A differentiable N-body code for transit timing and dynamical modelling -- II. Photodynamics

TL;DR

This paper introduces a fully differentiable photodynamical model for analyzing multiplanet transit light curves with timing variations, enabling more efficient Bayesian inference using gradient-based methods.

Contribution

It presents a novel, fully differentiable model implemented in Julia for transit timing variation analysis, improving inference efficiency over traditional methods.

Findings

Gradient-based inference outperforms traditional MCMC in efficiency.

The model accurately captures transit timing variations.

Open-source implementation available on GitHub.

Abstract

Exoplanet transits contain substantial information about the architecture of a system. By fitting transit light curves we can extract dynamical parameters and place constraints on the properties of the planets and their host star. Having a well-defined probabilistic model plays a crucial role in making robust measurements of these parameters, and the ability to differentiate the model provides access to more robust inference tools. Gradient-based inference methods can allow for more rapid and accurate sampling of high-dimensional parameter spaces. We present a fully differentiable photodynamical model for multiplanet transit light curves that display transit timing variations. We model time-integrated exposures, compute the dynamics of a system over the full length of observations, and provide analytic expressions for derivatives of the flux with respect to the dynamical and photometric model parameters. The model has been implemented in the Julia language and is available open-source on GitHub. We demonstrate with a simulated data set that Bayesian inference with the NUTS HMC algorithm, which uses the model gradient, can outperform the affine invariant (e.g. emcee) MCMC algorithm in CPU time per effective sample, and we find that the relative sampling efficiency improves with the number of model parameters.