Source-linked AI summary
Juliet: a versatile modelling tool for transiting and non-transiting exoplanetary systems
Néstor Espinoza, Diana Kossakowski, Rafael Brahm
TL;DR
Exoplanet analyses need to combine heterogeneous photometric and radial-velocity data while comparing competing physical and noise models. juliet provides flexible joint modelling for transiting and non-transiting multi-planet systems, using Gaussian Processes and nested sampling. The paper demonstrates these capabilities on K2-140b and K2-32b and reports formal Bayesian-evidence comparisons, while noting limitations in evidence reliability and data-dependent model conclusions.
Problem
Existing joint-fitting tools generally lack formal model comparison, despite its importance for assessing additional planets, eccentricity, and non-planetary signals.
Method
juliet jointly fits multi-instrument photometry and radial velocities for transiting or non-transiting systems, supports Gaussian Processes with shared hyperparameters, and uses nested sampling.
Results
juliet efficiently fits multiple instruments, dilutions, Gaussian Processes, and multi-planetary systems while providing Bayesian model evidences for comparing model additions.
Takeaways & Limitations
The library supports parameter estimation and formal model comparison across photometric and radial-velocity analyses, including assessments of eccentricity, additional planets, and Gaussian-process components.
Takeaways & Limitations
Model evidences depend strongly on the chosen priors, and nested-sampling evidence errors may be underestimated; more data may be needed to distinguish orbital models confidently.
Abstract
from arXiv · showhide
Here we present juliet, a versatile tool for the analysis of transits, radial-velocities, or both. juliet is built over many available tools for the modelling of transits, radial-velocities and stochastic processes (here modelled as Gaussian Processes; GPs) in order to deliver a tool/wrapper which can be used for the analysis of transit photometry and radial-velocity measurements from multiple instruments at the same time, using nested sampling algorithms which allows it to not only perform a thorough sampling of the parameter space, but also to perform model comparison via bayesian evidences. In addition, juliet allows to fit transiting and non-transiting multi-planetary systems, and to fit GPs which might share hyperparameters between the photometry and radial-velocities simultaneously (e.g., stellar rotation periods), which might be useful for disentangling stellar activity in radial-velocity measurements. Nested Sampling, Importance Nested Sampling and Dynamic Nested Sampling is performed with publicly available codes which in turn give juliet multi-threading options, allowing it to scale the computing time of complicated multi-dimensional problems. We make juliet publicly available via GitHub.
1 INTRODUCTION
Existing exoplanet surveys and analysis tools support increasingly extensive photometric and radial-velocity datasets, but important gaps remain in joint modelling and formal model comparison. juliet addresses these gaps with flexible simultaneous fitting across instruments, data types, planetary systems, and stochastic processes.
- Motivation: Exoplanet surveys have expanded the known population from a few planets to thousands and revealed diverse worlds beyond the Solar System.The underlying datasets are extensive and require tools for detection, validation, and retrieval of physical and orbital parameters.
- Existing tools: Existing tools analyse photometry, radial velocities, or both, with some also jointly modelling stellar properties and observations.Several open-source tools can combine measurements from different instruments, but their capabilities differ substantially.
- Motivation: Tools that simultaneously fit multi-instrument photometry and radial velocities are increasingly important for characterizing planets discovered by surveys such as TESS.Bright-star discoveries are expected to receive extensive radial-velocity follow-up whose combined analysis can constrain transiting-object parameters.
- juliet: juliet provides simultaneous fitting for any number of transiting and non-transiting systems using photometry, radial velocities, or both, while supporting instrument-specific and shared Gaussian-process hyperparameters.Shared hyperparameters can encode information such as stellar rotation periods present in both photometry and radial velocities.
- juliet: juliet uses nested-sampling-based exploration and is presented as an open-source library whose organization includes data modelling, real-data tests, discussion, and conclusions.The tool is designed to explore parameter spaces and support the analyses described in the paper.
- Motivation: Most open-source joint-fitting tools lack formal model comparison for competing fits, limiting evidence assessment for additional planets, eccentricity, and stellar-activity signals.Frequentist fit statistics do not straightforwardly compare models because they rely on null-hypothesis frameworks and do not incorporate prior information or the broader model set.
2 DATA MODELLING WITHIN JULIET
juliet models photometric and radial-velocity data with instrument-specific or shared noise structures, planetary and instrumental components, and flexible transit and Keplerian formulations. It also supports stellar-density parameterization and nested-sampling-based exploration, while requiring care with planet-planet transits and evidence estimates.
- Probabilistic model: Each datum is modeled from a physical planetary or instrumental model, a linear component, and a zero-mean noise term that may use Gaussian Processes.The physical model includes transit or radial-velocity parameters, while linear regressors can represent trends such as instrument-specific polynomials.
- Noise models: juliet supports instrument-by-instrument likelihoods and global models in which a common noise process spans all instruments while jitters remain instrument-specific.The global formulation stacks data and parameters across instruments and uses a shared covariance structure with instrument-specific white-noise terms.
- Photometric modelling: Transit models can include multiple planets and use either direct radius-ratio and impact-parameter sampling or r1 and r2 sampling that enforces b < 1 + p.The implementation does not model planet-planet transits.
