Detection of periodic transit timing variations in warm sub-Saturn HD 332231 b

Abstract

Transit timing variations (TTVs) provide a powerful means to detect and characterise additional bodies in known planetary systems, even when they do not transit their host stars. We investigate the dynamical architecture of the HD 332231 system by analysing the TTVs of its close-in gas giant, HD 332231 b. Our goal is to assess whether the observed deviations from a linear ephemeris can be explained by the presence of an additional planetary companion. We refine the transit ephemeris of HD 332231 b using high-precision TESS photometry and complementary ground-based observations. We extract individual transit mid-times, construct an O-C diagram for transit timing data, and model the observed TTV signal through an extensive suite of N-body integrations covering a broad range of possible companion masses and orbital configurations. We detect a coherent TTV pattern with a period of approximately 6.7 years and an amplitude of about 45 minutes. Although numerous orbital configurations reproduce the observed TTVs, the combination of current radial velocity and photometric constraints yields a modest improvement in likelihood for solutions with an external planet on an orbit longer than 60 days, likely near a high-order mean-motion resonance and with moderate to high eccentricity. Our results suggest that HD~332231 b is part of a dynamically interacting multi-planet system. Continued transit monitoring and radial velocity follow-up will be essential to confirm the perturber's nature and refine the system's dynamical architecture.

Figures (10)

• Figure 1: Transit light curves of HD 332231 b observed with TESS in Sectors 15--82. Left: individual photometric time series sorted by the epoch of observation with numbering consistent with the refined ephemeris given in Sect. \ref{['sect:ephemeris']}. Best-fitting models are overlaid in red. Right: corresponding photometric residuals from the transit models.
• Figure 2: TESS instrumental light curves of HD 332231 in individual observing sectors. Black points represent photometric measurements with quality flag ${\rm QF} = 0$, which were included in the final analysis. Red points correspond to measurements with ${\rm QF} > 0$ that were excluded. The segments centred on transits of planet b used in transit modelling (Sect. \ref{['sect:TESSmodeling']}), are shown in blue, with individual transits marked by their epoch numbers.
• Figure 3: Transit of HD 332231 b in Sector 14. Panels a and b compare the Sector 14 transit light curve (red points) with the phase-folded data from other sectors (grey points), zoomed in on ingress and egress to highlight discrepancies. The corresponding best-fitting models are shown as red and black/white lines. Panel c shows the raw instrumental flux around the Sector 14 transit, illustrating systematics affecting the measurements.
• Figure 4: Corner plot showing the posterior distributions of the fitted parameters for the transit model of HD 332231 b, based on the TESS data. The diagonal panels show marginalized 1D distributions, while the off-diagonal panels display joint 2D projections to illustrate parameter covariances. Contours correspond to 1$\sigma$, 2$\sigma$, and 3$\sigma$ confidence levels. The orbital parameters $e_{\rm b}$ and $\omega_{\rm b}$ were sampled under Gaussian priors taken from 2022AA...660A..99K. The fit was performed using the TAP model described in Sect. \ref{['sect:TESSmodeling']}, and informed the dynamical simulations discussed in later sections.
• Figure 5: Results of the preliminary analysis of the transit-timing dataset. Panel a: Transit-timing residuals relative to a trial linear ephemeris. The symbol coding follows that in Fig. \ref{['fig:ttoc']} and is explained in the legend. Timing uncertainties for the TESS data are smaller than the symbol size. The uncertainty of the trial ephemeris is illustrated by 100 posterior realisations, shown in orange. Panel b: AoV periodogram of the residuals obtained after subtracting the refined linear ephemeris shown in panel a. Horizontal lines indicate the false-alarm probability (FAP) levels, estimated using a bootstrap procedure applied to 100,000 resampled datasets. The strongest peak, near 96 epochs, has a FAP of 1.9% and is marked by a vertical line. Several harmonics of this signal are also visible.