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REVIEW 4 major objections 5 minor 115 references

Stellar obliquities of eight close-in gas giant exoplanets

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read Seven close-in gas giants get first spin-orbit measurements; one is clearly tilted.

desk verdict Useful new obliquity measurements from archival spectra; the core lambda values are sound, but the headline true obliquity for TOI-2046 rests on an unvalidated rotation period and the abstract overclaims. read the letter →

arxiv 2501.05615 v1 pith:TTUC6T6P submitted 2025-01-09 astro-ph.EP

classification astro-ph.EP
keywords Rossiter-McLaughlineffectstellarobliquityhotJupitersspin-orbitalignmentexoplanetmigrationHARPS/HARPS-Nspectroscopyrotationperiodmulti-starsystems
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using archival HARPS and HARPS-N spectra, the paper measures the Rossiter-McLaughlin effect for eight close-in gas giants and reports first-time projected stellar obliquities for seven of them. The central result is that HAT-P-50b is prograde but misaligned, with $\lambda = 41^\circ\,^{+10}_{-9}$, while the other seven planets are consistent with alignment, $|\lambda| \le 13^\circ$. For four systems the paper also derives the true three-dimensional obliquity, finding that TOI-2046b is genuinely misaligned at $\psi = 42^\circ\,^{+10}_{-8}$ even though its projected value looks aligned. The paper further argues that TOI-2046 and Qatar-4 are much older than previously claimed, at least 700 Myr and 350$-$500 Myr respectively. These measurements matter because spin-orbit alignment is a diagnostic of whether hot Jupiters migrated gently through a disk or were scattered into eccentric orbits by companions.

What carries the argument

The central object is the Rossiter-McLaughlin anomaly, the transient spectral-line distortion that shifts apparent radial velocities during transit. The paper fits it with ARoMEpy, a Python implementation of the Boué et al. model, jointly with a Keplerian orbit via MCMC, using literature priors on transit parameters and fixed limb-darkening coefficients. For true obliquity, the paper uses the spherical law of cosines $\cos\psi = \sin i_* \sin i \cos|\lambda| + \cos i_* \cos i$, following the Masuda & Winn approach to handle the dependency between $v$ and $v\sin i_*$. Rotation periods come from Lomb-Scargle periodograms of ASAS-SN and TESS light curves. Age estimates use lithium non-detection, gyrochronology, and $R'_{HK}$ activity indices.

What would settle it

Compare the 4.05-day and 4.29-day periodicities in TOI-2046 with independent rotation indicators, such as spot-modulated line-profile variations or a longer TESS baseline; if the true rotation period is 4.29 days instead of 4.05 days, recomputing $\sin i_*$ changes the inferred $\psi = 42^\circ$, and the misalignment claim would fail.

Watch

Extended reading notes

Core claim

The paper analyzes archival HARPS and HARPS-N transit time series of eight gas giants on short orbits and fits the Rossiter-McLaughlin anomaly with a Keplerian plus R-M model. It reports first-time projected obliquities for WASP-48b, WASP-59b, WASP-140 Ab, WASP-173 Ab, TOI-2046b, HAT-P-50b and Qatar-4b, together with an updated value for HAT-P-41 Ab. The headline result is that HAT-P-50b is prograde but misaligned ($\lambda = 41^\circ\,^{+10}_{-9}$), while the other seven are consistent with alignment ($|\lambda| \le 13^\circ$). For four systems with measured stellar rotation periods, the paper derives true obliquities via the spherical law of cosines, finding $\psi = 42^\circ\,^{+10}_{-8}$ for TOI-2046b, $\psi = 30^\circ\,^{+18}_{-15}$ for WASP-140 Ab, $\psi = 21^\circ\,^{+9}_{-10}$ for WASP-173 Ab, and $\psi = 32^\circ\,^{+14}_{-13}$ for Qatar-4b. It also revises the ages of TOI-2046 and Qatar-4 upward, concluding that both systems are substantially older than previous estimates.

