Orbital Decay of WASP-12 b

• The paper establishes WASP-12 b's orbital period derivative (~ -30 ms/yr) using a quadratic ephemeris fitted to extensive transit and occultation data.
• It employs heterogeneous datasets from TESS, CHEOPS, Spitzer, and ground-based observations with rigorous Bayesian model selection favoring the decay model.
• Measured decay indicates a low stellar tidal quality factor (Q'_∗ ≈ 1.5–2.1×10^5), challenging traditional equilibrium-tide theories in hot Jupiter systems.

WASP-12 b is a highly inflated hot Jupiter in a 1.09-day circular orbit around a slightly evolved F-type star. Decades of transit and occultation timing demonstrate, with overwhelming statistical significance, that WASP-12 b’s orbit is decaying at an exceptional rate, providing a unique benchmark for studies of tidal dissipation in star–planet systems.

1. Measurement of the Orbital Decay Rate

Systematic analyses of WASP-12 b’s orbital evolution employ high-precision transit and occultation mid-times spanning 2008–2025, derived from extensive datasets comprising ground-based, TESS, CHEOPS, Spitzer, and amateur transit observatories. Timing models fit a quadratic ephemeris,

$T_c(E) = T_0 + P_0 E + \tfrac12 \dot{P} E^2$

where $E$ is the transit epoch and $\dot{P}$ encodes a secular period change.

Consensus across all major campaigns yields an orbital period derivative

$$\dot{P} = -29.5\,\text{ms\,yr}^{-1} \text{ to } -31.3\,\text{ms\,yr}^{-1}$$

with typical uncertainties of 0.8–4 ms yr$^{-1}$ (Akinsanmi et al., 2024, Wong et al., 2022, Kutluay et al., 1 Feb 2026, Adams et al., 2024, Biswas et al., 8 Oct 2025, Leonardi et al., 2024). Representative recent values include:

• $\dot{P} = -30.13\pm0.82$ ms yr$^{-1}$ (Akinsanmi et al., 2024) (CHEOPS, TESS, Spitzer, literature)
• $\dot{P} = -29.81\pm0.94$ ms yr$^{-1}$ (Wong et al., 2022) (TESS, ground + orbital occultations)
• $\dot{P} = -30.31\pm0.92$ ms yr$^{-1}$ (Biswas et al., 8 Oct 2025) (391 transits, homogeneous model)

The orbital decay timescale is $\tau = P/|\dot{P}| \approx 3\,\text{Myr}$. All analyses yield a Bayesian Information Criterion (BIC) preference for quadratic (decaying) ephemerides over strictly linear fits, generally at $>8\sigma$ significance, and several confirm the specificity of the decay model against plausible alternatives, including apsidal precession (Biswas et al., 8 Oct 2025, III et al., 2024, Leonardi et al., 2024).

Reference	$\dot P$ (ms yr$^{-1}$)	Data Set and Timespan	Notes/Model Comparison
(Biswas et al., 8 Oct 2025)	$-30.31\pm0.92$	391 transits, 2008–2025	$\Delta$BIC$= 1000+$ against linear model
(Akinsanmi et al., 2024)	$-30.13\pm0.82$	CHEOPS, TESS, Spitzer, literature, 2008–2024	$3.13\pm0.09$ Myr decay time
(Leonardi et al., 2024)	$-30.7\pm2.7$	Asiago + literature (356 times), 2008–2022	$Q'_* = 2.13\pm0.18\times10^5$
(Kutluay et al., 1 Feb 2026)	$-29.4\pm4.0$	TESS + ground, 233 times, 2008–2025	$Q'_* = 1.72\pm0.18\times10^5$
(Wong et al., 2022)	$-29.81\pm0.94$	TESS + all published, $\sim$12 yr	$>31\sigma$ detection
(Adams et al., 2024)	$-29.8\pm1.6$	15yr, 5077 epochs, TESS, ground, amateur	Only UHJ with robust decay detected

2. Data Sources, Methodology, and Transit Timing Analysis

State-of-the-art orbital decay measurements employ heterogenous but precisely cross-calibrated datasets:

