PyORBIT: the ultimate tool for exoplanet characterization

Abstract

Stellar activity poses a critical challenge to the precise measurement of mass and radius of planets, at any phase of stellar evolution. The problem is exacerbated at young stellar ages, as the intense stellar activity may completely hinder the radial velocity signal of a planet and even inhibit its detection in photometric time series.
PyORBIT is a robust, versatile, and user-friendly package for the complete characterization of planetary systems. Originally developed back in 2015 as the first public Python code for the analysis of radial velocities (RVs) in a Bayesian framework, PyORBIT has been constantly improved to expand its functionalities since then, proving to be a fundamental tool for the characterization of young planets around temperamental stars.
Featured in tenths of referenced papers, PyORBIT can perform all the tasks you would expect from an advanced exoplanetary characterization tool. Photometry, RVs, and activity indexes can be modelled simultaneously for improved characterization of orbital parameters. PyORBIT implements both polynomial and exponential detrending as a function of any independent variable (airmass, target position on the sensor..) for photometric analysis, including a special module tailored for CHEOPS observations. Dilution factor, independent limb darkening coefficients for observations obtained in different bands, and polynomial normalization for single-transit observations are supported as well. Radial velocity can be modelled with a mixture of transiting and non-transiting planets, either in circular or eccentric orbits, with the best parametrization according to each specific case. Markov Chain and Nested Sampling Monte Carlo are both supported, allowing the use of priors on derived parameters with the former and the computation of Bayesian evidence with the latter.
The real strength of PyORBIT relies on its versatility for stellar activity modelling in both photometric and spectroscopic datasets. State-of-the-art activity modelling for precise mass and radius determination nowadays relies on Gaussian Process (GP) regression, which is implemented in PyORBIT in a variety of flavours. For example, it is possible to model stellar granulation, oscillations, and rotational modulations simultaneously in the photometric times series using scalable GP regression (e.g., through the celerite package) while using a non-approximated quasi-periodic kernel (e.g., through the george package) for the radial velocity and activity index time series, while sharing some hyperparameters related to the intrinsic properties of the star, such as the star’s rotational period and the decay timescale of the active regions, and let other hyperparameters being seasonally dependent. Multidimensional GP regression is available with no restriction on the number of datasets that can be employed.
either as a direct implementation or through the recently developed tinyGP library, allowing the use of GPU acceleration.
Other features of general interest include the modelling of the Rossiter-McLaughlin (RM) effect in all the current fashions (classic, reloaded, revolution), the ability to measure the time of inferior conjunction of individual transits for Transit-Timing Variation (TTV) analysis, and dynamical modelling of TTV/transits and radial velocities through N-body simulations, among other things. Other cutting-edge features, such as a GP framework for low-res transit spectroscopy and astrometry fitting, are currently under implementation.
In this talk, I will first provide a short overview of the most successful approaches for the characterization of planets around stars with strong stellar activity. I will then illustrate how easily you can exploit these models to fit your data with PyORBIT. I will also point out useful tips to navigate the documentation and the example repository for people interested in other features.
Finally, I will showcase some notable examples of young objects analyzed with PyORBIT, including the precise density measurement of TOI-1807b, one of the youngest ultra-short period planets currently known and the only super-Earth with a precisely measured mass so far.

Main features of PyORBIT

PyORBIT is a robust, versatile framework for the characterization of planetary systems.
With PyORBIT you can model light curves (LC), radial velocities (RV), activity indexes (AI), and transit time variations (TTV)

Advanced modelling options

Stellar activity modelling on radial velocity and light curves using Gaussian Processes

Rossiter-McLaughlin effect (Standard, Reloaded, Revolution)

Light curve fitting of multi-band/multi-instrument photometry, with independent dilution factors and out-of-transit normalizations

Lightcurve detrending using linear/exponential correlations with observational parameters

Simultaneous CHEOPS detrending and light curve fitting

Correlation between datasets

Sinusoids and Polynomial trends with independent or shared parameters across datasets

Sinusoids with polynomial modulation, with independent or shared parameters across datasets

Samplers

Priors

Markov Chain Monte Carlo through emcee with starting points selected with Differential Evolution Global Optimization through PyDE

