The treatment of systematic noise is a significant aspect of transit exoplanet data processing due to the signal strength of systematic noise relative to a transit signal. Typically the standard approach to transit detection is to estimate and remove systematic noise independently of and prior to a transit detection test. If a transit signal is present in a light curve, the process of systematic noise removal may distort the transit signal by overfitting and thereby reduce detection efficiency. We present a Bayesian framework for joint detection of transit signals and systematic noise characterization and describe the implementation of these detectors as optimal Neyman-Pearson likelihood ratio tests. The joint detectors reduce to closed form as matched filters under the assumption of a Gaussian Bayesian prior for the systematic noise. The performance of the exploratory detectors was evaluated in injection tests and show $\sim 2\%$ improvement in overall detection efficiency relative to the standard approach. We find that joint detection efficiency is specifically improved for short-period, low transit-depth exoplanet transits, providing evidence in support of the hypothesis that joint detection may indeed help to mitigate overfitting. In addition, an initial feasibility test to detect known exoplanets in Kepler data using the joint detectors produced encouraging preliminary results.
We introduce BASE (Bayesian astrometric and spectroscopic exoplanet detection and characterisation tool), a novel program for the combined or separate Bayesian analysis of astrometric and radial-velocity measurements of potential exoplanet hosts and binary stars. The capabilities of BASE are demonstrated using all publicly available data of the binary Mizar A.
Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources. Combining repeated observations of periodic events, simultaneous observations with multiple telescopes, different observation techniques, and existing information from theory and prior research can help to disentangle the systematics from the planetary signals, and offers synergistic advantages over analysing observations separately. Bayesian inference provides a…
We present Kepler exoplanet occurrence rates inferred with approximate Bayesian computation (ABC). By using the same planet catalogue, stellar sample, and characterization of completeness and reliability as Bryson et al. (2020), we are able to provide the first direct comparison of results from ABC to those derived with the popular Poisson-likelihood method. For planets with orbital periods between 50 and 400 days and radii between 0.75 and 2.5 $R_{\oplus}$, we find an integrated occurrence rate $F_{0} = 0.596_{-0.099}^{+0.092}$ planets per GK dwarf star. After correcting for reliability again…
Constraining the lives and times of exoplanets through evolutionary Bayesian retrievals
Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）；Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；Helmholtz AI, Technical University of Munich（慕尼黑工业大学赫尔姆霍兹人工智能）；University of Technology Nuremberg（纽伦堡技术大学）
Rigorously quantifying the information in high contrast imaging data is important for informing follow-up strategies to confirm the substellar nature of a point source, constraining theoretical models of planet-disk interactions, and deriving planet occurrence rates. However, within the exoplanet direct imaging community, non-detections have almost exclusively been defined using a frequentist detection threshold (i.e. contrast curve) and associated completeness. This can lead to conceptual inconsistencies when included in a Bayesian framework. A Bayesian upper limit is such that the true value…
We present a Bayesian surrogate model for the analysis of periodic or quasi-periodic time series data. We describe a computationally efficient implementation that enables Bayesian model comparison. We apply this model to simulated and real exoplanet observations. We discuss the results and demonstrate some of the challenges for applying our surrogate model to realistic exoplanet data sets. In particular, we find that analyses of real world data should pay careful attention to the effects of uneven spacing of observations and the choice of prior for the "jitter" parameter.