- Radial-velocity modelling: Radial-velocity models combine any number of Keplerian planetary signals with instrument-dependent systemic velocities and optional common linear or quadratic long-term trends.The trend terms can represent additional long-period companions or activity whose periods are unconstrained by the data.
- Stellar density modelling: A prior on stellar density is transformed internally into a/R_* for each transiting planet, constraining transit models while reducing the number of fitting parameters.This formulation is also useful for singly transiting exoplanets.
- Sampling and model comparison: Nested sampling efficiently explores multimodal parameter spaces, but evidence comparisons require carefully selected priors and repeated runs to assess consistency.The paper notes that evidence estimates can be sensitive to priors and that quoted errors may be underestimated in some radial-velocity-only cases.
3 MODELLING PLANETARY SYSTEMS WITH juliet
juliet is demonstrated on photometric, radial-velocity, joint, and multi-planetary analyses, using nested-sampling evidences, Gaussian Processes, and stellar-density information to compare models and constrain systems. The case studies show strong planetary-signal evidence, unresolved eccentricity, and effective joint fitting of K2-32.
- K2-140b analyses: juliet analyses K2-140b through photometric, radial-velocity, joint, and stellar-density-informed fits, while also addressing dilution and systematics.The demonstrations examine dilution factors, Gaussian-Process corrections, eccentricity, and the impact of stellar-density information.
- K2-140b analyses: Δln Z > 2 favored fixing both K2 and LCOGT dilution factors to 1 over the alternative dilution models.The remaining models were statistically indistinguishable from one another, while nearby-source evidence did not support substantial K2 dilution.
- K2-140b analyses: Δln Z = 10 favored a planetary radial-velocity model over the null model, with period and transit-center posteriors agreeing with the photometric ephemerides.The planetary model was described as 4 orders of magnitude more likely than the null model, and the posterior was multimodal because transit times separated by integer periods are also solutions.
- K2-140b analyses: Δln Z = 0.20 favored the eccentric over circular radial-velocity model, leaving both statistically indistinguishable and unable to establish eccentricity from radial velocities alone.The joint fit remained formally indistinguishable, while adding stellar density shifted the evidence to Δln Z = 1.7 in favor of a circular orbit; more data were needed to rule out significant eccentricity.
- K2-32 multi-planetary system: juliet efficiently fit the K2-32 multi-planetary system, with Gaussian Processes capturing the long-term photometric trend and the joint fit producing an excellent fit.The resulting posterior parameters agreed well with previous values but were more precise, likely because stellar-density information improved timing ephemerides and semi-amplitude estimates.
4 DISCUSSION
The discussion highlights juliet’s flexibility for joint exoplanet analyses, including shared GP hyperparameters, model detection, and nested-sampling evidence, while noting computational costs that grow with problem complexity.
- GP hyperparameter sharing within juliet: juliet shares GP hyperparameters across photometric datasets and between photometry and radial-velocity data, supporting consistent joint activity modelling.Kernel amplitudes and jitter terms can remain instrument-specific while parameters such as characteristic periods are shared.
- juliet as a planet detection tool: juliet can analyze transiting and non-transiting systems and search for additional planets, although kima is more efficient because it fits planet number as a free parameter.juliet instead requires separate fits for different models, while offering broader kernel, instrument, transit, and radial-velocity flexibility.
- Computing speed of juliet: Single photometry or radial-velocity analyses generally take minutes, while joint single-instrument analyses without GPs take tens of minutes.These timings were measured on a laptop and depend on fit complexity.
- Computing speed of juliet: GP-inclusive runs tested by the authors took tens of minutes, and problems with roughly 20 dimensions could require several hours or about a day with several GPs.The authors report that larger priors and greater model complexity slow convergence.
- Computing speed of juliet: A 29-parameter K2-32 fit with a time GP took 1 hour using dynesty with 10 cores in multi-threading mode.The analysis modeled K2 systematics and was run on an Intel Xeon machine.
5 CONCLUSIONS AND FUTURE WORK
The conclusions present juliet as an open-source tool for efficient, evidence-based joint fitting of exoplanet data, and outline extensions for additional photometric effects and GP kernels.
- 5 CONCLUSIONS AND FUTURE WORK: juliet fits photometry, radial velocities, or both while exploring parameter spaces and estimating Bayesian model evidences for formal model comparison.The demonstrated applications include multiple instruments, dilution, GPs, and multi-planet systems.
- 5 CONCLUSIONS AND FUTURE WORK: Analyses of K2-140b and K2-32b demonstrate juliet’s ability to fit multiple instruments, dilutions, GPs, and multi-planetary systems.These capabilities support questions about eccentricity, GP kernels, and additional signals.
- 5 CONCLUSIONS AND FUTURE WORK: Future work includes support for secondary eclipses and additional photometric effects through integrations with batman, starry, and spiderman.The planned extensions aim to broaden juliet into a characterization toolbox.
- 5 CONCLUSIONS AND FUTURE WORK: The authors plan to implement additional GP kernels as requested, building on the existing george and celerite packages.They report that adding new kernels is relatively easy within juliet’s current framework.
- 5 CONCLUSIONS AND FUTURE WORK: Full documentation for juliet was published alongside the paper.