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

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).

Figures (10)

• 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 $R_{\mathrm{J}}$. The numbers of transits are shown in different colors.
• 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 time of inferior conjunction at BJD 2458765.64897.
• Figure 3: Schematic illustration of exotrojan orbits near a hot Jupiter. The figure shows both tadpole orbits, which librate around the Lagrangian points $L_4$ and $L_5$, and horseshoe orbits, which encompass a horseshoe-shaped region from $L_4$ to $L_5$. The host star and hot Jupiter are indicated, and the rotating reference frame is centered on the star-hot Jupiter barycenter.
• 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.
• 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 ($K_{\Delta M}$). The horizontal red dashed line indicates the observed TTV RMS. The intersections determine the upper mass limits for each specific libration amplitude. The $1\sigma$ uncertainty of the observed RMS, calculated via error propagation, determines the lower and upper bounds of the derived mass upper limit.