Stellar tidal systematics in apsidal-motion searches for circumbinary planets: CH Ind and SW CMa

Qunfeng Jiang

REVIEW 1 major objections 4 minor 31 references

Stellar tidal systematics in apsidal-motion searches for circumbinary planets: CH Ind and SW CMa

T0 review · 1 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Computing stellar apsidal motion from measured binary dimensions removes the excess that suggested circumbinary planets around CH Ind and SW CMa.

desk verdict A careful, honest re-analysis that removes two apsidal-motion planet candidates, with SW CMa decisive and CH Ind limited by timing precision. read the letter →

arxiv 2608.13269 v1 pith:Q4GH2HD5 submitted 2026-08-13 astro-ph.EP astro-ph.SR

Qunfeng Jiang This is my paper · ORCID

classification astro-ph.EPastro-ph.SR

keywords apsidalmotioncircumbinaryplanetseclipsingbinariesstellarinteriorsapsidal-motionconstantTESSCHIndSWCMa

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

A bulk search of TESS eclipsing-binary timings reported 27 non-transiting circumbinary-planet candidates from excess apsidal motion, but its stellar corrections used catalogue temperatures, main-sequence relations, and a fixed $k_2=0.01$. This paper re-checks two of those candidates, CH Ind and SW CMa, whose component masses and radii have been measured in dedicated studies, by computing the stellar contribution directly. For CH Ind the target-specific prediction of $2.05^{+0.43}_{-0.34}\times10^{-3}\,\mathrm{deg\,cycle^{-1}}$ is consistent with the observed rate of $1.82^{+0.99}_{-0.94}\times10^{-3}\,\mathrm{deg\,cycle^{-1}}$, and for SW CMa the published prediction agrees with the observed rate, leaving neither system with a significant extra prograde component. The paper's message is that bulk search algorithms are useful for selecting candidates but cannot replace target-specific binary models when deciding whether a residual is planetary.

What carries the argument

The load-bearing machinery is the first-order apsidal-motion decomposition $\dot{\omega}_{\rm obs}=\dot{\omega}_{\rm GR}+\dot{\omega}_{\rm rot}+\dot{\omega}_{\rm tide}+\dot{\omega}_{\rm extra}$, with the classical contribution $\dot{\omega}_{\rm CL}=360\,\sum_i k_{2,i}(c_i^{\rm rot}+c_i^{\rm tide})$ containing terms proportional to $(R_i/a)^5$ and to the apsidal-motion constant $k_2$ (the internal-structure constant tabulated by stellar models, twice the fluid Love number). The differential timing variable $D(t)\equiv[(O-C)_{\rm pri}-(O-C)_{\rm sec}]/2$ isolates the apsidal signal from common-mode ephemeris or LTTE trends, and the paper also introduces a radius-sensitivity screen $f_R=[(\dot{\omega}_{\rm obs}-\dot{\omega}_{\rm GR})/\dot{\omega}_{\rm CL,bulk}]^{1/5}$ that flags candidates where an incorrect luminosity class or evolutionary state could dominate the claimed excess.

What would settle it

A longer TESS baseline providing more than six independent sector nodes for CH Ind would test the observed slope: if it moved outside $1.82^{+0.99}_{-0.94}\times10^{-3}$ deg cycle$^{-1}$ by more than the method scatter, the stellar-prediction comparison would change. Separately, independent $k_2$ values from asteroseismic modeling of CH Ind's 46 pulsation frequencies would test the adopted internal-structure constants: if the true $k_2$ pair differs from the inferred values by more than the adopted systematic, the stellar prediction could shift enough to either create a false excess or conceal a real one.

Watch

Extended reading notes

Core claim

The central claim is that the two candidate circumbinary planets identified by the bulk search are not supported once the stellar contributions are computed from measured binary parameters. For CH Ind, a coeval fit to the measured component masses, radii, temperatures, and rotation yields $\dot{\omega}_{\rm stars}=2.05^{+0.43}_{-0.34}\times10^{-3}$ deg cycle$^{-1}$, compared with the observed $\dot{\omega}_{\rm obs}=1.82^{+0.99}_{-0.94}\times10^{-3}$ deg cycle$^{-1}$; the extra component $\dot{\omega}_{\rm extra}=-0.26^{+1.06}_{-1.04}\times10^{-3}$ deg cycle$^{-1}$ is consistent with zero. For SW CMa, the observed rate $0.690\pm0.050\times10^{-3}$ deg cycle$^{-1}$ matches the target-specific prediction $0.670\pm0.020\times10^{-3}$ deg cycle$^{-1}$. The paper therefore concludes that the classical stellar terms in the bulk search were too small by factors of 24 and 16, because the candidate stars are evolved with radii of 2.5–3.0 $R_\odot$ rather than unevolved main-sequence values.

