Detecting Secular Perturbations in Kepler Planetary Systems Using Simultaneous Impact Parameter Variation Analysis (SIPVA)

TL;DR

The paper tackles the difficulty of constraining masses and eccentricities in Kepler multi-planet systems given degeneracies and limited observational baselines. It proposes SIPVA, a Bayesian, assumption-light approach that models impact parameter variation linearly with time and fits all transits concurrently within an MCMC, bypassing full N-body dynamics. In synthetic tests SIPVA outperforms the Individual Fit in recovery rate and accuracy, and when applied to Kepler TDV signals it detects significant TbV trends in 10 of 16 planets (versus 4 for the Individual Fit). The work also employs probabilistic modeling to compare recovered distributions with a theoretical expectation, illustrating a framework that relies on Bayesian inference without strong dynamical priors.

Abstract

Recovering impact parameter variations in multi-planet systems is an effective approach for detecting non-transiting planets and refining planetary mass estimates. Traditionally, two methodologies have been employed: the Individual Fit, which fits each transit independently to analyze impact parameter changes, and the Dynamical Fit, which simulates planetary dynamics to match transit light curves. We introduce a new fitting method, Simultaneous Impact Parameter Variation Analysis (SIPVA), which demonstrates advantages over the Individual Fit and avoids the computational cost of N-body integrations required by the Dynamical Fit. SIPVA directly incorporates a linear time-dependent model for impact parameters into the Markov Chain Monte Carlo (MCMC) framework by fitting all transits simultaneously. We evaluate SIPVA and the Individual Fit on artificial systems with varying log-likelihood ratios and find that SIPVA consistently outperforms the Individual Fit in recovery rates and accuracy. When applied to selected Kepler planetary candidates exhibiting significant transit duration variations (TDVs), SIPVA identifies significant impact parameter trends in 10 out of 16 planets, whereas the Individual Fit does so in only 4. We also employ probabilistic modeling to simulate the theoretical distribution of planets with significant impact parameter variations across all observed Kepler systems and compare the distribution of recovered candidates by the Individual Fit and Dynamical Fit from previous work with our theoretical distribution. Our findings offer an alternative framework for analyzing planetary transits, relying solely on Bayesian inference without requiring prior assumptions about the planetary system's dynamical architecture.