• Space-based: TESS (Sectors 20, 43–45, 71–72; 2-min cadence; 100+ transits), CHEOPS (22 transits, 26 occultations), Spitzer phase curve photometry.
• Ground-based: Copernico/Schmidt telescopes (Asiago), amateur Exoplanet Transit Database (ETD) and ExoClock, additional multi-site photometric campaigns (Leonardi et al., 2024).
• Homogenization: Times are reduced to BJD$_\mathrm{TDB}$; transit and occultation times are measured using nested-sampling or MCMC Bayesian inference (e.g., emcee, UltraNest, PyORBIT, TAP, PyLightcurve), incorporating up-to-date photometric noise models, limb darkening, and systematics (Biswas et al., 8 Oct 2025, Leonardi et al., 2024).

Model selection between linear and quadratic ephemerides through BIC/AIC and $\chi_r^2$ robustly favors the inclusion of the quadratic (decay) term. Tests with cubic ephemerides yield null results for $\ddot{P}$ (III et al., 2024), confirming the decay rate has not accelerated at detectable levels.

Extensive O–C (observed minus calculated) diagrams and periodogram analyses exclude (at $>99\%$ significance) significant periodic timing residuals or short-timescale systematics (Nediyedath et al., 2023, Biswas et al., 8 Oct 2025).

3. Systematic and Statistical Errors, Model Assumptions, and Caveats

The dominant source of uncertainty is the per-epoch mid-transit timing error, ranging from $\sim20$–$30$ s for high-S/N space observatories down to 1–5 minutes for small telescopes (Akinsanmi et al., 2024, Leonardi et al., 2024). The large number of epochs (hundreds) and inclusion of space-based timings ensure internal consistency.

Excess timing scatter above photon/statistical errors, with $\chi^2_r\approx1.5$–$5$ for some ground-based datasets, is attributed to low-level stellar activity or unmodeled systematic effects. Correction for correlated (“red”) noise and careful vetting of outliers mitigate bias in $\dot{P}$ values (Leonardi et al., 2024).

All major decay measurements assume:

• Strictly circular orbits ($e<10^{-3}$; light-curve fits and occultation constraints).
• No significant third-body perturbations or Rømer effect; precise RVs rule out secular acceleration (Yee et al., 2019).
• Planetary mass loss negligible for $\dot{P}$ compared to tidal decay timescales, as the mass-loss timescale is $\gg\,\tau$ (Turner et al., 2020).
• Uniform weighting across datasets after time system homogenization and epoch alignment.

Apsidal precession, which can mimic a quadratic trend for small eccentricities ($e\sim0.002–0.003$), has been tested in full timing models; decay remains the statistically favored solution, but subtle precessional signatures may remain undetectable at current precision (Biswas et al., 8 Oct 2025, Patra et al., 2017). High-precision occultation timings remain the most sensitive discriminant.

4. Physical Interpretation: Tidal Dissipation and Host Star Tidal Quality

The observed decay rates imply an extraordinarily efficient dissipation of orbital energy into the host star, parameterized by the modified stellar tidal quality factor $Q'_*$: $$\dot{P} = -\frac{27\pi}{2\,Q'_*}\left(\frac{M_p}{M_*}\right)\left(\frac{R_*}{a}\right)^5 P$$ Inverting for $$Q'_* = -\frac{27\pi}{2}\frac{M_p}{M_*}\left(\frac{R_*}{a}\right)^5 \frac{P}{\dot P}$$ and inserting system parameters yields

$Q'_* \approx (1.5\,\text{–}\,2.1)\times10^5$

(Akinsanmi et al., 2024, Adams et al., 2024, Wong et al., 2022, III et al., 2024), an order of magnitude (or more) lower than expected for MS F-stars ($Q'_* \sim 10^6\text{–}10^8$). This strongly points to enhanced tidal dissipation from dynamical tide mechanisms (e.g., gravity wave breaking at the radiative–convective boundary) operating in slightly evolved (subgiant) hosts (Sun et al., 24 Nov 2025). State-of-the-art models using non-adiabatic mode calculations (e.g., GYRE-tides) independently confirm that linear radiative and convective damping fall short of the observed $\dot{P}$ by multiple orders of magnitude, highlighting the likely necessity for nonlinear or fully damped regimes (Sun et al., 24 Nov 2025).