We present the open-source Bayesian Atmospheric Radiative Transfer (BART) retrieval package, which produces estimates and uncertainties for an atmosphere's thermal profile and chemical abundances from observations. Several BART components are also stand-alone packages, including the parallel Multi-Core Markov chain Monte Carlo (MC3), which implements several Bayesian samplers; a line-by-line radiative-transfer model, transit; a code that calculates Thermochemical Equilibrium Abundances, TEA; and a test suite for verifying radiative-transfer and retrieval codes, BARTTest. The codes are in Pytho…
With the growing number of spectroscopic observations and observational platforms capable of exoplanet atmospheric characterization, there is a growing need for analysis techniques that can distill information about a large population of exoplanets into a coherent picture of atmospheric trends expressed within the statistical sample. In this work, we develop a Hierarchical Bayesian Atmospheric Retrieval (HBAR) model to infer population-level trends in exoplanet atmospheric characteristics. We demonstrate HBAR on the case of inferring a trend in atmospheric CO2 with incident stellar flux, predi…
The recovery of an exoplanet's atmospheric parameters from its spectrum requires accurate knowledge of the spectral errors and covariances. Unfortunately, the complex image processing used in high-contrast integral-field spectrograph (IFS) observations generally produces spectral covariances that are poorly understood and often ignored. In this work, we show how to measure the spectral errors and covariances and include them self-consistently in parameter retrievals. By combining model exoplanet spectra with a realistic noise model generated from GPI early science data, we show that ignoring s…
Atmospheric retrieval of exoplanets from spectroscopic observations requires an extensive exploration of a highly degenerate and high-dimensional parameter space to accurately constrain atmospheric parameters. Retrieval methods commonly conduct Bayesian parameter estimation and statistical inference using sampling algorithms such as Markov Chain Monte Carlo (MCMC) or Nested Sampling. Recently several attempts have been made to use machine learning algorithms either to complement or replace fully Bayesian methods. While much progress has been made, these approaches are still at times unable to …
Future space telescopes will directly image extrasolar planets at visible wavelengths. Time-resolved reflected light from an exoplanet encodes information about atmospheric and surface inhomogeneities. Previous research has shown that the light curve of an exoplanet can be inverted to obtain a low-resolution map of the planet, as well as constraints on its spin orientation. Estimating the uncertainty on 2D albedo maps has so far remained elusive. Here we present exocartographer, a flexible open-source Bayesian framework for solving the exo-cartography inverse problem. The map is parameterized …
The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While the Kepler Space Telescope mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve the characterization of exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling and originally designed to analyze archived Kepler Space Telescope and CoR…
We propose a novel approach to utilize low-cadence photometric surveys for exoplanetary transit search. Even if transits are undetectable in the survey database alone, it can still be useful for finding preferred times for directed follow-up observations that will maximize the chances to detect transits. We demonstrate the approach through a few simulated cases. These simulations are based on the Hipparcos Epoch Photometry data base, and the transiting planets whose transits were already detected there. In principle, the approach we propose will be suitable for the directed follow-up of the ph…
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian Inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian Model Selection, a unique aspect of EXONEST is the capability to distinguish …
The relationship between mass and radius (M-R relation) is the key for inferring the planetary compositions and thus valuable for the studies of formation and migration models. However, the M-R relation alone is not enough for planetary characterization due to the dependence of it on other confounding variables. This paper provides a non-trivial extension of the M-R relation by including the incident flux as an additional variable. By using Bayesian hierarchical modeling (BHM) that leverages the flexibility of finite mixture models, a probabilistic mass-radius-flux relationship (M-R-F relation…
(abridged) We develop Bayesian methods and detection criteria for orbital fitting, and revise the detectability of exoplanets in light of the in-flight properties of Gaia. Limiting ourselves to one-planet systems as a first step of the development, we simulate Gaia data for exoplanet systems over a grid of S/N, orbital period, and eccentricity. The simulations are then fit using Markov chain Monte Carlo methods. We investigate the detection rate according to three information criteria and the delta chi^2. For the delta chi^2, the effective number of degrees of freedom depends on the mission le…
Improving exoplanet mass characterisation with Bayesian model selection using the Learned Harmonic Mean Estimator
Mullard Space Science Laboratory, Department of Space & Climate Physics, University College London（伦敦大学学院穆拉德空间科学实验室空间与气候物理系）；Department of Statistical Science, University College London（伦敦大学学院统计科学系）
