We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, approximate Bayesian computing (ABC), and sequential ...importance sampling. For this study, we adopt a simple 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (Rp < 1.25 R⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2 R⊕ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives, and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.
About one-third of the ~1200 transiting planet candidates detected in the first four months of Kepler data are members of multiple candidate systems. There are 115 target stars with two candidate ...transiting planets, 45 with three, 8 with four, and 1 each with five and six. We characterize the dynamical properties of these candidate multi-planet systems. The distribution of observed period ratios shows that the vast majority of candidate pairs are neither in nor near low-order mean-motion resonances. Nonetheless, there are small but statistically significant excesses of candidate pairs both in resonance and spaced slightly too far apart to be in resonance, particularly near the 2:1 resonance. We find that virtually all candidate systems are stable, as tested by numerical integrations that assume a nominal mass-radius relationship. Several considerations strongly suggest that the vast majority of these multi-candidate systems are true planetary systems. Using the observed multiplicity frequencies, we find that a single population of planetary systems that matches the higher multiplicities underpredicts the number of singly transiting systems. We provide constraints on the true multiplicity and mutual inclination distribution of the multi-candidate systems, revealing a population of systems with multiple super-Earth-size and Neptune-size planets with low to moderate mutual inclinations.
We present a statistical analysis that demonstrates that the overwhelming majority of Kepler candidate multiple transiting systems (multis) indeed represent true, physically associated transiting ...planets. Binary stars provide the primary source of false positives among Kepler planet candidates, implying that false positives should be nearly randomly distributed among Kepler targets. In contrast, true transiting planets would appear clustered around a smaller number of Kepler targets if detectable planets tend to come in systems and/or if the orbital planes of planets encircling the same star are correlated. There are more than one hundred times as many Kepler planet candidates in multi-candidate systems as would be predicted from a random distribution of candidates, implying that the vast majority are true planets. Most of these multis are multiple-planet systems orbiting the Kepler target star, but there are likely cases where (1) the planetary system orbits a fainter star, and the planets are thus significantly larger than has been estimated, or (2) the planets orbit different stars within a binary/multiple star system. We use the low overall false-positive rate among Kepler multis, together with analysis of Kepler spacecraft and ground-based data, to validate the closely packed Kepler-33 planetary system, which orbits a star that has evolved somewhat off of the main sequence. Kepler-33 hosts five transiting planets, with periods ranging from 5.67 to 41 days.
We confirm 27 planets in 13 planetary systems by showing the existence of statistically significant anticorrelated transit timing variations, which demonstrates that the planet candidates are in the ...same system, and long-term dynamical stability, which places limits on the masses of the candidates - showing that they are planetary. All of these newly confirmed planetary systems have orbital periods that place them near first-order mean motion resonances (MMRs), including six systems near the 2:1 MMR, five near 3:2, and one each near 4:3, 5:4 and 6:5. In addition, several unconfirmed planet candidates exist in some systems (that cannot be confirmed with this method at this time). A few of these candidates would also be near first-order MMRs with either the confirmed planets or other candidates. One system of particular interest, Kepler-56 (KOI-1241), is a pair of planets orbiting a twelfth magnitude, giant star with radius over three times that of the Sun and effective temperature of 4900 K - among the largest stars known to host a transiting exoplanetary system.
Doppler planet searches have discovered that giant planets follow orbits with a wide range of orbital eccentricities, revolutionizing theories of planet formation. The discovery of hundreds of ...exoplanet candidates by NASA's Kepler mission enables astronomers to characterize the eccentricity distribution of small exoplanets. Measuring the eccentricity of individual planets is only practical in favorable cases that are amenable to complementary techniques (e.g., radial velocities, transit timing variations, occultation photometry). Yet even in the absence of individual eccentricities, it is possible to study the distribution of eccentricities based on the distribution of transit durations (relative to the maximum transit duration for a circular orbit). We analyze the transit duration distribution of Kepler planet candidates. We find that for host stars with T eff > 5100 K we cannot invert this to infer the eccentricity distribution at this time due to uncertainties and possible systematics in the host star densities. With this limitation in mind, we compare the observed transit duration distribution with models to rule out extreme distributions. If we assume a Rayleigh eccentricity distribution for Kepler planet candidates, then we find best fits with a mean eccentricity of 0.1-0.25 for host stars with T eff <= 5100 K. We compare the transit duration distribution for different subsets of Kepler planet candidates and discuss tentative trends with planetary radius and multiplicity. High-precision spectroscopic follow-up observations for a large sample of host stars will be required to confirm which trends are real and which are the results of systematic errors in stellar radii. Finally, we identify planet candidates that must be eccentric or have a significantly underestimated stellar radius.