Load-bearing premise

That the two apsidal-motion constants $k_2$ inferred for CH Ind's components are accurate within the adopted 0.05–0.20 dex common uncertainty, even though the coeval stellar model fit does not perfectly reproduce the measured radii and temperatures ($\chi^2=8.79$ for 3 degrees of freedom, $p=0.032$, and the more massive star is observed to be the smaller one).

Editorial extensions

If this is right

CH Ind and SW CMa should be removed from the list of secure (or even probable) circumbinary-planet candidates unless new data revive the excess.
The remaining 25 candidates need the same target-specific treatment: measured masses, radii, rotations, and evolutionary-state-dependent $k_2$ values before a third-body interpretation.
The $f_R$ screen (median 1.97, with 14 of 26 finite cases requiring radius scale factors above 2.0) identifies which candidates are most vulnerable to stellar-radius errors.
A validation hierarchy emerges: component dimensions first, rotation bounds second, a coeval pair of $k_2$ values third, then a covariance-aware timing analysis whose independent units are observing sectors, not individual eclipses.
The reported CH Ind LTTE (2.0 min, 10056 d period) cannot account for the nominal apsidal excess: a circular, nearly coplanar companion at that radius would contribute only about $1.6\times10^{-6}$ deg cycle$^{-1}$, roughly 600 times below the claimed excess.

Reading between the lines

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

Inference: The radius-sensitivity statistic $f_R$ could be used as a ranking metric for follow-up of the entire candidate list, with resources directed first to systems where a modest radius revision could erase the excess (e.g., $f_R\lesssim1.2$); the paper suggests this prioritization but does not fully develop it.
Inference: An independent test of the CH Ind $k_2$ values via asteroseismology (the system pulsates with 46 frequencies) could confirm or refute the adopted internal-structure constants without waiting for a longer timing baseline.
Inference: Extending the $f_R$ screen to a full grid in $k_2$ and rotation could turn it from a screening statistic into a prior for Bayesian model comparison of third-body versus stellar hypotheses.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this paper deserves a serious referee and will probably be accepted after minor revision. It does something useful and does it honestly. The SW CMa re-analysis is the strongest part: using measured dimensions and the published stellar k2, the classical term is 16x larger than the bulk estimate, and the predicted apsidal rate (0.670±0.020) agrees with the observed (0.690±0.050). The excess is 0.020±0.065, i.e. nothing. That alone is a cautionary result for bulk searches.

The CH Ind part is newer but less precise. The author measures a sector-level rate of 1.82+0.99/-0.94 from six independent TESS nodes, and predicts 2.05+0.43/-0.34 from a coeval MESA fit. The two overlap, and the excess is -0.26+1.06/-1.04. That is consistent with no planet, but it is also consistent with the original 1.30±0.10 rate from Thornton et al. The paper cannot reconstruct that rate because the underlying timings were not published, so the discriminating power is low. The stellar fit itself is imperfect too: χ²=8.79 for 3 dof (p=0.032), and the models want the more massive star to be the bigger one, contrary to observation. The author flags all of this explicitly and runs robustness checks (leave-one-out, different detrending, joint model). None of that rescues the precision, but it does mean the negative conclusion is not overclaimed.

The f_R radius-sensitivity screen is a nice lightweight addition, and the paper ships code and data on Zenodo, which is good practice. The SW CMa result is not new in the sense that Claret et al. already published it, but the independent reproduction is useful for validating the method.

Soft spots, proportionately: the CH Ind measurement would need a longer baseline or published individual timings to decide whether the original candidate is truly dead. The paper is honest about this. The Thornton et al. tidal equation typo is a side observation, correctly not central to the argument.

Who is this for: anyone doing apsidal-motion searches or using eclipse timings to claim circumbinary planets. It is a proper cautionary paper that belongs in the literature. I would accept it for peer review.

