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We present the discovery of the Kepler-20 planetary system, which we initially identified through the detection of five distinct periodic transit signals in the Kepler light curve of the host star 2MASS J19104752+4220194. From high-resolution spectroscopy of the star, we find a stellar effective temperature T eff = 5455 ± 100 K, a metallicity of [Fe/H] = 0.01 ± 0.04, and a surface gravity of log g = 4.4 ± 0.1. We combine these estimates with an estimate of the stellar density derived from the transit light curves to deduce a stellar mass of M sstarf = 0.912 ± 0.034 M ☉ and a stellar radius of R sstarf = 0.944+0.060 –0.095 R ☉. For three of the transit signals, we demonstrate that our results strongly disfavor the possibility that these result from astrophysical false positives. We accomplish this by first identifying the subset of stellar blends that reproduce the precise shape of the light curve and then using the constraints on the presence of additional stars from high angular resolution imaging, photometric colors, and the absence of a secondary component in our spectroscopic observations. We conclude that the planetary scenario is more likely than that of an astrophysical false positive by a factor of 2 × 105 (Kepler-20b), 1 × 105 (Kepler-20c), and 1.1 × 103 (Kepler-20d), sufficient to validate these objects as planetary companions. For Kepler-20c and Kepler-20d, the blend scenario is independently disfavored by the achromaticity of the transit: from Spitzer data gathered at 4.5 μm, we infer a ratio of the planetary to stellar radii of 0.075 ± 0.015 (Kepler-20c) and 0.065 ± 0.011 (Kepler-20d), consistent with each of the depths measured in the Kepler optical bandpass. We determine the orbital periods and physical radii of the three confirmed planets to be 3.70 days and 1.91+0.12 –0.21 R ⊕ for Kepler-20b, 10.85 days and 3.07+0.20 –0.31 R ⊕ for Kepler-20c, and 77.61 days and 2.75+0.17 –0.30 R ⊕ for Kepler-20d. From multi-epoch radial velocities, we determine the masses of Kepler-20b and Kepler-20c to be 8.7 ± 2.2 M ⊕ and 16.1 ± 3.5 M ⊕, respectively, and we place an upper limit on the mass of Kepler-20d of 20.1 M ⊕ (2σ)., Astronomy

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., Astronomy

We present a method to confirm the planetary nature of objects in systems with multiple transiting exoplanet candidates. This method involves a Fourier-Domain analysis of the deviations in the transit times from a constant period that result from dynamical interactions within the system. The combination of observed anti-correlations in the transit times and mass constraints from dynamical stability allow us to claim the discovery of four planetary systems Kepler-25, Kepler-26, Kepler-27, and Kepler-28, containing eight planets and one additional planet candidate., Astronomy

Multiple object tracking is a task commonly used to investigate the architecture of human visual attention. Human participants show a distinctive pattern of suc- cesses and failures in tracking experiments that is often attributed to limits on an object system, a tracking module, or other specialized cognitive structures. Here we use a computational analysis of the task of object tracking to ask which human failures arise from cognitive limitations and which are consequences of inevitable perceptual uncertainty in the tracking task. We find that many human perfor- mance phenomena, measured through novel behavioral experiments, are naturally produced by the operation of our ideal observer model (a Rao-Blackwelized par- ticle filter). The tradeoff between the speed and number of objects being tracked, however, can only arise from the allocation of a flexible cognitive resource, which can be formalized as either memory or attention., Psychology