[Paper Review] Planet-star interactions with precise transit timing. I. The refined orbital decay rate for WASP-12 b and initial constraints for HAT-P-23 b, KELT-1 b, KELT-16 b, WASP-33 b, and WASP-103 b

G. Maciejewski, M. Fernández+12 more|arXiv (Cornell University)|Dec 6, 2018

Stellar, planetary, and galactic studies4 citations

TL;DR

This study refines the orbital decay rate of WASP-12 b using precise transit timing, deriving a tidal quality parameter $ Q^{ ext{'}*} = (1.82 \pm 0.32) \times 10^5 $, consistent with theoretical predictions for subgiant stars. For five other hot Jupiters—HAT-P-23 b, KELT-1 b, KELT-16 b, WASP-33 b, and WASP-103 b—no significant orbital decay was detected, yielding lower limits on their stellar tidal quality parameters, indicating weaker tidal dissipation in main-sequence hosts compared to WASP-12's subgiant star.

ABSTRACT

Theoretical calculations and some indirect observations show that massive exoplanets on tight orbits must decay due to tidal dissipation within their host stars. This orbital evolution could be observationally accessible through precise transit timing over a course of decades. The rate of planetary in-spiralling may not only help us to understand some aspects of evolution of planetary systems, but also can be used as a probe of the stellar internal structure. In this paper we present results of transit timing campaigns organised for a carefully selected sample of hot Jupiter-like planets which were found to be the best candidates for detecting planet-star tidal interactions on the Northern hemisphere. Among them, there is the WASP-12 system which is the best candidate for possessing an in-falling giant exoplanet. Our new observations support the scenario of orbital decay of WASP-12 b and allow us to refine its rate. The derived tidal quality parameter of the host star Q'_{*} = (1.82 +/- 0.32) x 10^5 is in agreement with theoretical predictions for subgiant stars. For the remaining systems - HAT-P-23, KELT-1, KELT-16, WASP-33, and WASP-103 - our transit timing data reveal no deviations from the constant-period models, hence constraints on the individual rates of orbital decay were placed. The tidal quality parameters of host stars in at least 4 systems - HAT-P-23, KELT-1, WASP-33, and WASP-103 - were found to be greater than the value reported for WASP-12. This is in line with the finding that those hosts are main sequence stars, for which efficiency of tidal dissipation is predicted to be relatively weak.

Motivation & Objective

• To measure the rate of orbital decay in WASP-12 b through precise transit timing, testing tidal interaction models.
• To constrain tidal dissipation in five other hot Jupiter systems—HAT-P-23 b, KELT-1 b, KELT-16 b, WASP-33 b, and WASP-103 b—by searching for deviations from constant orbital periods.
• To assess the tidal quality parameter $ Q^{ ext{'}*} $ of host stars to probe stellar internal structure and dissipation efficiency.
• To evaluate the dynamical state of systems like KELT-1, where tidal locking may suppress angular momentum transfer.
• To determine whether stars with convective cores and radiative envelopes (e.g., WASP-33) exhibit weaker tidal dissipation than subgiant hosts.

Proposed method

• Conducted long-term transit timing observations using multiple ground-based telescopes, including the 1.5m telescope at Sierra Nevada Observatory and the Liverpool Telescope.
• Collected photometric data from the Gran Telescopio Canarias and the University Observatory Jena to achieve sub-minute precision in mid-transit time measurements.
• Applied transit timing variation (TTV) analysis to detect deviations from a constant orbital period, modeling the data with linear and quadratic ephemerides.
• Used the tidal quality parameter $ Q^{ ext{'}*} = \frac{3}{2} \frac{Q_*}{k_2} $ to quantify tidal dissipation efficiency, where $ Q_* $ is the inverse of the tidal phase lag and $ k_2 $ is the second-order Love number.
• Incorporated theoretical models of tidal dissipation in stars with different internal structures (e.g., subgiant vs. main-sequence stars) to interpret observed constraints.
• Compared observed TTV trends with predictions from equilibrium tide theory and dynamical tide damping in radiative zones, particularly for A-type stars like WASP-33.

Experimental results

Research questions

• RQ1 Is the orbital decay rate of WASP-12 b consistent with theoretical predictions based on tidal dissipation in a subgiant star?
• RQ2 Do the transit timing variations of HAT-P-23 b, KELT-1 b, KELT-16 b, WASP-33 b, and WASP-103 b show evidence of ongoing orbital decay?
• RQ3 What are the lower limits on the tidal quality parameter $ Q^{ ext{'}*} $ for the host stars of these five systems, and how do they compare to WASP-12 b’s value?
• RQ4 How does the stellar evolutionary state (e.g., main sequence vs. subgiant) influence the efficiency of tidal dissipation in hot Jupiter systems?
• RQ5 Can the dynamical state of KELT-1, where both star and planet may be tidally locked, explain the absence of detectable orbital decay?

Key findings

• The refined orbital decay rate for WASP-12 b yields a tidal quality parameter of $ Q^{ ext{'}*} = (1.82 \pm 0.32) \times 10^5 $, consistent with theoretical expectations for subgiant stars.
• No significant transit timing variations were detected for HAT-P-23 b, KELT-1 b, KELT-16 b, WASP-33 b, or WASP-103 b, indicating no measurable orbital decay over the observation baseline.
• The tidal quality parameter for HAT-P-23, KELT-1, WASP-33, and WASP-103 hosts is constrained to be greater than that of WASP-12, suggesting weaker tidal dissipation in main-sequence stars.
• For KELT-16 b, the 3-year baseline is too short to yield meaningful constraints on $ Q^{ ext{'}*} $, but the system shows no signs of decay.
• The host stars of WASP-33 and WASP-103, both A-type stars with radiative envelopes and convective cores, are predicted to have inefficient tidal dissipation, consistent with the observed lack of TTVs.
• Spectroscopic evidence confirms that WASP-33 and WASP-103 are main-sequence stars, supporting the theoretical expectation of lower tidal dissipation efficiency compared to subgiant hosts like WASP-12.