Load-bearing premise

The claim that TOI-2046b is genuinely misaligned ($\psi = 42^\circ$) rests on interpreting a 4.05-day TESS periodicity as the stellar rotation period of TOI-2046, even though short-cadence data give 4.29 days; if that period is wrong, the stellar inclination and hence the true obliquity are not determined.

Editorial extensions

If this is right

  • HAT-P-50b's 41-degree misalignment, together with its 327 au stellar companion and a Kozai-Lidov timescale of roughly 0.1$-$1 Gyr, makes high-eccentricity migration a plausible formation route.
  • The other seven systems are aligned to within 13 degrees, with tidal alignment timescales longer than their ages, so their current spin-orbit angles likely reflect their initial configurations and are consistent with slow disk migration.
  • TOI-2046b is misaligned in three dimensions ($\psi = 42^\circ$) even though its projected obliquity is near zero, showing that projection can hide real misalignment.
  • TOI-2046 and Qatar-4 are not the young ($<200$ Myr) systems previously claimed; lithium non-detection and gyrochronology place them at $\ge 700$ Myr and $\ge 350$-$500$ Myr, respectively.
  • The updated alignment of HAT-P-41 Ab reconciles its high atmospheric metallicity with disk migration and removes the tension that led to its withdrawal from a homogeneous JWST atmospheric sample.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If HAT-P-41 Ab's orbit is indeed aligned as newly measured, the planet's high atmospheric metallicity becomes consistent with disk migration, resolving a tension; a subsequent solar-metallicity measurement would reopen the question.
  • The hidden misalignment of TOI-2046b demonstrates that projected obliquities alone can miss true misalignments, so expanding true-obliquity samples with reliable rotation periods would clarify how common such projection-hiding geometries are.
  • The two systems with line-of-sight orbit-orbit misalignment (WASP-140 and HAT-P-41) could be re-tested with forthcoming Gaia astrometry, which would either confirm or dissolve the current $\gamma$ values.
  • Doppler tomography of HAT-P-50b would provide an independent check of the 41-degree misalignment without relying on the assumptions of the Boué-model R-M fit.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper analyzes archival HARPS/HARPS-N transit time series of eight close-in gas giants and models the Rossiter-McLaughlin effect to derive sky-projected stellar obliquities. It reports first-time λ measurements for seven systems and an updated value for HAT-P-41 Ab, finding HAT-P-50b to be prograde but misaligned (λ=41+10/−9 deg) and all others consistent with aligned orbits. For four systems (WASP-140 Ab, WASP-173 Ab, TOI-2046b, Qatar-4b) the paper derives true obliquities from photometric rotation periods, with TOI-2046b showing a misaligned ψ=42+10/−8 deg. The paper also presents revised age estimates for TOI-2046 (≥700 Myr) and Qatar-4 (350–500 Myr), and reports orbit-orbit angles for multi-star systems.

Significance. The main projected-obliquity measurements are valuable: they add seven new systems to the TEPCat sample, use standard R-M fitting with literature priors and MCMC diagnostics, and identify HAT-P-50b as a genuinely misaligned hot Jupiter in a binary, which is a useful constraint for migration scenarios. The paper also provides rotation periods and true-obliquity estimates for four systems, extending the three-dimensional obliquity census. The age estimates for TOI-2046 and Qatar-4, if supported, would correct earlier claims that these systems are very young. The strengths of the paper include full MCMC corner plots and residual figures for every target, explicit prior choices, and the use of archival data, which makes the main λ results transparent and reproducible.

