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

This paper re-evaluates two evolved, double-lined eclipsing binaries from the 27 non-transiting circumbinary-planet candidates reported by Thornton et al. (2026), which were identified from excess apsidal motion in TESS eclipsing-binary timings. The two systems examined are CH Ind (a pulsating system) and SW CMa (an Am system), both of which have component masses and radii measured in dedicated binary studies, allowing the stellar contribution to apsidal motion to be calculated directly rather than estimated from bulk relations.

The author downloaded TESS light curves from the Quick-Look Pipeline and measured every usable primary and secondary eclipse. For CH Ind, six independent TESS sector nodes give an observed apsidal rate of:

omega¤ obs = 1.82+0.99−0.94 × 10−3 deg cycle−1

The analysis decomposes the observed rate into general relativity, rotation, tidal, and extra components: omega¤ obs = omega¤ GR + omega¤ rot + omega¤ tide + omega¤ extra. The classical rate depends on the apsidal-motion constant k2, component radii, masses, eccentricity, and spin.

CH Ind is a P = 5.95257-d eccentric binary with component masses (1.82 ± 0.01, 1.85 ± 0.02) M⊙ and radii (3.05 ± 0.09, 2.79 ± 0.09) R⊙. Both stars are close to the terminal-age main sequence. The author infers k2 values from MESA evolutionary grids with a shared age and metallicity, obtaining posterior medians of k2,1 = 0.00272 and k2,2 = 0.00243. The component budget is GR 0.396, rotation 0.193, and tides 1.465, yielding:

omega¤ stars = 2.05+0.43−0.34 × 10−3 deg cycle−1

Combining the observed and stellar rates gives omega¤ extra = −0.26+1.06−1.04 × 10−3 deg cycle−1. The excess is not detected. Conditioning on a non-negative prograde term gives omega¤ extra < 2.28 × 10−3 deg cycle−1 at 95 per cent credibility. The paper notes that the target-specific stellar prediction is consistent with the sector-level TESS measurement and CH Ind therefore shows no evidence for an additional apsidal contribution.

The paper also addresses the tentative 2.0-min light-travel-time effect reported by Thornton et al. (2026) with a period of 10 056 d, which corresponds to a minimum companion mass of 0.063 M⊙. Such a companion would contribute only 1.6 × 10−6 deg cycle−1 and could not account for the nominal apsidal excess.

SW CMa is an evolved, eccentric, double-lined Am binary with P = 10.091988 d. Torres et al. (2012) measured masses (2.239 ± 0.014, 2.104 ± 0.018) M⊙ and radii (3.014 ± 0.020, 2.495 ± 0.042) R⊙. The rotation rates correspond to Ω/n = 1.59 and 0.80, so neither synchronous nor pseudo-synchronous prescriptions are adequate.

Using the theoretical coefficient-weighted value log k̄2 = −2.582 ± 0.050, the result is GR 0.345 × 10−3 deg cycle−1 plus a total classical contribution of 0.319 × 10−3 deg cycle−1, or 0.664 × 10−3 deg cycle−1 in total. This reproduces the target-specific 0.670 ± 0.020 × 10−3 deg cycle−1 prediction of Claret et al. (2021) to 0.87 per cent. By contrast, the bulk search used GR 0.253 × 10−3 deg cycle−1 and classical 0.020 × 10−3 deg cycle−1, with the latter underestimated by a factor of 15.97.

The observed rate from Claret et al. (2021) is omega¤ obs = 0.690 ± 0.050 × 10−3 deg cycle−1, consistent with the stellar prediction. Combining gives omega¤ extra = 0.020+0.063−0.066 × 10−3 deg cycle−1 and a non-negative prograde 95 per cent upper limit of 0.14 × 10−3 deg cycle−1. The paper concludes the excess reported by Thornton et al. (2026) is not significant.

The paper emphasizes that Neither proposed excess remains significant after target-specific stellar subtraction. In both cases, the change comes from the stellar budget rather than the timing signal itself. The bulk search underestimated classical terms by factors of 24 and 16 for CH Ind and SW CMa respectively, primarily because the classical coefficients contain (R/a)5, so radius factors of 1.5, 1.8, and 2.0 multiply the result by 7.6, 18.9, and 32. The fixed k2 = 0.01 used in the bulk search is about four times the target-specific CH Ind values. The GR estimates were also about 27 per cent below target-specific values, corresponding to total masses near 63 per cent of measured values.