Abstract
Using the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) instrument installed on the 10.4-m Gran Telescopio Canarias (GTC), we acquired multicolour transit ...photometry of four small () short-period (P ≲ 6 d) planet candidates recently identified by the Kepler space mission. These observations are part of a programme to constrain the false positive rate for small, short-period Kepler planet candidates. Since planetary transits should be largely achromatic when observed at different wavelengths (excluding the small colour changes due to stellar limb darkening), we use the observed transit colour to identify candidates as either false positives (e.g. a blend with a stellar eclipsing binary either in the background/foreground or bound to the target star) or validated planets. Our results include the identification of KOI 225.01 and KOI 1187.01 as false positives and the tentative validation of KOI 420.01 and KOI 526.01 as planets. The probability of identifying two false positives out of a sample of four targets is less than 1 per cent, assuming an overall false positive rate for Kepler planet candidates of 10 per cent (as estimated by Morton & Johnson). Therefore, these results suggest a higher false positive rate for the small, short-period Kepler planet candidates than has been theoretically predicted by other studies which consider the Kepler planet candidate sample as a whole. Furthermore, our results are consistent with a recent Doppler study of short-period giant Kepler planet candidates. We also investigate how the false positive rate for our sample varies with different planetary and stellar properties. Our results suggest that the false positive rate varies significantly with orbital period and is largest at the shortest orbital periods (P < 3 d), where there is a corresponding rise in the number of detached eclipsing binary stars (i.e. systems that can easily mimic planetary transits) that have been discovered by Kepler. However, we do not find significant correlations between the false positive rate and other planetary or stellar properties. Our sample size is not yet large enough to determine if orbital period plays the largest role in determining the false positive rate, but we discuss plans for future observations of additional Kepler candidates and compare our programme focusing on relatively faint Kepler targets from the GTC with follow-up of Kepler targets that has been done with warm-Spitzer.
ABSTRACT
We present and discuss five candidate exoplanetary systems identified with the
Kepler
spacecraft. These five systems show transits from multiple exoplanet candidates. Should these objects ...prove to be planetary in nature, then these five systems open new opportunities for the field of exoplanets and provide new insights into the formation and dynamical evolution of planetary systems. We discuss the methods used to identify multiple transiting objects from the
Kepler
photometry as well as the false-positive rejection methods that have been applied to these data. One system shows transits from three distinct objects while the remaining four systems show transits from two objects. Three systems have planet candidates that are near mean motion commensurabilities—two near 2:1 and one just outside 5:2. We discuss the implications that multi-transiting systems have on the distribution of orbital inclinations in planetary systems, and hence their dynamical histories, as well as their likely masses and chemical compositions. A Monte Carlo study indicates that, with additional data, most of these systems should exhibit detectable transit timing variations (TTVs) due to gravitational interactions, though none are apparent in these data. We also discuss new challenges that arise in TTV analyses due to the presence of more than two planets in a system.
We present new multiband transit photometry of three small (R
p ≲ 6 R⊕), short-period (P ≲ 6 d) Kepler planet candidates acquired with the Gran Telescopio Canarias. These observations supplement the ...results presented in Colón & Ford and Colón, Ford & Morehead, where we used multicolour transit photometry of five Kepler planet candidates to search for wavelength-dependent transit depths and either validate planet candidates or identify eclipsing binary false positives within our sample. In those previous studies, we provided evidence that three targets were false positives and two targets were planets. Here, we present observations that provide evidence supporting a planetary nature for Kepler Object of Interest (KOI) 439.01 and KOI 732.01, and we find that KOI 531.01, a 6 R⊕ planet candidate around an M dwarf, is likely a false positive. We also present a discussion of the purported ‘sub-Jovian desert’ in the orbital period–planet radius plane, which cannot be easily explained by observational bias. Both KOI 439.01 and KOI 732.01 are likely planets located within the so-called desert and should be investigated with further follow-up observations. As only ∼30 of the ∼3600 currently active Kepler planet candidates are located within the sub-Jovian desert, it will be interesting to see if these candidates also survive the vetting process and fill in the gap in the period–radius plane. Confirming planets in this regime will be important for understanding planetary migration and evolution processes, and we urge additional follow-up observations of these planet candidates to confirm their nature.
We report on the orbital architectures of Kepler systems having multiple-planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. ...(2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic mass-radius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ~96% of the candidate planetary systems are correctly interpreted as true systems. We find that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near first-order resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1degrees.0-2degrees.2, for the packed systems of small planets probed by these observations.
To use reflective writing to evaluate a new required palliative care experience for third year medical students.
The authors used a constant comparison method based on grounded theory to conduct a ...thematic analysis of reflective writings produced by third-year medical students completing a mandatory week-long clinical rotation in palliative care during academic year 2010 at the University of Louisville.
Two broad thematic categories were identified: what the students learned and what the students experienced. Student writings revealed learning about palliative care (pain management, family meetings, goals of care, patient-family centered care, timing of palliative care, and delivering bad news); being a doctor (knowledge, communication, presence, empathy, not giving false hope, and person-focused care); the patient (importance of family, the experience of dying, and the uniqueness of each patient); and themselves (need to be non-judgmental, ability to do palliative care, self-limitations, becoming a better physician, and dealing with death). Student reflections centered on encounters with patients and families, internal emotional responses, and self-transformation.
Systematic analysis of reflective writing provides educators with valuable data about students' learning experiences. These results may inform the design and modification of the curriculum.
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