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Register a new userStability and Occurrence Rate Constraints on the Planetary Sculpting Hypothesis for Transitional Disks
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Ruobing Dong
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Transitional disks, protoplanetary disks with deep and wide central gaps, may be the result of planetary sculpting. By comparing numerical planet-opening-gap models with observed gaps, we find systems of 3-6 giant planets are needed in order to open gaps with the observed depths and widths. We explore the dynamical stability of such multi-planet systems using N-body simulations that incorporate prescriptions for gas effects. We find they can be stable over a typical disk lifetime, with the help of eccentricity damping from the residual gap gas that facilitates planets locking into mean motion resonances. However, in order to account for the occurrence rate of transitional disks, the planet sculpting scenario demands gap-opening-friendly disk conditions, in particular, a disk viscosity $alphalesssim0.001$. In addition, the demography of giant planets at $sim 3-30$ AU separations, poorly constrained by current data, has to largely follow occurrence rates extrapolated outward from radial velocity surveys, not the lower occurrence rates extrapolated inward from direct imaging surveys. Even with the most optimistic occurrence rates, transitional disks cannot be a common phase that most gas disks experience at the end of their life, as popularly assumed, simply because there are not enough planets to open these gaps. Finally, as consequences of demanding almost all giant planets at large separations participate in transitional disk sculpting, the majority of such planets must form early and end up in a chain of mean motion resonances at the end of disk lifetime.
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We assume a scenario in which transition discs (i.e. discs around young stars that have signatures of cool dust but lack significant near infra-red emission from warm dust) are associated with the presence of planets (or brown dwarfs). These are assumed to filter the dust content of any gas flow within the planetary orbit and produce an inner `opacity hole. In order to match the properties of transition discs with the largest (~50 A.U. scale) holes, we place such `planets at large radii in massive discs and then follow the evolution of the tidally coupled disc-planet system, comparing the systems evolution in the plane of mm flux against hole radius with the properties of observed transition discs. We find that, on account of the high disc masses in these systems, all but the most massive `planets (100 Jupiter masses) are conveyed to small radii by Type II migration without significant fading at millimetre wavelengths. Such behaviour would contradict the observed lack of mm bright transition discs with small (<10 A.U.) holes. On the other hand, imaging surveys clearly rule out the presence of such massive companions in transition discs. We conclude that this is a serious problem for models that seek to explain transition discs in terms of planetary companions unless some mechanism can be found to halt inward migration and/or suppress mm flux production. We suggest that the dynamical effects of substantial accretion on to the planet/through the gap may offer the best prospect for halting such migration but that further long term simulations are required to clarify this issue.
We use the optical and near-infrared photometry from the Kepler Input Catalog to provide improved estimates of the stellar characteristics of the smallest stars in the Kepler target list. We find 3897 dwarfs with temperatures below 4000K, including 64 planet candidate host stars orbited by 95 transiting planet candidates. We refit the transit events in the Kepler light curves for these planet candidates and combine the revised planet/star radius ratios with our improved stellar radii to revise the radii of the planet candidates orbiting the cool target stars. We then compare the number of observed planet candidates to the number of stars around which such planets could have been detected in order to estimate the planet occurrence rate around cool stars. We find that the occurrence rate of 0.5-4 Earth radius planets with orbital periods shorter than 50 days is 0.90 (+0.04/-0.03) planets per star. The occurrence rate of Earth-size (0.5-1.4 Earth radius) planets is constant across the temperature range of our sample at 0.51 (+0.06/-0.05) Earth-size planets per star, but the occurrence of 1.4-4 Earth radius planets decreases significantly at cooler temperatures. Our sample includes 2 Earth-size planet candidates in the habitable zone, allowing us to estimate that the mean number of Earth-size planets in the habitable zone is 0.15 (+0.13/-0.06) planets per cool star. Our 95% confidence lower limit on the occurrence rate of Earth-size planets in the habitable zones of cool stars is 0.04 planets per star. With 95% confidence, the nearest transiting Earth-size planet in the habitable zone of a cool star is within 21 pc. Moreover, the nearest non-transiting planet in the habitable zone is within 5 pc with 95% confidence.
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Kepler is a space telescope that searches Sun-like stars for planets. Its major goal is to determine {eta}_Earth, the fraction of Sunlike stars that have planets like Earth. When a planet transits or moves in front of a star, Kepler can measure the concomitant dimming of the starlight. From analysis of the first four months of those measurements for over 150,000 stars, Keplers science team has determined sizes, surface temperatures, orbit sizes and periods for over a thousand new planet candidates. In this paper, we characterize the period probability distribution function of the super-Earth and Neptune planet candidates with periods up to 132 days, and find three distinct period regimes. For candidates with periods below 3 days the density increases sharply with increasing period; for periods between 3 and 30 days the density rises more gradually with increasing period, and for periods longer than 30 days, the density drops gradually with increasing period. We estimate that 1% to 3% of stars like the Sun are expected to have Earth analog planets, based on the Kepler data release of Feb 2011. This estimate of is based on extrapolation from a fiducial subsample of the Kepler planet candidates that we chose to be nominally complete (i.e., no missed detections) to the realm of the Earth-like planets, by means of simple power law models. The accuracy of the extrapolation will improve as more data from the Kepler mission is folded in. Accurate knowledge of {eta}_Earth is essential for the planning of future missions that will image and take spectra of Earthlike planets. Our result that Earths are relatively scarce means that a substantial effort will be needed to identify suitable target stars prior to these future missions.
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