Referee Report

1 major / 4 minor

Summary. This paper revisits two circumbinary-planet candidates from the bulk apsidal-motion survey of Thornton et al. (2026), using target-specific stellar models. For CH Ind, the author obtains a TESS sector-level apsidal rate of 1.82 +0.99/-0.94 x 10^-3 deg/cycle and a coeval MESA-based stellar prediction of 2.05 +0.43/-0.34 x 10^-3, giving an extra prograde rate of -0.26 +1.06/-1.04 x 10^-3. For SW CMa, the adopted observed rate 0.690 +/- 0.050 matches the published target-specific prediction 0.670 +/- 0.020, with extra rate 0.020 +0.063/-0.066. The author concludes that neither candidate shows a significant prograde excess and that the bulk survey's classical stellar terms were too small by factors of 24 and 16; a radius-sensitivity screen f_R is introduced for all 27 candidates.

Significance. The paper's main contribution is a convincing demonstration that bulk apsidal-motion CBP searches can misattribute classical stellar contributions, because the (R/a)^5 scaling and adopted k2 matter for evolved binaries. The SW CMa branch closes the apsidal budget almost perfectly and is strong. The CH Ind branch is a useful consistency check supported by multiple timing-robustness tests. Strengths include the explicit formula audits, injection tests, machine-readable data and reproducibility statements, and honest discussion of limitations, including the unpublished Thornton timings and the imperfect coeval stellar fit. If accepted as a validation study, it should change how such candidates are followed up.

major comments (1)

[Section 3, Eq. (7)-(8); Conclusion (i)] The CH Ind comparison has limited discriminating power: the 95% non-negative upper limit of 2.28 x 10^-3 deg/cycle exceeds the nominal excess of about 1 x 10^-3 that originally motivated the candidate, so the CH Ind sector-level data alone cannot rule out a companion-induced excess at that level. The paper should state this explicitly and, for completeness, note that taking the published 1.30 +/- 0.10 x 10^-3 rate at face value would give an even more negative residual relative to the stellar prediction, also implying no prograde excess. Adding this sentence would directly address the otherwise unresolved difference between the two observed rates and would make the CH Ind branch a fairer consistency check rather than a precision test.

minor comments (4)

[Section 5, Eq. (10), Table 5, Fig. 3] The f_R values quoted in the text (1.71 for CH Ind, 1.97 for SW CMa) are computed from Thornton et al.'s catalogue rates (CH Ind 1.300, SW CMa 0.850), not from the rates adopted elsewhere in the main analysis (1.82 and 0.690); the table and figure should state this clearly, or the screen should be recomputed with the adopted rates, since the current presentation is confusing.
[Section 3 and SI Table 2] The statement that the nominally more massive component is observed to be the smaller one is important; a short main-text sentence quantifying how this mass-radius reversal affects the k2 posterior would be helpful, even though the separate-star fit already gives a consistent rate.
[Section 4 and SI Section 4] The SW CMa simplified fit has reduced chi-square 4.42 and is used only as a consistency check; the main text should say one sentence explaining why the historical subset is not combined with the adopted Claret et al. rate, since the reader otherwise sees two observed values.
[General] There are formatting placeholders such as 'MNRAS000' in the preprint, and the reference to Torres et al. 2010 should be formatted as A&ARv; these should be corrected in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the stellar apsidal predictions are built from external MESA structure constants and independently measured binary dimensions, with no fitted parameter drawn from the observed apsidal rates.

full rationale

The paper's derivation chain is self-contained against an external benchmark. For both targets, the observed apsidal rate comes from eclipse timings (Eq. 7 for CH Ind; Eq. 9 from Claret et al. 2021 for SW CMa), while the stellar prediction is computed from Sterne (1939) classical coefficients (Eqs. 4-6) using masses, radii, eccentricity, and rotation from dedicated binary studies (Liakos 2025; Torres et al. 2012). The only fitted parameters, the CH Ind sector jitter and the coeval MESA age and metallicity, are fit to the timing nodes and to the measured masses, radii, and temperatures respectively; neither fit uses the observed apsidal rate, so the stellar prediction cannot be a disguised re-statement of the observation. The CH Ind k2 values come from Claret (2023) MESA grids constrained by component dimensions, not from omega_dot_obs. For SW CMa, both the prediction (0.670±0.020) and the observation (0.690±0.050) originate from Claret et al. (2021), but the paper breaks any benchmark-dependency loop by independently recomputing the stellar term from Torres et al. (2012) parameters and a separately published theoretical k2bar, obtaining 0.664, within 0.87 per cent of the Claret et al. (2021) prediction, and by explicitly stating that the k2bar was a stellar-model prediction, not a value inferred from the observed apsidal rate. There are no self-citations (the sole author cites no prior work of their own) and no uniqueness or ansatz arguments are imported from the author's prior work. The limitations the skeptic's headline identifies, the poor CH Ind coeval fit (chi^2 = 8.79 for 3 dof, p = 0.032), the unreconciled Thornton et al. (2026) value of 1.30±0.10, and the large uncertainty of the new CH Ind rate, are genuine concerns about statistical power and model quality, but they are correctness risks, not circularity: no equation reduces to its own input, and no fitted parameter is renamed as a prediction. The honest finding is no significant circularity (score 0).

