Binning is sinning: morphological light-curve distortions due to finite integration time

We explore how finite integration times or equivalently temporal binning induces morphological distortions to the transit light-curve. These distortions, if uncorrected for, lead to the retrieval of erroneous system parameters and may even lead to some planetary candidates being rejected as ostensibly unphysical. We provide analytic expressions for estimating the disturbance to the various light-curve parameters as a function of the integration time. These effects are particularly crucial in light of the long-cadence photometry often used for discovering new exoplanets by, for example, Convection Rotation and Planetary Transits (COROT) and the Kepler Mission (8.5 and 30 min). One of the dominant effects of long integration times is a systematic underestimation of the light-curve-derived stellar density, which has significant ramifications for transit surveys. We present a discussion of numerical integration techniques to compensate for the effects and produce expressions to quickly estimate the errors of such techniques, as a function of integration time and numerical resolution. This allows for an economic choice of resolution before attempting fits of long-cadence light-curves. We provide a comparison of the short- and long-cadence light-curves of TrES-2b and show that the retrieved transit parameters are consistent using the techniques discussed here.Comment: Long delayed upload of the MNRAS accepted version, 10 pages, 3 figure

LUNA: An algorithm for generating dynamic planet-moon transits

It has been previously shown that moons of extrasolar planets may be detectable with the Kepler Mission, for moon masses above ~0.2 Earth masses Kipping et al. 2009c. Transit timing effects have been formerly identified as a potent tool to this end, exploiting the dynamics of the system. In this work, we explore the simulation of transit light curves of a planet plus a single moon including not only the transit timing effects but also the light curve signal of the moon itself. We introduce our new algorithm, LUNA, which produces transit light curves for both bodies, analytically accounting for shadow overlaps, stellar limb darkening and planet-moon dynamical motion. By building the dynamics into the core of LUNA, the routine automatically accounts for transit timing/duration variations and ingress/egress asymmetries for not only the planet, but also the moon. We then generate some artificial data for two feasibly detectable hypothetical systems of interest: a i) prograde and ii) retrograde Earth-like moon around a habitable-zone Neptune for a M-dwarf system. We fit the hypothetical systems using LUNA and demonstrate the feasibility of detecting these cases with Kepler photometry.Comment: Accepted in MNRAS, 2011 May 16. Minor typos corrected (thanks to S. Awiphan

An Objective Bayesian Analysis of Life's Early Start and Our Late Arrival

Life emerged on the Earth within the first quintile of its habitable window, but a technological civilization did not blossom until its last. Efforts to infer the rate of abiogenesis, based on its early emergence, are frustrated by the selection effect that if the evolution of intelligence is a slow process, then life's early start may simply be a prerequisite to our existence, rather than useful evidence for optimism. In this work, we interpret the chronology of these two events in a Bayesian framework, extending upon previous work by considering that the evolutionary timescale is itself an unknown that needs to be jointly inferred, rather than fiducially set. We further adopt an objective Bayesian approach, such that our results would be agreed upon even by those using wildly different priors for the rates of abiogenesis and evolution - common points of contention for this problem. It is then shown that the earliest microfossil evidence for life indicates that the rate of abiogenesis is at least 2.8 times more likely to be a typically rapid process, rather than a slow one. This modest limiting Bayes factor rises to 8.7 if we accept the more disputed evidence of C13 depleted zircon deposits (Bell et al. 2015). For intelligence evolution, it is found that a rare-intelligence scenario is slightly favored at 3:2 betting odds. Thus, if we re-ran Earth's clock, one should statistically favor life to frequently re-emerge, but intelligence may not be as inevitable

Bayesian priors for the eccentricity of transiting planets

Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes' theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased. Adopting the flexible Beta distribution as the underlying prior for eccentricity, we derive the marginalized transit probability as well as the a-priori joint probability distribution of eccentricity and argument of periastron, given that a planet is known to transit. These results allow to demonstrate that most planet occurrence rate calculations using Kepler data have overestimated the prevalence of planets by ~10%. Indeed, the true occurrence of planets from transit surveys is fundamentally intractable without a prior assumption for the eccentricity distribution. Further more, we show that previously extracted eccentricity distributions using Kepler data are positively biased. In cases where one wishes to impose an informative eccentricity prior, we provide a recursive algorithm to apply inverse transform sampling of our joint prior probability distribution. Computer code of this algorithm, ECCSAMPLES, is provided to enable the community to sample directly from the prior.Comment: 9 pages, 5 figures. Accepted to MNRAS. Code available at http://www.cfa.harvard.edu/~dkipping/ECCSAMPLES.htm