A Search for Transit Duration Variations in M dwarf Multi-Planet Systems

TL;DR

This paper addresses whether transit duration variations (TDVs) in close-in, compact M-dwarf multiplanet systems reveal nodal precession and possible obliquity states predicted by Laplace–Lagrange secular theory and Cassini State 2. It combines high-precision JWST NIRSpec BOTS white-light transit durations for 23 planets in 12 M-dwarf systems with archival discovery-era measurements to search for linear TDV trends over a baseline of roughly 3–10 years. The analysis finds no TDV detections at the $3\sigma$ level; the strongest hint is TRAPPIST-1d with a slope corresponding to $2.2\sigma$, while the null is consistent with small TDVs expected for low-impact-parameter configurations. The results place constraints on the allowed TDV parameter space and underscore the need for longer monitoring, system-specific secular modeling, and broader baselines to robustly test nodal precession and potential obliquity dynamics in these compact systems.

Abstract

The nominal habitable zone for exoplanets orbiting M dwarfs lies close to the host star, making dynamical considerations especially important. One consequence of this proximity is the expectation of spin synchronization, with implications for atmospheric circulation. Several mechanisms can maintain non-zero obliquities over long timescales in compact multi-planet systems, including capture into Cassini State 2 (CS2) and other forms of secular spin-orbit coupling; such pathways are plausible in the orbital architectures of close-in M-dwarf planets. In this study, we search for transit duration variations (TDVs) consistent with the nodal precession rates predicted by Laplace-Lagrange secular theory in compact M-dwarf multi-planet systems. Our sample includes 23 exoplanets orbiting 12 stars. We compare recent, high-precision transit durations obtained from JWST white-light curves with measurements published at the discovery epoch and afterward. The resulting transit duration variation ranges from seconds to minutes, and we fit a linear trend to duration versus time for each planet. All systems are consistent with flat (no TDV) at the 3σ level. The strongest candidate is TRAPPIST-1d, whose fitted slope differs from zero with 2.2σ confidence. We calculate the expected TDV signals predicted by secular precession and compare them to the observed limits. Our null detection is consistent with the low-impact-parameter regime, where theoretical TDVs are only a few seconds per decade and below our sensitivity. Higher-impact-parameter configurations predict substantially larger TDVs and are disfavored: under uniformly distributed geometries, at least half of the allowed configurations would be excluded.

Figures (5)

• Figure 1: Left panel: white-light curve of TRAPPIST-1b and TRAPPIST-1c during a simultaneous transit event, with best-fit model over-plotted. The transit of TRAPPIST-1c occurred first, followed by TRAPPIST-1b. Right: white-light curve of TOI-270b and TOI-270d during a simultaneous transit event, with best-fit model over-plotted. The transit of TOI-270b occurred first, followed by TOI-270d.
• Figure 2: Time evolution of transit duration for the TRAPPIST-1 system.
• Figure 3: Time evolution of transit duration for GJ-9827, TOI-776, GJ-357, K2-18, and L98-59.
• Figure 4: Time evolution of transit duration for L98-59, GJ-1132, LHS-1140, LP791-18, TOI-270, TOI-178, and LTT 3780.
• Figure 5: For each planet in our sample, the histogram in blue shows the predicted $\Delta\tau$ corresponding to the calculated precession rate $g$ and varying initial geometries. The histogram in orange shows the actual measured $\Delta\tau$ inferred from the analysis describined in Section \ref{['subsec:timeevolutionoftransitduration']}.