We describe a Bayesian rejection sampling algorithm designed to efficiently compute posterior distributions of orbital elements for data covering short fractions of long-period exoplanet orbits. Our implementation of this method, Orbits for the Impatient (OFTI), converges up to several orders of magnitude faster than two implementations of MCMC in this regime. We illustrate the efficiency of our approach by showing that OFTI calculates accurate posteriors for all existing astrometry of the exoplanet 51 Eri b up to 100 times faster than a Metropolis-Hastings MCMC. We demonstrate the accuracy of…
Understanding Exoplanet Habitability: A Bayesian ML Framework for Predicting Atmospheric Absorption Spectra
1 Department of Information Science, University at Albany, Albany, NY 12222, USA 2 Department of Physics, University at Albany, Albany, NY 12222, USA 3 NASA Goddard Institute for Space Studies, New York, NY 10025, USA 4 Theoretical Astrophysics, Department of Physics \& Astronomy, Uppsala University, 75105 Uppsala, Sweden
This and companion papers by Harrington et al. 2021, submitted and Cubillos et al. 2021, submitted describe an open-source retrieval framework, Bayesian Atmospheric Radiative Transfer (BART), available to the community under the reproducible-research license via https://github.com/exosports/BART . BART is a radiative-transfer code (transit, https://github.com/exosports/transit , Rojo 2009, 2009ASPC..420..321R), initialized by the Thermochemical Equilibrium Abundances (TEA, https://github.com/dzesmin/TEA , Blecic et al. 2016, arXiv:1505.06392) code, and driven through the parameter phase space …
This paper is to introduce an online tool for the prediction of exoplanet transit light curves. Small telescopes can readily capture exoplanet transits under good weather conditions when the combination of a bright star and a large transiting exoplanet results in a significant depth of transit. However, in reality there are many considerations that need to be made in order to obtain useful measurements. This paper and accompanying website layout a procedure based on time series differential photometry that has been successfully employed using 0.4m aperture telescopes to predict the expected pr…
This white paper advocates for the creation of a community-wide program to maintain precise mid-transit times of exoplanets that would likely be targeted by future platforms. Given the sheer number of targets that will require careful monitoring between now and the launch of the next generation of exoplanet characterization missions, this network will initially be devised as a citizen science project -- focused on the numerous amateur astronomers, small universities and community colleges and high schools that have access to modest sized telescopes and off-the-shelf CCDs.
A promising method to detect earth-sized exoplanets is the timing analysis of a known transit. The technique allows a search for variations in transit duration or center induced by the perturbation of a third body, e.g. a second planet or an exomoon. To this aim, TASTE (The Asiago Survey for Timing transit variations of Exoplanets) project will collect high-precision, short-cadence light curves for a selected sample of transits by using imaging differential photometry at the Asiago 1.82m telescope. The first light curves show that our project can already provide a competitive timing accuracy, …
Ground-based observing time is precious in the era of exoplanet follow-up and characterization, especially in high-precision radial velocity instruments. Blind-search radial velocity surveys thus require a dedicated observational strategy in order to optimize the observing time, which is particularly crucial for the detection of small rocky worlds at large orbital periods. We develop an algorithm with the purpose of improving the efficiency of radial velocity observations in the context of exoplanet searches, and we apply it to the K-dwarfs Orbited By habitable Exoplanets (KOBE) experiment. We…
The Laser Interferometer Space Antenna (LISA) will detect and characterize $\sim10^4$ Galactic Binaries consisting predominantly of two White Dwarfs (WD). An interesting prospect within this population is a third object--another WD star, a Circumbinary Exoplanet (CBP), or a Brown Dwarf (BD)--in orbit about the inner WD pair. We present the first fully Bayesian detection and posterior analysis of sub-stellar objects with LISA, focusing on the characterization of CBPs. We used an optimistic astrophysically motivated catalogue of these CBP third-body sources, including their orbital eccentricity …
Finding life on exoplanets from telescopic observations is an ultimate goal of exoplanet science. Life produces gases and other substances, such as pigments, which can have distinct spectral or photometric signatures. Whether or not life is found with future data must be expressed with probabilities, requiring a framework of biosignature assessment. We present a framework in which we advocate using biogeochemical "Exo-Earth System" models to simulate potential biosignatures in spectra or photometry. Given actual observations, simulations are used to find the Bayesian likelihoods of those data …
The precise derivation of transit depths from transit light curves is a key component for measuring exoplanet transit spectra, and henceforth for the study of exoplanet atmospheres. However, it is still deeply affected by various kinds of systematic errors and noise. In this paper we propose a new detrending method by reconstructing the stellar flux baseline during transit time. We train a probabilistic Long Short-Term Memory (LSTM) network to predict the next data point of the light curve during the out-of-transit, and use this model to reconstruct a transit-free light curve - i.e. including …
