ALBERT

Description: Stellar limb darkening affects a wide range of astronomical measurements and is frequently modelled with a parametric model using polynomials in the cosine of the angle between the line of sight and the emergent intensity. Two-parameter laws are particularly popular for cases where one wishes to fit freely for the limb darkening coefficients (i.e. an uninformative prior) due to the compact prior volume and the fact that more complex models rarely obtain unique solutions with the present data. In such cases, we show that the two limb darkening coefficients are constrained by three physical boundary conditions, describing a triangular region in the two-dimensional parameter space. We show that uniformly distributed samples may be drawn from this region with optimal efficiency by a technique developed by computer graphical programming: triangular sampling. Alternatively, one can make draws using a uniform, bivariate Dirichlet distribution. We provide simple expressions for these parametrizations for both techniques applied to the case of quadratic, square-root and logarithmic limb darkening laws. For example, in the case of the popular quadratic law, we advocate fitting for q 1  = ( u 1  +  u 2 ) 2 and q 2  = 0.5 u 1 ( u 1  +  u 2 ) –1 with uniform priors in the interval [0, 1] to implement triangular sampling easily. Employing these parametrizations allows one to derive model parameters which fully account for our ignorance about the intensity profile, yet never explore unphysical solutions, yielding robust and realistic uncertainty estimates. Furthermore, in the case of triangular sampling with the quadratic law, our parametrization leads to significantly reduced mutual correlations and provides an alternative geometric explanation as to why naively fitting the quadratic limb darkening coefficients precipitates strong correlations in the first place.

Description: 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 us to demonstrate that most planet occurrence rate calculations using Kepler data have overestimated the prevalence of planets by ~10 per cent. 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 ( availablehere ).

Description: Eclipsing systems, such as transiting exoplanets, allow one to measure the mean stellar density of the host star under various idealized assumptions. Asterodensity profiling (AP) compares this density to an independently determined value in order to check the validity of the assumptions and ultimately derive useful parameters. Several physical effects can cause said assumptions to become invalid, with the most well-known example being the so-called photoeccentric effect. In this work, we provide analytic expressions for five other effects which induce AP deviations: the photoblend, -spot, -timing, -duration and -mass effects. We find that these effects can easily reproduce large AP deviations and so we caution that extracting the eccentricity distribution is only viable with careful consideration of the prior distributions for these other effects. We also re-investigate the photoeccentric effect and derive a single-domain minimum eccentricity expression and the parameter range for which analytic formulae are valid. The latter result shows that the assumptions underlying the analytic model for the photoeccentric effect break down for close-in, highly eccentric planets, meaning that extreme care must be taken in this regime. Finally, we demonstrate that contaminated light fraction can be solved for, indicating that AP could be a potent tool for planet validation.

Description: 〈p〉Exomoons are the natural satellites of planets orbiting stars outside our solar system, of which there are currently no confirmed examples. We present new observations of a candidate exomoon associated with Kepler-1625b using the Hubble Space Telescope to validate or refute the moon’s presence. We find evidence in favor of the moon hypothesis, based on timing deviations and a flux decrement from the star consistent with a large transiting exomoon. Self-consistent photodynamical modeling suggests that the planet is likely several Jupiter masses, while the exomoon has a mass and radius similar to Neptune. Since our inference is dominated by a single but highly precise Hubble epoch, we advocate for future monitoring of the system to check model predictions and confirm repetition of the moon-like signal.〈/p〉

Description: The transit method is presently the most successful planet discovery and characterization tool at our disposal. Other advanced civilizations would surely be aware of this technique and appreciate that their home planet's existence and habitability is essentially broadcast to all stars lying along their ecliptic plane. We suggest that advanced civilizations could cloak their presence, or deliberately broadcast it, through controlled laser emission. Such emission could distort the apparent shape of their transit light curves with relatively little energy, due to the collimated beam and relatively infrequent nature of transits. We estimate that humanity could cloak the Earth from Kepler -like broad-band surveys using an optical monochromatic laser array emitting a peak power of ~30 MW for ~10 hours per year. A chromatic cloak, effective at all wavelengths, is more challenging requiring a large array of tunable lasers with a total power of ~250 MW. Alternatively, a civilization could cloak only the atmospheric signatures associated with biological activity on their world, such as oxygen, which is achievable with a peak laser power of just ~160 kW per transit. Finally, we suggest that the time of transit for optical Search for Extraterrestrial Intelligence (SETI) is analogous to the water-hole in radio SETI, providing a clear window in which observers may expect to communicate. Accordingly, we propose that a civilization may deliberately broadcast their technological capabilities by distorting their transit to an artificial shape, which serves as both a SETI beacon and a medium for data transmission. Such signatures could be readily searched in the archival data of transit surveys.

