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Spin-orbit angle measurements for six southern transiting planets; New insights into the dynamical origins of hot Jupiters
Amaury H. M. J. Triaud, Andrew Collier Cameron, Didier Queloz, David R. Anderson, Michaël Gillon, Leslie Hebb, Coel Hellier, Benoît Loeillet, Pierre F. Maxted, Michel Mayor, Francesco Pepe, Don Pollacco, Damien Ségransan, Barry Smalley, Stéphane Udry, Richard G. West, Peter J. Wheatley
TL;DR
The paper asks whether hot-Jupiter spin-orbit orientations can distinguish formation and migration mechanisms. It measures projected obliquities for six WASP planets with HARPS and long-term CORALIE radial velocities, then compares the enlarged angle distribution with dynamical models. The resulting distribution is consistent with Kozai-based predictions and indicates that many hot Jupiters are misaligned, challenging disc migration alone.
Problem
Hot-Jupiter formation mechanisms remain difficult to distinguish because disc migration does not explain observed orbital distributions, while spin-orbit angles provide a marker of dynamical history.
Method
The study measures Rossiter-McLaughlin angles for six WASP planets with HARPS, combines them with CORALIE radial velocities, and statistically transforms projected β measurements into real-angle ψ distributions.
Results
Up to 85% of hot Jupiters are inferred to have ψ > 30°, and the observed angle distribution closely matches Fabrycky and Tremaine’s Kozai-based prediction.
Takeaways & Limitations
The evidence supports a dynamical and tidal origin for hot Jupiters and indicates that disc migration alone cannot explain the observations.
Takeaways & Limitations
The statistical picture depends on additional transiting systems and follow-up observations to become clearer.
Abstract
from arXiv · showhide
For transiting planets, the Rossiter-McLaughlin effect allows the measurement of the sky-projected angle beta between the stellar rotation axis and a planet's orbital axis. Using the HARPS spectrograph, we observed the Rossiter-McLaughlin effect for six transiting hot Jupiters found by the WASP consortium. We combine these with long term radial velocity measurements obtained with CORALIE. We found that three of our targets have a projected spin-orbit angle above 90 degrees: WASP-2b: beta = 153 (+11 -15), WASP-15b: beta = 139.6 (+5.2 -4.3) and WASP-17b: beta = 148.5 (+5.1 -4.2); the other three (WASP-4b, WASP-5b and WASP-18b) have angles compatible with 0 degrees. There is no dependence between the misaligned angle and planet mass nor with any other planetary parameter. All orbits are close to circular, with only one firm detection of eccentricity on WASP-18b with e = 0.00848 (+0.00085 -0.00095). No long term radial acceleration was detected for any of the targets. Combining all previous 20 measurements of beta and our six, we attempt to statistically determine the distribution of the real spin-orbit angle psi and find that between about 45 and 85 % of hot Jupiters have psi > 30 degrees. Observations and predictions using the Kozai mechanism match well. If these observational facts are confirmed in the future, we may then conclude that most hot Jupiters are formed from a dynamical and tidal origin without the necessity to use type I or II migration. At present, standard disc migration cannot explain the observations without invoking at least another additional process.
1. Introduction
Hot-Jupiter formation and migration remain debated, motivating spin-orbit measurements as a marker of planetary dynamical history. The paper measures projected spin-orbit angles for six southern WASP planets and examines their implications for migration models.
- 1. Introduction: Hot-Jupiter formation and subsequent evolution remain unresolved despite widespread acceptance of inward disc migration.Alternative mechanisms include Kozai cycles and planet scattering.
- 1. Introduction: β measures the sky-projected angle between a star’s rotation axis and a planet’s orbital axis.The real obliquity is denoted ψ.
- 1. Introduction: Disc migration predicts near-equatorial orbits, whereas Kozai cycles and planet scattering predict excited obliquities and misaligned systems.This makes spin-orbit alignment a discriminator among formation mechanisms.
- 1. Introduction: The Rossiter-McLaughlin effect measures projected spin-orbit angles during planetary transits.A transiting planet blocks differently Doppler-shifted portions of the rotating stellar surface.
- 1. Introduction: The study reports β measurements for six southern WASP transiting planets using HARPS, combined with long-term CORALIE radial velocities.The analysis examines correlations and implications for planetary migration models.