The statistical validation of transiting exoplanets proved to be an efficient technique to secure the nature of small exoplanet signals which cannot be established by purely spectroscopic means. However, the spectroscopic diagnoses are providing us with useful constraints on the presence of blended stellar contaminants. In this paper, we present how a contaminating star affects the measurements of the various spectroscopic diagnoses as function of the parameters of the target and contaminating stars using the model implemented into the PASTIS planet-validation software. We find particular case…
The ability for citizen scientists to analyze image data and search for exoplanets using images from small telescopes has the potential to greatly accelerate the search for exoplanets. Recent work on the Exoplanet Transit Interpretation Code (EXOTIC) enables the generation of high-quality light curves of exoplanet transits given such image data. However, on large image datasets, the photometric analysis of the data and fitting light curves can be a time-consuming process. In this work, we first optimize portions of the EXOTIC codebase to enable faster image processing and curve fitting. Specif…
The James Webb Space Telescope (JWST) will perform exoplanet transit spectroscopy in the coming decade promising transformative science results. All four instruments on board can be used for this technique which reconstructs the atmospheric transmission or emission spectrum of an exoplanet from wavelength-dependent light curve measurements. Astrophysical and instrumental noise and systematics can affect the precision and accuracy of the final spectrum, and hence, the atmospheric properties derived from the spectrum. Correlated noise and time-dependent systematics that can bias the measured sig…
A promising method for detecting earth-sized exoplanets is the timing analysis of a known transit. The technique allows a search for variations in either the transit duration or the center induced by the perturbation of a third body, e.g. a second planet or an exomoon. By applying this method, the TASTE (The Asiago Search for Transit Timing variations of Exoplanets) project will collect high-precision, short-cadence light curves for a selected sample of transits by using imaging differential photometry at the Asiago 1.82m telescope. The first light curves show that our project can achieve a co…
We demonstrate the newly developed resource for exoplanet researchers - The Exoplanet Transit Database. This database is designed to be a web application and it is open for any exoplanet observer. It came on-line in September 2008. The ETD consists of three individual sections. One serves for predictions of the transits, the second one for processing and uploading new data from the observers. We use a simple analytical model of the transit to calculate the central time of transit, its duration and the depth of the transit. These values are then plotted into the observed - computed diagrams (O-…
I present RoadRunner, a fast exoplanet transit model that can use any radially symmetric function to model stellar limb darkening while still being faster to evaluate than the analytical transit model for quadratic limb darkening by Mandel & Agol (2002). CPU and GPU implementations of the model are available in the PyTransit transit modelling package, and come with platform-independent parallelisation, supersampling, and support for modelling complex heterogeneous time series. The code is written in numba-accelerated Python (and the GPU model in OpenCL) without C or Fortran dependencies, which…
We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work addresses analysis of stellar reflex motion data, where a planet is detected by observing the "wobble" of its host star as it responds to the gravitational tug of the orbiting planet. Newtonian mechanics specifies an analytical model for the resulting time series, but it is strongly nonlinear, yielding complex, multimodal likelihood functions;…
Context: The space telescope Gaia is dedicated mainly to performing high-precision astrometry, but also spectroscopy and epoch photometry which can be used to study various types of photometric variability. One such variability type is exoplanetary transits. The photometric data accumulated so far have finally matured enough to allow the detection of some exoplanets. Aims: In order to fully exploit the scientific potential of Gaia, we search its photometric data for the signatures of exoplanetary transits. Methods: The search relies on a version of the Box-Least-Square (BLS) method, applied to…
The XO project aims at detecting transiting exoplanets around bright stars from the ground using small telescopes. The original configuration of XO (McCullough et al. 2005) has been changed and extended as described here. The instrumental setup consists of three identical units located at different sites, each composed of two lenses equipped with CCD cameras mounted on the same mount. We observed two strips of the sky covering an area of 520 deg$^2$ for twice nine months. We build lightcurves for ~20,000 stars up to magnitude R~12.5 using a custom-made photometric data reduction pipeline. The …
We present a simple mathematical criterion for determining whether a given statistical model does not describe several independent sets of measurements, or data modes, adequately. We derive this criterion for two data sets and generalise it to several sets by using the Bayesian updating of the posterior probability density. To demonstrate the usage of the criterion, we apply it to observations of exoplanet host stars by re-analysing the radial velocities of HD 217107, Gliese 581, and \u{psion} Andromedae and show that the currently used models are not necessarily adequate in describing the pro…