Description: Observational biases distort our view of nature, such that the patterns we see within a surveyed population of interest are often unrepresentative of the truth we seek. Transiting planets currently represent the most informative data set on the ensemble properties of exoplanets within 1 au of their star. However, the transit method is inherently biased due to both geometric and detection-driven effects. In this work, we derive the overall observational biases affecting the most basic transit parameters from first principles. By assuming a trapezoidal transit and using conditional probability, we infer the expected distribution of these terms both as a joint distribution and in a marginalized form. These general analytic results provide a baseline against which to compare trends predicted by mission-tailored injection/recovery simulations and offer a simple way to correct for observational bias. Our results explain why the observed population of transiting planets displays a non-uniform impact parameter distribution, with a bias towards near-equatorial geometries. We also find that the geometric bias towards observed planets transiting near periastron is attenuated by the longer durations which occur near apoastron. Finally, we predict that the observational bias with respect to ratio-of-radii is super-quadratic, scaling as ( R P / R * ) 5/2 , driven by an enhanced geometric transit probability and modestly longer durations.

Description: The upcoming Transiting Exoplanet Survey Satellite ( TESS ) mission is expected to find thousands of transiting planets around bright stars, yet for three-quarters of the fields observed the temporal coverage will limit discoveries to planets with orbital periods below 13.7 d. From the Kepler catalogue, the mean probability of these short-period transiting planets having additional longer period transiters (which would be missed by TESS ) is 18 per cent, a value 10 times higher than the average star. In this work, we show how this probability is not uniform but functionally dependent upon the properties of the observed short-period transiters, ranging from less than 1 per cent up to over 50 per cent. Using artificial neural networks (ANNs) trained on the Kepler catalogue and making careful feature selection to account for the differing sensitivity of TESS , we are able to predict the most likely short-period transiters to be accompanied by additional transiters. Through cross-validation, we predict that a targeted, optimized TESS transit and/or radial velocity follow-up programme using our trained ANN would have a discovery yield improved by a factor of 2. Our work enables a near-optimal follow-up strategy for surveys following TESS targets for additional planets, improving the science yield derived from TESS and particularly beneficial in the search for habitable-zone transiting worlds.

Description: The Hubble Space Telescope and the Kepler space mission observed a large number of planetary transits showing anomalies due to starspot eclipses, with more such observations expected in the near future by the K2 mission and the Transiting Exoplanet Survey Satellite . To facilitate analysis of this phenomenon, we present spotrod , a model for planetary transits of stars with an arbitrary limb darkening law and a number of homogeneous, circular spots on their surface. A free, open source implementation written in c , ready to use in python , is available for download. We analyse Kepler observations of the planetary host star HAT-P-11, and study the size and contrast of more than 200 starspots. We find that the flux ratio of spots ranges at least from 0.6 to 0.9, corresponding to an effective temperature approximately 100–450 K lower than the stellar surface, although it is possible that some spots are darker than 0.5. The largest detected spots have a radius less than approximately 0.2 stellar radii.

Description: Amongst the many hundreds of transiting planet candidates discovered by the Kepler mission, one finds a large number of candidates with sizes between that of the Earth and Neptune. The composition of these worlds is not immediately obvious with no Solar system analogue to draw upon and there exists some ambiguity as to whether a given candidate is a rocky super-Earth or a gas-enveloped mini-Neptune. The potential scientific value and observability of the atmospheres of these two classes of worlds varies significantly, and given the sheer number of candidates in this size range, there is evidently a need for a quick, simple metric to rank whether the planets have an extended atmosphere or not. In this work, we propose a way to calculate the ‘minimum atmospheric height’ ( R MAH ) using only a planet's radius and mass as inputs. We assume and exploit the boundary condition that the bulk composition of a solid/liquid super-Earth cannot be composed of a material lighter than that of water. Mass–radius loci above a pure-water composition planet correspond to R MAH 〉 0. The statistical confidence of a planet maintaining an extended atmosphere can be therefore easily calculated to provide a simple ranking of target planets for follow-up observations. We also discuss how this metric can be useful in the interpretation of the spectra of observed planetary atmospheres.

Description: Exomoons are the natural satellites of planets orbiting stars outside our solar system, of which there are currently no confirmed examples. We present new observations of a candidate exomoon associated with Kepler-1625b using the Hubble Space Telescope to validate or refute the moon’s presence. We find evidence in favor of the moon hypothesis, based on timing deviations and a flux decrement from the star consistent with a large transiting exomoon. Self-consistent photodynamical modeling suggests that the planet is likely several Jupiter masses, while the exomoon has a mass and radius similar to Neptune. Since our inference is dominated by a single but highly precise Hubble epoch, we advocate for future monitoring of the system to check model predictions and confirm repetition of the moon-like signal.