Nested Sampling through dynesty or ultranest

Gaussian, Half (Positive/Negative) Gaussian, Jeffreys and Modified Jeffreys, truncated Raileigh, White Noise, Beta Distribution

All available for both MCMC and Nested Sampling

Additional Features

Parameter exploration in Linear or Logarithmic (base 2 / base 10) space (your choice)
Several parameterizations for eccentricity, argument of periastron, limb darkening…
Predisposition to run as a script for planet population studies

Short history of PyORBIT

PyORBIT debuted in 2016 with the discovery of the first multi-planet system in an open cluster (Malavolta et al. 2016), with substantial improvements thanks to the introduction of Gaussian Processes in 2018 for the characterization of an ultra-short period rocky super-Earth with a secondary eclipse and a Neptune-like companion around K2-141 (Malavolta et al. 2018)

PyORBIT was the first public Python code for the analysis of RVs in a Bayesian framework
Since then, PyORBIT has been constantly updated to integrate the latest findings in stellar activity mitigation and model selection

Some papers featuring PyORBIT

Orbital obliquity of the young planet TOI-5398 b and the evolutionary history of the system (Mantovan et al. 2024b)
Gliese 12 b, a temperate Earth-sized planet at 12 parsecs discovered with TESS and CHEOPS (Dholakia & Palethorpe et al. 2024)
The GAPS Programme at TNG. LIII. New insights on the peculiar XO-2 system (Ruggieri et al. 2024)
The GAPS programme at TNG. L. TOI-4515 b: An eccentric warm Jupiter orbiting a 1.2 Gyr-old G-star (Carleo et al. 2024)
GAPS XLIX. TOI-5398, the youngest compact multi-planet system composed of an inner sub-Neptune and an outer warm Saturn (Mantovan et al. 2024a)
Confronting compositional confusion through the characterization of the sub-Neptune orbiting HD 77946 (Palethorpe et al. 2024)
TASTE. V. A new ground-based investigation of orbital decay in the ultra-hot Jupiter WASP-12b (Leonardi et al. 2024)
A new dynamical modeling of the WASP-47 system with CHEOPS observations (Nascimbeni et al. 2023)
GAPS XXXVII. A precise density measurement of the young ultra-short period planet TOI-1807 b (Nardiello et al. 2022)
Investigating the architecture and internal structure of the TOI-561 system planets with CHEOPS, HARPS-N, and TESS (Lacedelli et al. 2022)
Independent validation of the temperate Super-Earth HD79211 b using HARPS-N (DiTommaso et al. 2022)
Multi-mask least-squares deconvolution: extracting RVs using tailored masks (Lienhard et al. 2022)
Kepler-102: Masses and Compositions for a Super-Earth and Sub-Neptune Orbiting an Active Star (Brinkman et al. 2022)
TIC 257060897b: An inflated, low-density, hot-Jupiter transiting a rapidly evolving subgiant star (Montalto et al. 2022)
A PSF-based Approach to TESS High quality data Of Stellar clusters (PATHOS) - IV. Candidate exoplanets around stars in open clusters: frequency and age-planetary radius distribution (Nardiello et al. 2021)
An unusually low density ultra-short period super-Earth and three mini-Neptunes around the old star TOI-561 (Lacedelli et al. 2021)
GAPS XXIX. No detection of reflected light from 51 Peg b using optical high-resolution spectroscopy (Scandariato et al. 2021)
GAPS XXVIII. A pair of hot-Neptunes orbiting the young star TOI-942 (Carleo et al. 2021)
K2-111: an old system with two planets in near-resonance (Mortier et al. 2020)
Masses and radii for the three super-Earths orbiting GJ 9827, and implications for the composition of small exoplanets (Rice et al. 2019)
A possibly inflated planet around the bright young star DS Tucanae A (Benatti et al. 2019)
K2-291b: A Rocky Super-Earth in a 2.2 day Orbit (Kosiarek et al. 2019)
GAPS XVII. Line profile indicators and kernel regression as diagnostics of radial-velocity variations due to stellar activity in solar-like stars (Lanza et al. 2018)
GAPS XII. Characterization of the planetary system around HD 108874 (Benatti et al. 2017)

... and many more that I may have missed

Main features of PyORBIT

Expand this image to know more about a configuration file

Short history of PyORBIT

Heading…

Stellar Activity with Gaussian Processes