BYU Physics and Astronomy

Abstract: 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.

Abstract: 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).

Abstract: The Sun's equator and the planets' orbital planes are nearly aligned, which is presumably a consequence of their formation from a single spinning gaseous disk. For exoplanetary systems this well-aligned configuration is not guaranteed: dynamical interactions may tilt planetary orbits, or stars may be misaligned with the protoplanetary disk through chaotic accretion(1), magnetic interactions(2) or torques from neighbouring stars. Indeed, isolated 'hot Jupiters' are often misaligned and even orbiting retrograde(3,4). Here we report an analysis of transits of planets over starspots(5-7) on the Sun-like star Kepler-30 (ref. 8), and show that the orbits of its three planets are aligned with the stellar equator. Furthermore, the orbits are aligned with one another to within a few degrees. This configuration is similar to that of our Solar System, and contrasts with the isolated hot Jupiters. The orderly alignment seen in the Kepler-30 system suggests that high obliquities are confined to systems that experienced disruptive dynamical interactions. Should this be corroborated by observations of other coplanar multi-planet systems, then star-disk misalignments would be ruled out as the explanation for the high obliquities of hot Jupiters, and dynamical interactions would be implicated as the origin of hot Jupiters.

Abstract: We present the results of a search for planetary companions orbiting near hot Jupiter planet candidates (Jupiter-size candidates with orbital periods near 3 d) identified in the Kepler data through its sixth quarter of science operations. Special emphasis is given to companions between the 2: 1 interior and exterior mean-motion resonances. A photometric transit search excludes companions with sizes ranging from roughly two-thirds to five times the size of the Earth, depending upon the noise properties of the target star. A search for dynamically induced deviations from a constant period (transit timing variations) also shows no significant signals. In contrast, comparison studies of warm Jupiters (with slightly larger orbits) and hot Neptune-size candidates do exhibit signatures of additional companions with these same tests. These differences between hot Jupiters and other planetary systems denote a distinctly different formation or dynamical history.

Abstract: Eighty planetary systems of two or more planets are known to orbit stars other than the Sun. For most, the data can be sufficiently explained by non-interacting Keplerian orbits, so the dynamical interactions of these systems have not been observed. Here we present four sets of light curves from the Kepler spacecraft, each which of shows multiple planets transiting the same star. Departure of the timing of these transits from strict periodicity indicates that the planets are perturbing each other: the observed timing variations match the forcing frequency of the other planet. This confirms that these objects are in the same system. Next we limit their masses to the planetary regime by requiring the system remain stable for astronomical timescales. Finally, we report dynamical fits to the transit times, yielding possible values for the planets' masses and eccentricities. As the timespan of timing data increases, dynamical fits may allow detailed constraints on the systems' architectures, even in cases for which high-precision Doppler follow-up is impractical.

Abstract: We present a new method for confirming transiting planets based on the combination of transit timing variations (TTVs) and dynamical stability. Correlated TTVs provide evidence that the pair of bodies is in the same physical system. Orbital stability provides upper limits for the masses of the transiting companions that are in the planetary regime. This paper describes a non-parametric technique for quantifying the statistical significance of TTVs based on the correlation of two TTV data sets. We apply this method to an analysis of the TTVs of two stars with multiple transiting planet candidates identified by Kepler. We confirm four transiting planets in two multiple-planet systems based on their TTVs and the constraints imposed by dynamical stability. An additional three candidates in these same systems are not confirmed as planets, but are likely to be validated as real planets once further observations and analyses are possible. If all were confirmed, these systems would be near 4:6:9 and 2:4:6:9 period commensurabilities. Our results demonstrate that TTVs provide a powerful tool for confirming transiting planets, including low-mass planets and planets around faint stars for which Doppler follow-up is not practical with existing facilities. Continued Kepler observations will dramatically improve the constraints on the planet masses and orbits and provide sensitivity for detecting additional non-transiting planets. If Kepler observations were extended to eight years, then a similar analysis could likely confirm systems with multiple closely spaced, small transiting planets in or near the habitable zone of solar-type stars.