major comments (4)
  1. [Section 4.1] The true obliquity of TOI-2046b (ψ=42+10/−8 deg) is entirely conditional on the assumption that the 4.05 d TESS periodicity is the stellar rotation period. The authors state this assumption explicitly ('This periodicity, that we assume to be due to differential rotation'), and the short-cadence data give a different period of 4.29 d. No independent confirmation of a rotational origin (e.g., phase stability across sectors, activity-index modulation, or spot modeling) is provided. If the 4.05 d signal is not rotation but a pulsation or a blended variable, then the derived v_eq, the stellar inclination i*, and hence the headline ψ are unconstrained. The paper should either add such confirmation or present ψ as conditional on the rotation interpretation, and it should propagate the 4.05/4.29 ambiguity into the quoted uncertainty.
  2. [Abstract and Section 4.3] The abstract's statement that the aligned orbits 'rule out violent events that would excite the orbits over the history of these systems' is too strong and is internally contradicted. Section 4.3 explicitly states for WASP-173 Ab that 'the high-eccentricity migration scenario cannot be ruled out from the stellar obliquity measurements alone' because the system is likely older than its tidal alignment timescale. Furthermore, TOI-2046b has a misaligned true orbit (ψ=42 deg), so it cannot be counted among the aligned orbits that rule out violent histories. The conclusion should be qualified to say that the projected obliquities are consistent with disk migration for most targets, while noting that tidal realignment or the TOI-2046 true-obliquity result limits any general claim.
  3. [Appendix B] The Doppler-shadow cross-check for HAT-P-41 Ab is not an independent confirmation because the adopted Gaussian prior on λ is centered at −13.1 deg, the mean of the Johnson et al. (2017) value and the authors' own R-M result. The resulting posterior (λ_b=−7.6+7.7/−8.0 deg) is therefore a weighted compromise between the two, so the statement in the main text that this analysis is 'consistent with our classical R-M effect analysis' is partly circular. The authors should either run the fit with a uniform prior and report the (possibly bimodal) posterior, or explicitly label the result as prior-dependent rather than as an independent check.
  4. [Appendix C] The new age lower limit for TOI-2046 (≥700 Myr) is based on lithium non-detection, but the authors' own gyrochronology analysis gives an age of 0.46+0.25/−0.15 Gyr, which is below that limit. The claim in Section C that 'the broad agreement among the various indicators is that these systems are older than previously reported' is not supported for TOI-2046, since the gyro and lithium methods disagree. The paper should discuss this discrepancy explicitly (e.g., possible F-star gyrochronology systematics) or soften the age claim to a lithium-based lower limit that is presented as method-dependent.
minor comments (5)
  1. [Table 2] The entry for HAT-P-50's T0 − 2450000 lists 56285.99093±0.00034, which is clearly a typo (it should be near 7737, as in Table 3). This should be corrected.
  2. [Section 5] In the summary, 'WASP-40b' is a typo for WASP-48b, and the phrase 'for and ψ =32+14/−13 deg' contains a duplicated 'for'.
  3. [Figure A.1] The caption contains LaTeX/Unicode artifacts ('uni00A0') that should be cleaned up.
  4. [References] Blanco-Cuaresma et al. (2014a) and (2014b) appear to be the same reference with identical author lists and journals; the distinction should be clarified or merged.
  5. [Section 4.3] The symbol 'τCe' should be 'τCE' for consistency with the text and equations.

Circularity Check

1 steps flagged · score 4.0 of 10

The eight λ measurements come from genuine R-M fits with uniform λ priors; the main circular step is the Appendix B Doppler-shadow 'confirmation' of HAT-P-41 Ab, whose Gaussian prior is the mean of the two values it claims to adjudicate.

  1. self definitional [Appendix B (Doppler Shadow of HAT-P-41 Ab), Table B.1 and Fig. B.2]
    "Setting a uniform uninformative prior on λ did not allow us to meaningfully distinguish between the results from Johnson et al. (2017) and the results we have previously derived. Hence, we have set a Gaussian prior on λ to -13.1 deg as the mean value between the λ from Johnson et al. (2017), and the one that we previously derived using the classical RM effect. The obtained result of λb = -7.6+7.7 −8.0 deg favors an aligned orbit of the planet in agreement with our classical R-M effect analysis."