King’s College London（伦敦国王学院）；University of Central Florida（中佛罗里达大学）；University of Pittsburgh（匹兹堡大学）；Luxembourg Institute of Science and Technology（卢森堡科学技术研究院）；University of Oxford（牛津大学）；University of Bern（伯尔尼大学）；Google Cloud（谷歌云）；NASA Astrobiology Institute（美国国家航空航天局天体生物学研究所）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）
Over the past decade, the study of extrasolar planets has evolved rapidly from plain detection and identification to comprehensive categorization and characterization of exoplanet systems and their atmospheres. Atmospheric retrieval, the inverse modeling technique used to determine an exoplanetary atmosphere's temperature structure and composition from an observed spectrum, is both time-consuming and compute-intensive, requiring complex algorithms that compare thousands to millions of atmospheric models to the observational data to find the most probable values and associated uncertainties for…
The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, HAT-P-7b. EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Mo…
We present here the first release of the open-source python package ExoTETHyS, which aims to provide a stand-alone set of tools for modeling spectro-photometric observations of the transiting exoplanets. In particular, we describe: (1) a new calculator of stellar limb-darkening coefficients that outperforms the existing software by one order of magnitude in terms of light-curve model accuracy, i.e., down to <10 parts per million (ppm); (2) an exact transit light-curve generator based on the entire stellar intensity profile rather than limb-darkening coefficients. New tools will be added in lat…
I describe ongoing work on development of Bayesian methods for exploring periodically varying phenomena in astronomy, addressing two classes of sources: pulsars, and extrasolar planets (exoplanets). For pulsars, the methods aim to detect and measure periodically varying signals in data consisting of photon arrival times, modeled as non-homogeneous Poisson point processes. For exoplanets, the methods address detection and estimation of planetary orbits using observations of the reflex motion "wobble" of a host star, including adaptive scheduling of observations to optimize inferences.
Radial velocity (RV) surveys have detected hundreds of exoplanets through their gravitational interactions with their host stars. Some will be transiting, but most lack sufficient follow-up observations to confidently detect (or rule out) transits. We use published stellar, orbital, and planetary parameters to estimate the transit probabilities for nearly all exoplanets that have been discovered via the RV method. From these probabilities, we predict that $25.5^{+0.7}_{-0.7}$ of the known RV exoplanets should transit their host stars. This prediction is more than double the amount of RV exopla…
Inferring the number of planets $N$ in an exoplanetary system from radial velocity (RV) data is a challenging task. Recently, it has become clear that RV data can contain periodic signals due to stellar activity, which can be difficult to distinguish from planetary signals. However, even doing the inference under a given set of simplifying assumptions (e.g. no stellar activity) can be difficult. It is common for the posterior distribution for the planet parameters, such as orbital periods, to be multimodal and to have other awkward features. In addition, when $N$ is unknown, the marginal likel…
Transit observations have found the majority of exoplanets to date. Spectroscopic observations of transits and eclipses are the most commonly used tool to characterize exoplanet atmospheres and will be used in the search for life. However, an exoplanet's orbit must be aligned with our line of sight to observe a transit. Here we ask, from which stellar vantage points would a distant observer be able to search for life on Earth in the same way? We use the TESS Input Catalog and data from Gaia DR2 to identify the closest stars that could see Earth as a transiting exoplanet: We identify 1,004 Main…
In this work, we present transit timing variations detected for the exoplanet TrES-5b. To obtain the necessary amount of photometric data for this exoplanet, we have organized an international campaign to search for exoplanets based on the Transit Timing Variation method (TTV) and as a result of this we collected 30 new light curves, 15 light curves from the Exoplanet Transit Database (ETD) and 8 light curves from the literature for the timing analysis of the exoplanet TrES-5b. We have detected timing variations with a semi-amplitude of A ~ 0.0016 days and a period of P ~ 99 days. We carried o…
A machine learning technique with two-dimension convolutional neural network is proposed for detecting exoplanet transits. To test this new method, five different types of deep learning models with or without folding are constructed and studied. The light curves of the Kepler Data Release 25 are employed as the input of these models. The accuracy, reliability, and completeness are determined and their performances are compared. These results indicate that a combination of two-dimension convolutional neural network with folding would be an excellent choice for the future transit analysis.
Several attempts have been made in the past to assess the expected number of exoplanetary transits that the Gaia space mission will detect. In this Letter we use the updated design of Gaia and its expected performance, and apply recent empirical statistical procedures to provide a new assessment. Depending on the extent of the follow-up effort that will be devoted, we expect Gaia to detect a few hundreds to a few thousands transiting exoplanets.
