arxiv: 2603.27215 · v1 · submitted 2026-03-28 · 🌌 astro-ph.EP

Recognition: no theorem link

Constraining the presence of exotrojans in hot Jupiter systems using TTV observations from TESS

Zixin Zhang , Wenqin Wang , Xinyue Ma , Zhangliang Chen , Yonghao Wang , Cong Yu , Shangfei Liu , Yang Gao

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Baitian Tang Dichang Chen Bo Ma

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Pith reviewed 2026-05-14 22:07 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords exotrojanshot Jupiterstransit timing variationsTESSco-orbital companionsexoplanet dynamicsTTV analysis

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The pith

TESS transit timing analysis rules out Earth-mass exotrojans in half of 260 hot Jupiter systems

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses TESS photometry of 260 hot Jupiters with known masses to search for co-orbital Trojan companions through their gravitational effect on transit times. Observed timing residuals are compared against signals predicted by N-body simulations of 1:1 resonant orbits. Upper mass limits are derived after accounting for the trade-off between Trojan mass and libration amplitude. For a representative 15-degree libration, companions above one Earth mass are excluded in 130 systems, or about half the sample. These population-level constraints on massive exotrojans in short-period systems are further tightened by requiring dynamical stability of the resonance.

Core claim

We analyze TESS photometry for 260 confirmed hot Jupiters and derive upper mass limits on possible Trojan companions by comparing observed transit timing variations to N-body simulations. Accounting for the degeneracy with libration amplitude, we rule out exotrojans more massive than 1 Earth mass in 130 systems for a 15 deg amplitude, or 3 Earth masses in a more conservative analysis. These limits are further combined with dynamical stability requirements for the 1:1 resonance.

What carries the argument

Transit timing variation residuals compared to co-orbital models generated by REBOUND N-body simulations, with degeneracy between Trojan mass and libration amplitude

If this is right

Exotrojans above 1 Earth mass are ruled out in approximately 50 percent of the hot Jupiter sample at typical libration amplitudes.
A conservative chi-square analysis raises the mass threshold to 3 Earth masses when accounting for observational uncertainties.
Dynamical stability constraints exclude unstable 1:1 resonance configurations.
The analysis framework can be extended to future missions providing higher precision photometry.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The non-detection implies that hot Jupiters rarely retain massive co-orbitals, consistent with migration scenarios that would clear or prevent such companions.
Higher-precision timing from upcoming missions could extend the search to sub-Earth-mass Trojans or reveal TTVs from other dynamical sources.
If stellar activity contributes to the timing residuals, the reported mass limits become upper bounds on the combined effect rather than on Trojans alone.

Load-bearing premise

The assumption that undetected TTV signals would be produced solely by a co-orbital Trojan rather than by stellar activity, additional planets, or other noise sources.

What would settle it

A statistically significant periodic TTV signal in any of the 130 systems whose amplitude matches the prediction for a Trojan companion heavier than 1 Earth mass would falsify the upper limit reported for that system.

Figures

Figures reproduced from arXiv: 2603.27215 by Baitian Tang, Bo Ma, Cong Yu, Dichang Chen, Shangfei Liu, Wenqin Wang, Xinyue Ma, Yang Gao, Yonghao Wang, Zhangliang Chen, Zixin Zhang.

**Figure 1.** Figure 1: Radius and period properties of the sample of 260 hot-Jupiter systems studied in this work. Most of them have orbital periods ranging from 2 to 6 days and radii between 0.8 and 1.6 RJ . The numbers of transits are shown in different colors. analysis. Sect. 3 details the method for deriving upper mass limits for potential exotrojans and presents the results. We discuss the implications of these findings in… view at source ↗

**Figure 2.** Figure 2: TTV measurements for WASP-93 b derived using a linear ephemeris model. The blue square represents the combined TTV obtained from TESS sectors 17 and 57. The insets show individual TTV measurements from each observation within these sectors, offering a zoomed-in view. The overall RMS for the TTVs is 32 seconds, with individual sectors showing an RMS of 31-32 seconds. Epoch 0 corresponds to the reference … view at source ↗