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim depends on standard celestial mechanics, external stellar models, and measured binary parameters, plus several hand-chosen sensitivity allowances. There are no new physical entities. The most fragile inputs are the CH Ind k2 values from a coeval MESA fit with imperfect goodness of fit and the assumed synchronous rotation; both are acknowledged and bracketed by sensitivity tests.

free parameters (5)

Common log k2 systematic offset (CH Ind) = 0.08 dex, tested at 0.05, 0.10, 0.15, 0.20 dex
Added as one shared shift to both k2 values in each Monte Carlo draw. The paper explicitly states it is a sensitivity assumption, not a measured model error, and it directly widens the stellar apsidal prediction.
CH Ind spin ratio Omega/n = 1.0 +/- 0.1
Assumed near-synchronous rotation for both components with no measured stellar rotation. It enters the rotational apsidal term of 0.193e-3 deg per cycle and is stated as a sensitivity assumption in Section 3 and Supporting Information section 3.
CH Ind coeval age and metallicity grid = Age posterior median 1.240 Gyr; solar-metallicity grid weight 0.925
Fitted to the measured masses, radii, and temperatures while enforcing shared age and composition. The best fit has chi-square 8.79 for 3 degrees of freedom, so the resulting k2 values are model-dependent estimates.
Sector jitter j = 0.20 min at 50th percentile, 0.79 min at 95th percentile for the preferred variant
Shared non-negative jitter fitted to the six differential CH Ind timing nodes and marginalized in the reported posterior. It is a nuisance parameter but affects the observed-rate uncertainty.
SW CMa common log k2 systematic = 0.05 dex
Hand-chosen conservative allowance added around the Claret et al. (2021) theoretical log k2_bar of -2.581 +/- 0.015. It enters the SW CMa excess posterior and is described as a sensitivity allowance, not an empirical calibration.

assumptions (4)

domain assumption The apsidal-motion equations of Sterne (1939) and Gimenez (1985), with aligned spins and first-order eccentricity, describe the observed eclipse-timing drift.
The entire decomposition uses equations (1) through (6). Inclination and higher-order eccentricity terms are asserted to be below current sector-level timing uncertainty.
domain assumption The two components of CH Ind formed together and share age and metallicity.
Enforced in the k2 inference. Physically standard for a binary, but the best fit has p=0.032 and inverts the mass-radius ordering, so the assumption is not fully satisfied by the data.
domain assumption MESA stellar models from Claret (2023) provide reliable apsidal constants k2 for terminal-age main-sequence stars when interpolated in mass and age at fixed metallicity.
Adopted without an independent k2 measurement. The paper adds an ad hoc 0.05 to 0.20 dex common systematic precisely because this reliability is unverified.
domain assumption TESS Quick-Look Pipeline photometry and empirical eclipse templates recover eclipse centers with the quoted uncertainties.
Robustness tests cover detrending variants and frequency cleaning, but no independent photometry pipeline is used to validate the absolute timing scale.

