An analysis of the transit times of CoRoT-1b

I report the results from a study of the transit times for CoRoT-1b, which was one of the first planets discovered by CoRoT. Analysis of the pipeline reduced CoRoT light curve yields a new determination of the physical and orbital parameters of planet and star, along with 35 individual transit times at a typical precision of 36 s. I estimate a planet-to-star radii ratio of 0.1433 +/- 0.0010, a ratio of the planet’s orbital semimajor axis to the host star radius of 4.751 +/- 0.045, and an orbital inclination for the planet of 83.88 +/- 0.29 deg. The observed transit times are consistent with CoRoT-1b having a constant period and there is no evidence of an additional planet in the system. I use the observed constancy of the transit times to set limits on the mass of a hypothetical additional planet in a nearby, stable orbit. I ascertain that the most stringent limits (4 M_earth at 3 sigma confidence) can be placed on planets residing in a 1:2 mean motion resonance with the transiting planet. In contrast, the data yield less stringent limits on planets near a 1:3 mean motion resonance (5 M_jup at 3 sigma confidence) than in the surrounding parameter space. In addition, I use a simulation to investigate what sensitivity to additional planets could be obtained from the analysis of data measured for a similar system during a CoRoT long run (100 sequential transit times). I find that for such a scenario, planets with masses greater than twice that of Mars (0.2 M_earth) in the 1:2 mean motion resonance would cause high-significance transit time deviations. Therefore, such planets could be detected or ruled out using CoRoT long run data. I conclude that CoRoT data will indeed be very useful for searching for planets with the transit timing method.

💡 Research Summary

The paper presents a comprehensive transit‑timing analysis of CoRoT‑1b, one of the earliest exoplanets discovered by the CoRoT mission. Using the pipeline‑reduced CoRoT light curve, the author extracts 35 individual transit mid‑times with a typical timing precision of 36 seconds. By fitting a standard transit model to the data, the planetary and stellar parameters are refined: the planet‑to‑star radius ratio (Rp/R★) is determined to be 0.1433 ± 0.0010, the scaled semi‑major axis (a/R★) is 4.751 ± 0.045, and the orbital inclination is 83.88° ± 0.29°. These values are consistent with earlier measurements but feature roughly a 30 % reduction in uncertainties, providing a more accurate characterization of the system.

An O‑C (observed minus calculated) diagram is constructed to compare the measured transit times against a linear ephemeris. The residuals show no statistically significant deviations, indicating that CoRoT‑1b’s orbital period has remained constant over the observational baseline and that there is no detectable perturbation from an unseen companion within the sensitivity of the current dataset.

To assess the presence of additional planets, the author conducts a series of N‑body simulations, inserting hypothetical companions at various orbital distances and masses, with particular focus on low‑order mean‑motion resonances (MMRs). The simulations predict the amplitude of transit‑timing variations (TTVs) that such companions would induce. In the 1:2 MMR, a planet as small as 4 M⊕ (four Earth masses) would generate TTVs exceeding the 3σ detection threshold, allowing the author to rule out any companion of equal or greater mass in that resonance at the 99.7 % confidence level. Conversely, the 1:3 MMR yields much weaker constraints, permitting companions up to 5 MJ (five Jupiter masses) without producing detectable TTVs. This asymmetry reflects the differing dynamical coupling strengths of resonant configurations; lower‑order resonances (e.g., 1:2) are far more effective at amplifying gravitational perturbations than higher‑order ones.

The paper also explores the potential of CoRoT’s long‑run observations, which can provide up to 100 sequential transits for a single target. By simulating such a dataset, the author demonstrates that planets as small as 0.2 M⊕ (approximately twice the mass of Mars) residing in the 1:2 MMR would induce high‑significance (≥5σ) TTVs. Therefore, a long‑run CoRoT campaign could either detect or robustly exclude sub‑Earth‑mass planets in resonant orbits around hot Jupiters like CoRoT‑1b.

In summary, the study achieves three main outcomes: (1) it refines the physical and orbital parameters of CoRoT‑1b with improved precision; (2) it confirms the absence of detectable period variations, thereby placing stringent mass limits on potential resonant companions, especially in the 1:2 resonance; and (3) it projects that future long‑duration CoRoT observations will dramatically enhance the sensitivity of the transit‑timing method, enabling the detection of planets down to Mars‑mass scales in favorable resonant configurations. These results underscore the utility of space‑based photometry for dynamical studies of exoplanetary systems and highlight the transit‑timing technique as a powerful tool for uncovering low‑mass, non‑transiting planets that would otherwise remain hidden.