**Figure 3.** Figure 3: Schematic illustration of exotrojan orbits near a hot Jupiter. The figure shows both tadpole orbits, which librate around the Lagrangian points L4 and L5, and horseshoe orbits, which encompass a horseshoeshaped region from L4 to L5. The host star and hot Jupiter are indicated, and the rotating reference frame is centered on the star-hot Jupiter barycenter. grated a subsequent stability selection step (de… view at source ↗

**Figure 4.** Figure 4: Observed TTV of the hot Jupiter system WASP-93 b, compared with simulated TTV signals induced by co-orbital exotrojans of varying masses. Different curves represent exotrojan masses ranging from Earth-mass to sub-Neptune mass, illustrating the mass-dependent amplitude and periodicity of the induced TTV signals. 10 2 10 1 10 0 10 1 10 2 10 3 Trojan mass [M ] 10 1 10 0 10 1 10 2 10 3 10 4 TTV RMS [s] K M =… view at source ↗

**Figure 5.** Figure 5: RMS variations of simulated TTVs as a function of exotrojan mass for WASP-93 b, assuming different libration amplitudes. The colored curves represent different libration amplitudes (K∆M). The horizontal red dashed line indicates the observed TTV RMS. The intersections determine the upper mass limits for each specific libration amplitude. The 1σ uncertainty of the observed RMS, calculated via error propag… view at source ↗

**Figure 6.** Figure 6: Stability and dynamics heatmap for WASP-93 b. The color scale and contours represent the libration amplitude corresponding to the initial period ratio and Trojan mass. The red dashed line marks the 30◦ libration contour, shown here as a practical reference line within the tadpole zone. Our conservative upper mass limits are strictly derived from the subset of configurations that remain dynamically stable… view at source ↗

**Figure 7.** Figure 7: Cumulative probability distribution of the upper mass limit for potential exotrojans in 260 hot Jupiter systems. The left panel shows the results from the RMS method, compared with Troy project results in red. The right panel displays the results from our χ 2 analysis, offering a more conservative but statistically robust upper limit. Reference masses for Neptune, Saturn, and Jupiter are shown. Note that s… view at source ↗

**Figure 8.** Figure 8: Median upper mass limits of potential exotrojans in 260 hot Jupiter systems, binned by orbital period (1–30 days) and planetary radius (0.5–2.2 RJup). Colors represent the median mass limit in each bin. smaller libration amplitude would result in weaker mass constraints. This dependency on the dynamical configuration is a key limitation of our method compared to full dynamical fits. In [PITH_FULL_IMAGE… view at source ↗

**Figure 9.** Figure 9: The upper mass limits of planets from the Troy project I, II, III, and this work (ExoEcho). The x-axis displays planet names, and the y-axis presents mass limits on a logarithmic scale. Colors and markers distinguish each study. Red triangles represent our results assuming a libration amplitude of ∼ 15◦ . Error bars indicate the 1σ uncertainty but are omitted when smaller than 15% of the mass limit for … view at source ↗

**Figure 10.** Figure 10: Cumulative probability distribution of the upper mass limit for a subset of systems with eccentricity e > 0.05. The gray dotted line represents the results assuming circular orbits, while the colored solid line shows the results using the measured eccentricities. The inclusion of eccentricity generally tightens the mass constraints. Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗

read the original abstract

Co-orbital bodies (Trojans) share a 1:1 mean-motion resonance with a planet. Although Trojans are common in the Solar System, none has yet been confirmed in an exoplanetary system. Hot Jupiters are not expected to retain primordial co-orbitals efficiently, but their deep and frequent transits make them favorable targets for observational constraints using transit timing variations (TTVs). As part of the ExoEcho project, we analyze TESS photometry for 260 confirmed hot Jupiters with published RV-based masses to search for TTV signals compatible with Trojan companions. We derive transit times and compare the observed residuals with co-orbital models computed with REBOUND N-body simulations. Accounting for the degeneracy between Trojan mass and libration amplitude, we place upper mass limits on possible companions over a range of typical libration amplitudes. For a representative libration amplitude of 15 deg, we rule out exotrojans more massive than 1 Earth mass in 130 systems, corresponding to about 50% of the sample. A more conservative chi-square analysis that incorporates observational uncertainties raises this threshold to 3 Earth masses. We further combine these limits with dynamical-stability constraints for the 1:1 resonance to exclude unstable configurations. Our results provide population-level constraints on massive exotrojans in short-period systems and establish a framework for future high-precision searches with missions such as PLATO and ET (Earth 2.0).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper sets the first large-sample upper limits on exotrojans around hot Jupiters from TESS TTV data, with the 1-Earth-mass threshold for half the sample holding only under a specific libration assumption.