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Cite this review

Pith. "Pith review of Stellar tidal systematics in apsidal-motion searches for circumbinary planets: CH Ind and SW CMa." pith.science (2026). https://pith.science/paper/Q4GH2HD5

@misc{pith2026260813269,
  author       = {Pith},
  title        = {Pith review of: Stellar tidal systematics in apsidal-motion searches for circumbinary planets: CH Ind and SW CMa},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q4GH2HD5}},
  note         = {Machine review of arXiv:2608.13269}
}

abstract

Thornton et al. (2026) reported 27 non-transiting circumbinary-planet candidates from excess apsidal motion in TESS eclipsing-binary timings. The classical stellar contribution is sensitive to target-specific radii, apsidal constants $k_2$, and rotation. We re-evaluate two evolved, double-lined eclipsing binaries in that sample: the pulsating system CH Ind and the Am system SW CMa. Their component masses and radii have been measured in dedicated binary studies, allowing the stellar contribution to be calculated directly. For CH Ind, six independent TESS sector nodes give $\dot{\omega}_{\rm obs}=1.82^{+0.99}_{-0.94}\times10^{-3}\ {\rm deg\,cycle^{-1}}$, while a coeval fit to the measured binary components predicts $\dot{\omega}_{\rm stars}=2.05^{+0.43}_{-0.34}\times10^{-3}\ {\rm deg\,cycle^{-1}}$. For SW CMa, its measured dimensions raise the classical term by a factor of about 16; the published target-specific prediction, $0.670\pm0.020\times10^{-3}\ {\rm deg\,cycle^{-1}}$, agrees with the observed $0.690\pm0.050\times10^{-3}\ {\rm deg\,cycle^{-1}}$. Neither system shows a significant excess prograde component. The comparison shows that candidates from a bulk search require target-specific binary models before a third-body interpretation is assigned.

Figures

Figures reproduced from arXiv: 2608.13269 by the authors.

**Figure 2.** CH Ind timing and inference. Top: the six differential nodes 𝐷 from equation (1); subtracting primary and secondary O–C values removes their common ephemeris or LTTE trend and isolates the first-order apsidal signal. Bottom: Monte Carlo posteriors for the displayed 0.08-dex common log 𝑘2 systematic; horizontal segments show central 68 per cent intervals. Alt text: CH Ind differential eclipse timings and posterior di… view at source ↗

**Figure 3.** Radius-sensitivity screen for the 27 final candidates of Thornton et al. (2026), sorted by 𝑓𝑅. CH Ind and SW CMa are highlighted; the arrow marks the object whose bulk classical term was rounded to zero. The statistic holds 𝑘2, rotation, and component weights fixed and is a prioritization aid, not a reclassification. Alt text: Required stellar-radius scale factors for the 27 candidates, highlighting CH Ind and SW CM… view at source ↗

Figures from the paper (3 more)

**Figure 1.** Figure 1: Left: leave-one-sector-out CH Ind rates. Right: sensitivity to the adopted common log 𝑘2 systematic. 0.4 min and an outer period of 10 056 ± 1020 d. Using 𝑀1 + 𝑀2 = 3.67 M⊙, the central values give 𝑎AB sin 𝑖3 = 𝑐𝐴LTTE = 0.240 au, (5) 𝑓 (𝑀3) = 4𝜋 2 (𝑎AB sin 𝑖3) 3 𝐺𝑃2 3 …

**Figure 2.** Figure 2: SW CMa unit test using the effective classical total. The calculation agrees with the published prediction to within one per cent. dard result. Thus the published classical values 0.070 and 0.020 × 10−3 deg cycle−1 would become 0.079 and 0.0267 ×10−3 deg cycle−1 if the…

**Figure 3.** Figure 3: SW CMa eclipse timings relative to the secondary-eclipse phase at the reference epoch. Open points are low-precision photographic minima; filled points are the precise historical subset, and diamonds are sector-level TESS differences. The preferred rate is the full tar…

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Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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2026 , volume =

Detection of 27 candidate circumbinary planets through apsidal precession of eclipsing binaries observed by TESS , journal =. 2026 , volume =

work page 2026

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2011 , volume =

Kepler-16: A Transiting Circumbinary Planet , journal =. 2011 , volume =

work page 2011

[3] [3]

2021 , volume =

TIC 172900988: A Transiting Circumbinary Planet Detected in One Sector of TESS Data , journal =. 2021 , volume =

work page 2021

[4] [4]

2015 , volume =

Circumbinary planets - why they are so likely to transit , journal =. 2015 , volume =

work page 2015

[5] [5]

2023 , volume =

Radial-velocity discovery of a second planet in the TOI-1338/BEBOP-1 circumbinary system , journal =. 2023 , volume =

work page 2023

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MNRAS , year =

A 5 M _. MNRAS , year =

work page

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1968 , volume =

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1939 , volume =

Apsidal motion in binary stars , journal =. 1939 , volume =

work page 1939