    The Doppler-shadow analysis is presented as an independent validation of the classical R-M result, but its Gaussian prior on λ is exactly the mean of the two values it is supposed to adjudicate between: Johnson et al. (2017)'s -22.1 deg and the paper's own R-M value -4.4 deg, giving -13.1 deg with sigma = 8.7 deg. The posterior (-7.6 deg) is therefore pulled toward a prior that already contains the paper's own R-M result, so the claimed agreement is enforced by construction rather than measured independently. The same construction is applied to v sin i*, where the prior 17.7 km/s is the mean of 19.6 km/s (literature) and 15.8 km/s (own R-M fit). Thus Appendix B does not provide independent support for the HAT-P-41 obliquity.

full rationale

The central obliquity measurements are not circular. For each target the projected obliquity λ is drawn from a uniform U(-180, 180) prior and fitted to the R-M anomaly shape using a physical model (Boue et al. 2013 via ARoMEpy), with Gaussian priors only on transit parameters (P, Rp/Rs, e, Tc, i, a/Rs) that come from independent literature values or from the separate TESS analysis in Appendix A. λ is therefore not an input to the fit. This holds for the first-time values for WASP-48b, WASP-59b, WASP-140 Ab, WASP-173 Ab, TOI-2046b, HAT-P-50b and Qatar-4b, and for the updated HAT-P-41 Ab value, all of which rest on the shape of the observed R-M anomaly. The TOI-2046 true obliquity psi = 42+10-8 deg is assumption-dependent (it adopts the 4.05 d TESS periodicity as the rotation period and explicitly 'assume[s]' differential rotation to reconcile the 4.05 d and 4.29 d periods), but an unverified physical assumption is a correctness or robustness concern, not circularity. The one genuine circular step is confined to Appendix B: the Doppler-shadow prior on λ is defined as the mean of Johnson et al. (2017) and the paper's own R-M λ, so the claimed consistency of the Doppler-shadow result with the classical R-M analysis is partly built into the prior. Since no headline claim depends on Appendix B, the main derivation remains self-contained and the overall circularity is limited.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The ledger contains no invented entities. The main fitted quantities are the projected obliquities and stellar rotation periods; all other inputs are standard literature values or calibration relations. The most fragile assumption is that the photometric period of TOI-2046 is the stellar rotation period, because this directly sets the true obliquity claim.

free parameters (5)
  • Sky-projected obliquity lambda (fitted per target) = HAT-P-50b: 41 +10/-9 deg; seven others: -13 to +9 deg (Table 3)
    The central measured quantities from the R-M fits, obtained with uniform priors on lambda.
  • Stellar rotation periods P_rot (4 stars) = 10.44, 7.97, 4.05, 7.07 d (WASP-140, WASP-173, TOI-2046, Qatar-4)
    Periodogram peaks in ASAS-SN or TESS photometry; used to convert v sin i* to stellar inclination for psi.
  • Projected rotation velocity v sin i* (4 stars used for psi) = 3.0, 6.2, 8.9, 5.1 km/s (WASP-140, WASP-173, TOI-2046, Qatar-4)
    Fitted in the R-M MCMC; combined with P_rot to derive i* and psi.
  • TESS transit parameters for WASP-59b = a/Rs=23.58, i=88.60 deg, Rp/Rs=0.1389, P=7.919567 d
    From Appendix A TESS light-curve fit; used as priors in the WASP-59 R-M model.
  • Quadratic limb-darkening coefficients (fixed) = Computed with ExoCTK/ATLAS9; values not tabulated
    Fixed in the R-M model; different limb darkening would slightly shift lambda.
assumptions (6)
  • domain assumption The Boue et al. (2013) R-M anomaly model accurately describes HARPS/HARPS-N CCF radial velocities during transit.
    The entire lambda measurement depends on this model; Section 2.1 notes it yields lower v sin i* than other models but agrees on lambda.
  • domain assumption Literature values of orbital period, eccentricity, and planet-star radius ratio used to fix the R-M fit are correct.
    Section 2.1 states P, Rp/Rs, and e are fixed to literature values; biased ephemerides would shift the R-M anomaly phase and bias lambda.
  • domain assumption Detected photometric periods are stellar rotation, notably the 4.05 d period for TOI-2046.
    Section 4.1, TOI-2046 paragraph: the authors adopt 4.05 d over 4.29 d and say they 'assume' the variability is due to differential rotation; this drives the claimed psi=42 deg.
  • domain assumption Age-calibration relations (gyrochronology, R'HK activity) apply to the target stars with published scatter.
    Appendix C derives lower ages for TOI-2046 and Qatar-4 using gyro-interp, stardate, and Mamajek and Hillenbrand (2008); the authors list systematic limitations for F-type stars.
  • domain assumption Tidal alignment timescale formulas of Albrecht et al. (2012) are valid for these planets.
    Section 4.3 uses these formulas to argue most systems have not been tidally realigned, linking current obliquity to initial conditions.
  • standard math The spherical law of cosines with the Masuda and Winn (2020) approach yields true obliquity from i, i*, and lambda.
    Section 4.1 uses cos psi = sin i* sin i cos|lambda| + cos i* cos i; this is a standard trigonometric relation.