read the letter

The main thing to know is that the authors analyzed TESS transit timing for 260 hot Jupiters with known masses and compared the residuals to REBOUND co-orbital simulations. For a representative 15-degree libration they rule out Trojans above 1 Earth mass in 130 systems, and a more conservative chi-square run that includes uncertainties raises the limit to 3 Earth masses. They also cross-check against dynamical stability criteria for the 1:1 resonance. That is the concrete new output: population-level observational bounds derived from public data on a well-defined sample. The methods are standard but applied at scale with explicit handling of the mass-libration degeneracy, which is a reasonable step forward from earlier single-system studies. The paper is transparent about the assumptions and supplies both the headline and the conservative numbers. The limits are model-dependent on the chosen libration amplitude, and the analysis treats any undetected TTV as potentially due to a Trojan rather than stellar activity or extra planets. Those are standard caveats in TTV work and the authors flag them, but they do mean the numbers are not model-independent. No circular fitting or hidden parameters appear in the core comparison. This is useful for people modeling hot Jupiter migration and stability who need observational anchors, or for teams planning higher-precision photometry with PLATO. It is not a breakthrough in technique but the sample size and conservative treatment make it worth a referee's time. I would send it for review.

Referee Report

0 major / 0 minor

Summary. The manuscript analyzes TESS photometry for 260 hot Jupiters with RV masses to search for TTV signals from co-orbital Trojan companions. Transit times are derived and compared to REBOUND N-body co-orbital simulations; upper mass limits are placed as a function of libration amplitude after accounting for the mass-libration degeneracy. For a representative 15° libration amplitude the authors rule out Trojans more massive than 1 M⊕ in 130 systems (~50% of the sample); a conservative χ² analysis incorporating observational uncertainties raises the threshold to 3 M⊕. Limits are further combined with 1:1 resonance dynamical-stability criteria to exclude unstable configurations.

Significance. If the results hold, the work supplies population-level upper limits on massive exotrojans in short-period systems where such bodies are not expected to survive, together with an explicit framework for future high-precision TTV searches. Strengths include the direct use of REBOUND simulations, explicit treatment of the mass-libration degeneracy, and the conservative χ² threshold that folds in measurement uncertainties; these features make the reported limits more robust than a simple non-detection claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review, detailed summary of our methods, and recommendation to accept the manuscript. We appreciate the recognition of the strengths in our direct use of REBOUND simulations, explicit handling of the mass-libration degeneracy, and the conservative χ² approach that incorporates observational uncertainties.

Circularity Check

0 steps flagged

Derivation is self-contained; no circular steps identified

full rationale

The paper derives transit times from TESS photometry, compares residuals against REBOUND N-body co-orbital simulations, and sets upper mass limits via chi-square thresholds that explicitly fold in observational uncertainties and the degeneracy with libration amplitude. Limits are reported parametrically (e.g., for 15° amplitude) and cross-checked against independent external dynamical-stability criteria for the 1:1 resonance. No quantity is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing premise reduces to a self-citation chain; the central results remain data-driven and externally benchmarked.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on standard N-body gravitational dynamics and the assumption that observed timing residuals can be attributed to co-orbital companions after subtracting the known planetary orbit.

free parameters (1)

representative libration amplitude
15 deg chosen as typical value; limits scale with this choice and degeneracy is noted but not marginalized over in the headline result.

axioms (2)

domain assumption REBOUND N-body integrations accurately reproduce co-orbital TTV signals for the mass and amplitude range considered
Invoked when generating model transit times for comparison to observations.
domain assumption Dynamical stability maps for 1:1 resonance apply directly to the observed systems
Used to exclude unstable configurations after the TTV analysis.

pith-pipeline@v0.9.0 · 5599 in / 1409 out tokens · 41995 ms · 2026-05-14T22:07:07.254267+00:00 · methodology

discussion (0)

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