2. The Observations
The observations combine dense, high-precision HARPS radial-velocity sampling across transits with CORALIE measurements outside transit and over longer baselines. This design supports Rossiter-McLaughlin modeling, activity-offset estimation, and searches for long-term orbital variability.
- 2. The Observations: HARPS observations densely sampled each transit from 90 minutes before ingress to 90 minutes after egress.Two additional high-precision points were taken the night before and after transit.
- 2. The Observations: The stellar spectroscopic rotation broadening and stellar mass estimates were used as priors in model fitting.Table 2 also reports microturbulence and macroturbulence parameters.
- 2. The Observations: Pre-ingress and post-egress measurements allowed activity-related offsets in the system’s effective centre-of-mass velocity to be estimated.These observations help separate stellar activity from the transit signal.
- 2. The Observations: CORALIE radial velocities supplemented HARPS data to search for long-term variability in the periodic radial-velocity signal.The CORALIE spectrograph was mounted on the 1.2 m Euler Telescope.
- 2. The Observations: HARPS stability was better than 1 m s−1 across a night, below the individual error bars.The observations were conducted without simultaneous Thorium-Argon spectra.
3. The Data Analysis
The analysis jointly fits photometry, Keplerian radial velocities, and the Rossiter-McLaughlin signal with MCMC, using parameterizations and priors designed to reduce correlations. It also tests radial-velocity drift and accounts for stellar and instrumental considerations.
- 3.3. Model fitting: Photometry, Keplerian radial velocities, and the Rossiter-McLaughlin effect were fitted simultaneously with MCMC.A single parameter set describes the photometry and radial velocities, with χ2 quantifying fit quality.
- 3.3. Model fitting: The fitted parameters included transit, orbital, eccentricity, stellar rotation, and projected spin-orbit variables.The RM angle was represented through V sin I cos β and V sin I sin β.
- 3.3. Model fitting: Using paired trigonometric variables reduces correlations and allows solutions near zero to be explored more efficiently.The parameterization pairs eccentricity with periastron angle and projected rotation with β.
- 3.3. Model fitting: A spectroscopically determined v sin I prior can curb overestimation of V sin I when low impact parameter creates degeneracy with β.This degeneracy affects Rossiter-McLaughlin modeling.
- 3.3. Model fitting: No fitted radial-velocity drift was significantly different from zero for any target.Upper limits were reported for each star.
- 3.3. Model fitting: The MCMC perturbs free parameters with Gaussian random steps and adapts a control factor to target a 25% acceptance rate.The step size is tuned during initial analyses and then held fixed.
4. The Survey Results
The six WASP targets show a mix of aligned and strongly misaligned projected spin–orbit angles, while their orbits are generally close to circular and show no significant long-term radial-velocity trends.
- WASP-2b: β = 153° +11/-15° for WASP-2b, significantly excluding an aligned orbit.The posterior places 99.73% of probability at V sin I > 0.2 km s−1 and β > 77.26°.
- WASP-4b: β = −4° +43/-34° for WASP-4b, with the high-S/N RM signal excluding a projected retrograde orbit.A small impact parameter creates a strong β–V sin I degeneracy, even with a rotation prior.
- WASP-5b: β = −12.1° +10.0/-?° for WASP-5b is compatible with zero, but the fit is affected by low-impact-parameter degeneracy and residual dispersion.The HARPS sequence has residuals larger than its average error bar, and the MCMC posterior is not clean.
- WASP-15b: β = 139.6° +5.2/-4.3° for WASP-15b provides a clear retrograde-orbit detection.Its eccentricity is constrained to e < 0.087, and the long-term radial-velocity trend is constrained to |˙γ| < 11 m s−1 yr−1.
- WASP-17b and WASP-18b: WASP-17b has a severely misaligned orbit, whereas WASP-18b has β = −4.0° +2.5/-5.0° and a firm eccentricity detection of e = 0.00848 +0.00085/-?°.WASP-17b’s circular solution gives a radius of 1.986 +0.089/-0.074 RJ and no detected acceleration; WASP-18b’s eccentricity is detected above 9σ.