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Cite this review

Pith. "Pith review of Stellar obliquities of eight close-in gas giant exoplanets." pith.science (2026). https://pith.science/paper/TTUC6T6P

@misc{pith2026250105615,
  author       = {Pith},
  title        = {Pith review of: Stellar obliquities of eight close-in gas giant exoplanets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TTUC6T6P}},
  note         = {Machine review of arXiv:2501.05615}
}
abstract

The Rossiter-McLaughlin effect allows us to measure the projected stellar obliquity of exoplanets. From the spin-orbit alignment, planet formation and migration theories can be tested to improve our understanding of the currently observed exoplanetary population. Despite having the spin-orbit measurements for more than 200 planets, the stellar obliquity distribution is still not fully understood, warranting additional measurements to sample the full parameter space. We analyze archival HARPS and HARPS-N spectroscopic transit time series of eight gas giant exoplanets on short orbits and derive their projected stellar obliquity $\lambda$. We report a prograde, but misaligned orbit for HAT-P-50b ($\lambda =41^\circ\ ^{+10}_{-9}$), possibly hinting at previous high-eccentricity migration given the presence of a close stellar companion. We measured sky-projected obliquities that are consistent with aligned orbits for the rest of the planets: WASP-48b ($\lambda =-4^\circ\ \pm$ 4), WASP-59b ($\lambda =-1^\circ\ ^{+20}_{-21}$), WASP-140 Ab ($\lambda =-1^\circ\ \pm$ 3), WASP-173 Ab ($\lambda =9^\circ\ \pm$ 5), TOI-2046b ($\lambda =1^\circ\ \pm$ 6), HAT-P-41 Ab ($\lambda =-4^\circ\ ^{+5}_{-6}$), and Qatar-4b ($\lambda =-13^\circ\ ^{+15}_{-19}$). We measure the true stellar obliquity $\psi$ for four systems. We infer a prograde, but misaligned, orbit for TOI-2046b with $\psi=$42$^{+10}_{-8}$\,deg. Additionally, $\psi = 30^\circ\ ^{+18}_{-15}$ for WASP-140 Ab, $\psi = 21^\circ\ ^{+9}_{-10}$ for WASP-173 Ab, and $\psi = 32^\circ\ ^{+14}_{-13}$ for Qatar-4b. The aligned orbits are consistent with slow disk migration, ruling out violent events that would excite the orbits over the history of these systems. Finally, we provide a new age estimate for TOI-2046 of at least 700 Myr and for Qatar-4 of at least 350-500 Myr, contradicting previous results.

Figures

Figures reproduced from arXiv: 2501.05615 by the authors.

Figure 3
Figure 3. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (2 more)
Figure 8
Figure 8. Figure 8: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]
Figure 9
Figure 9. Figure 9: Projected obliquity versus stellar effective temperature. Our targets are plotted with squares. The gray area shows the po￾sition of the Kraft break as derived in Spalding & Winn (2022). The literature values were retrieved from the TEPCat catalogue (Southworth 2011). …

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.