Astrometric and photometric indicators place WASP-12’s host near the terminal main sequence or at the onset of the subgiant branch (Leonardi et al., 2024, Efroimsky et al., 2021). Tidal dissipation efficiency scaled by $Q'_*$ rises dramatically post–turn-off due to gravity-wave absorption, consistent with population-level non-detections of decay in hot Jupiters orbiting unevolved MS hosts (Adams et al., 2024, Maciejewski et al., 2018).

5. Alternative Explanations and Theoretical Models

Apsidal Precession: For $e\gtrsim0.003$, a precessing, nearly circular orbit can partially mimic the observed timing drift. However, fits to the complete occultation + transit dataset consistently find the quadratic (decay) model statistically favored, with $\Delta$BIC often $>500$ (Biswas et al., 8 Oct 2025, Patra et al., 2017).

Obliquity Tides: A proposed scenario is runaway decay driven by obliquity tides, should WASP-12 b’s spin axis be trapped in a secular Cassini resonance with a perturbing planet. For $Q'_p\sim10^6–10^7$ and $\epsilon\gtrsim50^\circ$, the measured decay rate can be reproduced, with resonance maintained by a hypothetical $10$–$20\,M_\oplus$ companion at $a<0.04$ AU. Such a planet remains undetected but potentially discoverable, making this an open but less favored alternative (Millholland et al., 2018).

Planetary vs. Stellar Tides: While most analyses focus on stellar tides, recent work demonstrates that the inferred planetary modified quality factor $Q_p'\sim1.1\times10^5$ (matching Jupiter’s) can explain the measured decay if even a small eccentricity is present ($e\approx0.04$). However, the observed near-circularity and lack of an eccentricity-pumping companion limit this channel’s efficiency, favoring stellar as the dominant dissipation locus (Efroimsky et al., 2021).

6. Comparative Context: WASP-12 b Among Hot Jupiters

WASP-12 b remains the decisive case of tidal orbital decay among $\gtrsim40$ well-monitored ultra-short-period hot Jupiters. Surveys able to exclude decay at the $|\dot{P}|>2$ ms yr$^{-1}$ level in many systems reveal only Kepler-1658 b as a comparable candidate, and no others approaching the $\sim30$ ms yr$^{-1}$ decay of WASP-12 b (Adams et al., 2024). This exceptional rate has been linked to the evolved status of the host, as similar decay is unexplained by standard equilibrium-tide prescriptions in main-sequence F stars.

Planet	$\dot P$ (ms yr$^{-1}$)	$Q'_*$ (inferred)	Reference
WASP-12 b	$-30$ (all recent)	$\sim1.5$–$2.1\times10^5$	(Akinsanmi et al., 2024, Biswas et al., 8 Oct 2025)
Kepler-1658 b	$\sim-8$	$\sim2\times10^5$	(Adams et al., 2024)
Other UHJs	$<2$ (typ.)	$>10^6$	(Adams et al., 2024, Maciejewski et al., 2018)

7. Future Prospects and Theoretical Implications

WASP-12 b is expected to reach Roche-lobe overflow and tidal disruption within $2$–$3$ Myr at the observed decay rate (Wong et al., 2022, Akinsanmi et al., 2024), making it an archetype for the late stages of hot Jupiter evolution. Ongoing and future space-based photometry (JWST, ARIEL) and multi-wavelength occultation monitoring will continue to refine $\dot{P}$ and search for higher-order timing effects or precessional signatures (Nediyedath et al., 2023, Akinsanmi et al., 2024).

The decisive detection and characterization of WASP-12 b's orbital decay have initiated a new era of tidal dissipation studies, challenging equilibrium-tide theory and highlighting both the importance of stellar evolution (terminal MS and early subgiant phases) and the role of nonlinear dynamical tides. Open questions include the physical origins and universality of low $Q'_*$, the detailed interaction of gravity waves with stellar interiors, the impact of latent planetary or obliquity-induced channels, and the emergence of diversity in hot Jupiter fate across the exoplanet population (Sun et al., 24 Nov 2025, Adams et al., 2024, Efroimsky et al., 2021).