5. Overall results
The six systems show a mixed spin-orbit architecture: three are closely aligned, while three have apparently retrograde orbits; all are near-circular, with eccentricity detected significantly only for WASP-18b. The broader analysis finds no clear correlation between spin-orbit angle and planetary parameters, while the inferred real-angle distribution is limited by geometric and measurement constraints.
- Spin-orbit alignment: Three of six systems appear closely aligned, while three exhibit highly inclined, apparently retrograde orbits.All six systems show planetary spectroscopic transit signatures.
- Orbital eccentricities: All six orbits appear close to circular, with significant eccentricity detected only for the massive WASP-18b.The authors note that detecting small eccentricities is difficult when radial-velocity sampling or amplitude is inadequate.
- Spin-orbit alignment: Five sky-projected angles β were measured with precision better than 15°, and three appear retrograde.Including WASP-6b and WASP-8b, four of eight measured angles exceed 90°.
- Inference of ψ: The real angle ψ is inferred from β using the geometric relation cos ψ = cos I cos i + sin I sin i cos β.A Monte Carlo calculation assumes an isotropic stellar-spin orientation and propagates uncertainties in i and β.
- Measurement limitations: Rossiter-McLaughlin measurements can miss stars viewed nearly pole-on, and WASP-2b may be affected because of its small V sin I.The authors report a broader ψ distribution for WASP-2b than for the other targets.
- Parameter correlations: No clear correlation is evident between β and planetary radii, masses, eccentricities, orbital periods, or V sin I.The authors caution that apparent parameter distributions may reflect observational or follow-up biases.
6. Discussion
The expanded Rossiter–McLaughlin sample reveals many strongly misaligned systems, while statistical deprojection suggests that misalignment is common. The observed angle distribution broadly matches Kozai-based predictions better than standard disc migration alone.
- 8 of 26 planets show severe projected misalignment, including 5 with apparent retrograde orbits.
- The inferred ψ distribution remains hypothesis-dependent because β measures only the sky projection and deconvolution requires assumptions about stellar-axis orientations.
- About 55% of planets are predicted to appear with β < 30°, and Fabrycky–Tremaine models closely match the observed β distribution.Nagasawa-model predictions cover the observed range but do not reproduce its shape, particularly the number of aligned systems.
- Disc migration alone would produce a steep β distribution reaching unity before 30°, unlike the observed broad range of angles.
- 43.6%–86.2% of systems have ψ > 30%, depending on the assumed stellar-axis distribution.The authors interpret these extremes as 45%–85% of systems being misaligned.
- Kozai cycles driven by an outer companion, followed by tidal friction, can move planets inward and circularize their orbits.
7. Conclusions
The study expands the measured obliquity sample and finds that hot Jupiters commonly have substantial spin–orbit misalignment. The authors conclude that dynamical and tidal processes are favored over standard disc migration alone, while emphasizing that the statistical picture remains provisional.
- The sample grows from 20 to 26 transiting planets with measured sky-projected obliquities, including 8 significantly misaligned systems.
- Up to 85% of hot Jupiters are inferred to be misaligned after transforming projected β measurements into real ψ angles.
- The overall ψ distribution is consistent with Kozai-driven inward migration followed by tidal orbital shrinkage and circularization.
- The evidence points toward a dynamical and tidal origin for hot Jupiters rather than type I or II disc migration alone.The authors state that disc migration alone cannot explain the observations without another process.
- The emerging statistical picture should become clearer as more transiting systems receive comparable follow-up observations.
Appendix A: Comparative tables for each star
The appendix records the comparative fit results used to select the reported solutions for each star.
- Comparative fit tables document χ2 values for radial-velocity datasets and separate contributions from each observation set.
Appendix B: Journal of Observations
The appendices provide the extracted radial-velocity data and comparative fit information underlying the stellar analyses.
- Radial-velocity data are extracted from Gaussian fits to cross-correlation functions and organized by instrument, dataset, and chronology.
- The appendix includes comparative fit tables for WASP-2b, WASP-4b, WASP-5b, WASP-15b, WASP-17b, and WASP-18b.
- The tabulated parameters include projected stellar rotation, β, eccentricity, and argument of periastron for alternative fits.
- Values labeled V sin I in the WASP-18b analysis may instead represent an amplitude parameter for fitting the Rossiter–McLaughlin effect.