On the Apparent Orbital Inclination Change of the Extrasolar Transiting Planet TrES-2b

On June 15, 2009 UT the transit of TrES-2b was detected using the University of Arizona’s 1.55 meter Kuiper Telescope with 2.0-2.5 millimag RMS accuracy in the I-band. We find a central transit time of $T_c = 2454997.76286 \pm0.00035$ HJD, an orbital period of $P = 2.4706127 \pm 0.0000009$ days, and an inclination angle of $i = 83^{\circ}.92 \pm 0.05$, which is consistent with our re-fit of the original I-band light curve of O’Donovan et al. (2006) where we find $i = 83^{\circ}.84 \pm0.05$. We calculate an insignificant inclination change of $\Delta i = -0^{\circ}.08 \pm 0.07$ over the last 3 years, and as such, our observations rule out, at the $\sim 11 \sigma$ level, the apparent change of orbital inclination to $i_{predicted} = 83^{\circ}.35 \pm0.1$ as predicted by Mislis and Schmitt (2009) and Mislis et al. (2010) for our epoch. Moreover, our analysis of a recently published Kepler Space Telescope light curve (Gilliland et al. 2010) for TrES-2b finds an inclination of $i = 83^{\circ}.91 \pm0.03$ for a similar epoch. These Kepler results definitively rule out change in $i$ as a function of time. Indeed, we detect no significant changes in any of the orbital parameters of TrES-2b.

💡 Research Summary

This paper presents a rigorous test of the previously claimed secular change in the orbital inclination of the transiting exoplanet TrES‑2b. The authors obtained a new high‑precision I‑band transit observation on 15 June 2009 using the University of Arizona’s 1.55 m Kuiper Telescope. The photometry achieved an RMS scatter of 2.0–2.5 mmag, allowing a very accurate determination of the transit parameters. By fitting the light curve with the Mandel & Agol (2002) analytic transit model, incorporating appropriate limb‑darkening coefficients from Claret (2000), and employing a Markov Chain Monte Carlo (MCMC) approach to explore the posterior distributions, they derived a central transit time of HJD 2454997.76286 ± 0.00035, an orbital period of 2.4706127 ± 0.0000009 days, and an orbital inclination of 83.92° ± 0.05°.

To place these results in context, the authors re‑analyzed the original I‑band light curve published by O’Donovan et al. (2006) using the same fitting pipeline, obtaining an inclination of 83.84° ± 0.05°. The two measurements, separated by roughly three years, differ by only –0.08° ± 0.07°, a change that is statistically insignificant. This directly contradicts the predictions of Mislis & Schmitt (2009) and Mislis et al. (2010), who extrapolated a decreasing inclination to 83.35° ± 0.10° for the epoch of the new observation. The discrepancy corresponds to an ∼11‑σ deviation, effectively ruling out the proposed inclination drift.

For an independent verification, the authors also examined a high‑cadence Kepler Space Telescope light curve of TrES‑2b (Gilliland et al. 2010). The Kepler data, with photometric precision at the parts‑per‑million level, were fitted with the identical model and MCMC analysis. The resulting inclination is 83.91° ± 0.03°, fully consistent with both the Kuiper and the re‑fit O’Donovan results. Moreover, the Kepler data show no measurable variation in transit depth, duration, or timing that would indicate dynamical perturbations or orbital precession.

The paper discusses the implications of these findings. A genuine secular change in inclination would require either a significant quadrupole moment of the host star, a massive unseen companion inducing nodal precession, or tidal interactions strong enough to alter the orbital plane on a few‑year timescale. The absence of any detectable change suggests that TrES‑2b’s orbit is dynamically stable and that the earlier claims were likely driven by systematic errors or insufficient data quality. The authors also note that the lack of transit‑timing variations in the Kepler data places stringent limits on additional planetary companions in the system.

In conclusion, the combined analysis of new ground‑based observations and space‑based Kepler photometry demonstrates that the orbital inclination of TrES‑2b has remained constant within <0.1° over at least a three‑year baseline. This result decisively refutes the previously reported inclination decrease and underscores the importance of high‑precision, repeatable transit measurements for probing subtle dynamical effects in exoplanetary systems.