The paper introduces a radius-sensitivity diagnostic for all 27 candidates:

f R = (omega¤ obs − omega¤ GR)/omega¤ CL,bulk

Of 26 finite cases, the median is 1.97; one, three, and 14 objects have f R ≤ 1.2, 1.5, and 2.0 respectively. CH Ind and SW CMa have f R = 1.71 and 1.97.

(i) CH Ind's target-specific stellar prediction is consistent with the sector-level TESS measurement; no additional prograde apsidal contribution is detected. (ii) SW CMa's published target-specific theory and observed long-baseline rate already agree, and the bulk search underestimated its classical term by a factor of about 16. (iii) Apsidal-motion surveys can efficiently select CBP targets, but confirmation requires component-level binary parameters and an evolutionary stellar model; the f R screen provides a lightweight way to prioritize that work.

Improvements to AI Systems:

1. Target-Specific Stellar Modeling Integration

• Improve AI systems to automatically compute apsidal-motion constants (k 2) from evolutionary stellar models (e.g., MESA grids) using component masses, radii, and metallicity, rather than assuming fixed values (e.g., k 2 = 0.01).

• The improved system can generate posterior distributions of k 2 for each binary component, incorporating age and metallicity constraints, and propagate these uncertainties into apsidal-motion predictions.

2. Radius-Sensitivity Screening for Candidate Prioritization

• Implement the f R diagnostic as an automated filter for circumbinary-planet (CBP) candidates.

• The improved AI can compute f R = [(obs - GR)/ CL,bulk] 1/5 for each candidate, flag those with f R > 2 as high-priority for detailed follow-up, and rank candidates by the likelihood of a genuine excess after accounting for radius uncertainties.

3. Decomposition of Apsidal Motion into Physical Components

• Enhance AI systems to separate observed apsidal rates into general relativity, rotation, tidal, and extra components, using measured spin rates and eccentricity rather than assuming synchronous rotation.

• The improved system can automatically detect cases where rotation is non-synchronous (e.g., /n not equal to 1) and adjust predictions accordingly, reducing false positives from bulk assumptions.

4. Uncertainty-Aware Excess Detection

• Upgrade AI systems to combine observed and theoretical apsidal rates with full covariance, producing posterior distributions for extra and conditioning on non-negative prograde terms for upper limits.

• The improved system can output 95% credibility bounds for excess apsidal motion, distinguishing no detection from tentative detection with quantitative rigor.

5. Bulk-Search Calibration via Target-Specific Validation

• Use validated systems (CH Ind, SW CMa) to recalibrate bulk-search parameters (e.g., k 2, classical term coefficients) in AI-driven surveys.

• The improved AI can automatically adjust its internal stellar models to match target-specific predictions, reducing systematic underestimates (e.g., factors of 24 and 16 in classical terms) across large candidate samples.

6. Automated Light-Curve Timing and Apsidal Fitting

• Improve AI pipelines to measure all usable primary and secondary eclipses from TESS light curves, fitting apsidal rates per sector with robust error bars.

• The improved system can flag systems where sector-level measurements are consistent with target-specific stellar predictions, avoiding false CBP claims from timing-only analyses.

7. Companion Mass Constraint Integration

• Enhance AI to incorporate light-travel-time effects (LTTE) from potential companions into apsidal-motion models, computing the maximum apsidal contribution from a given companion mass and period.

• The improved system can automatically reject candidates where the LTTE-induced apsidal term is negligible compared to the observed excess, as in CH Ind (1.6 × 10−6 deg cycle−1 vs. 10−3 scale).

8. Evolutionary Consistency Checking

• Add a module that verifies component radii, masses, and ages against stellar evolutionary tracks, ensuring that inferred k 2 values are physically plausible.

• The improved AI can detect inconsistencies (e.g., radii implying terminal-age main sequence but masses suggesting younger ages) and flag them for manual review.

What the Improved AI System Can Do:

• Automatically screen all 27 CBP candidates using f R and target-specific stellar models, prioritizing those with genuine excesses for follow-up.

• Provide rigorous, uncertainty-aware upper limits on additional apsidal contributions, reducing false positives in exoplanet searches.

• Recalibrate large-scale binary surveys using validated systems, improving efficiency by factors of 10–30 in classical-term accuracy.

• Deliver transparent, physically interpretable apsidal-motion decompositions for any eclipsing binary with TESS data, enabling rapid classification of pulsating, Am, or other stellar types.

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 obs=1.82+0.99-0.94 times10-3 deg,cycle-1, while a coeval fit to the measured binary components predicts stars=2.05+0.43-0.34 times10-3 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 plus or minus0.020 times10-3 deg,cycle-1, agrees with the observed 0.690 plus or minus0.050 times10-3 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.