R) = 2.9(-0.4)(+0.5), alpha = -1.92 +/- 0.11, and R equivalent to R-p/R-circle plus. This rapid increase in planet occurrence with decreasing planet size agrees with the prediction of core-accretion formation but disagrees with population synthesis models that predict a desert at super-Earth and Neptune sizes for close-in orbits. Planets with orbital periods shorter than 2 days are extremely rare; for R-p > 2 R-circle plus we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50 days, we measure occurrence of 0.130 +/- 0.008, 0.023 +/- 0.003, and 0.013 +/- 0.002 planets per star for planets with radii 2-4, 4-8, and 8-32 R-circle plus, in agreement with Doppler surveys. We fit occurrence as a function of P to a power-law model with an exponential cutoff below a critical period P-0. For smaller planets, P-0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over a broader stellar T-eff range of 3600-7100 K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R-circle plus planets in the Kepler field increases with decreasing T-eff, with these small planets being seven times more abundant around cool stars (3600-4100 K) than the hottest stars in our sample (6600-7100 K).