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Updated Mass, Eccentricity, and Tidal Heating Constraints for the Earth-sized Planet LP 791-18 d

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read New transit timings halve the mass uncertainty of the Earth-sized exoplanet LP 791-18 d and show that its reported eccentricity, the basis for volcanic-heating predictions, was a fitting artifact — a question JWST secondary-eclipse timing…

desk verdict Solid TTV follow-up that halves the mass uncertainty of LP 791-18 d and exposes a parameterization bias in the prior mass/eccentricity claims, though the headline precision gain leans on a physically motivated but data-indifferent eccentricity prior. read the letter →

arxiv 2501.18700 v1 pith:6JW2AKA6 submitted 2025-01-30 astro-ph.EP

Michael Greklek-McKeon , Heather A. Knutson , W. Garrett Levine , Renyu Hu , Morgan Saidel , Jonathan Gomez Barrientos , Konstantin Batygin , Björn Benneke This is my paper · ORCID
classification astro-ph.EP
keywords LP791-18dtransittimingvariationstidalheatingeccentricitysecondaryeclipseMdwarfexoplanetsEarth-sizedplanetsJWST
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

LP 791-18 d is one of only a handful of temperate, Earth-sized planets known outside the solar system, and earlier work suggested its slightly eccentric orbit would tidally heat its interior enough to drive volcanic outgassing. This paper adds three high-precision transit timings of its outer companion, LP 791-18 c, and re-fits the whole timing data set. The updated mass is $M_d = 0.91 \pm 0.19\,M_\oplus$, reducing the uncertainty by more than a factor of two. The authors also find that the small non-zero eccentricities reported by the earlier study were an artifact of how the fit parameterized the orbit: with an unbiased parameterization and a physically motivated tidally-damped prior, the orbits are consistent with circular. The current data cannot distinguish this damped state from a higher-eccentricity state, but the paper shows that a single JWST secondary eclipse timing measurement can settle the question.

What carries the argument

The argument rests on three linked pieces of machinery. The first is the TTVFast n-body model, which converts the planet-star mass ratios and osculating orbital elements into transit times; the new data extend the baseline by about three years and reach sub-6-second precision, making them the most precise timing measurements of this system. The second is the eccentricity parameterization: fitting $e\cos\omega$ and $e\sin\omega$ imposes an effective linear prior on $e$ whose correction slightly overweights low eccentricity, producing spurious small non-zero values, whereas the $\sqrt{e}\cos\omega$ and $\sqrt{e}\sin\omega$ parameterization recovers a uniform prior. The third is the tidally damped free-eccentricity prior, constructed by running short REBOUND simulations at each MCMC step to split the osculating eccentricity into forced and free parts and then penalizing free eccentricities away from zero. The paper's decisive output is the predicted secondary-eclipse timing offset $\Delta t = 2P e\cos\omega/\pi$, which translates the two eccentricity solutions into observationally distinguishable predictions.

What would settle it

Measure the secondary eclipse of LP 791-18 d with JWST: the damped model predicts a timing offset of $-0.2^{+2.0}_{-2.7}$ minutes relative to a circular orbit, while the undamped model predicts $-117^{+41}_{-47}$ minutes, so an observed offset with magnitude greater than roughly 10–15 minutes would rule out the tidally damped state and an offset consistent with zero would confirm it.

Watch

Extended reading notes

Core claim

The paper's central claim is that the three new Palomar/WIRC transit observations of LP 791-18 c, with timing precisions of 3–6 seconds, tighten the dynamical constraints on the innermost Earth-sized planet and expose a bias in the earlier analysis. Re-fitting the complete set of transit times with the TTVFast n-body model, the authors obtain $M_d = 0.91 \pm 0.19\,M_\oplus$ under the tidally damped prior and $M_d = 0.98^{+0.29}_{-0.25}\,M_\oplus$ without it. When the eccentricity is parameterized as $\sqrt{e}\cos\omega$ and $\sqrt{e}\sin\omega$ rather than $e\cos\omega$ and $e\sin\omega$, the previously reported values $e_d \approx 0.0015$ and $e_c \approx 0.0008$ collapse to values consistent with zero, leading the authors to conclude those earlier detections were artifacts of the chosen parameterization. Absent the damped prior, the data instead prefer $e_d = 0.056^{+0.015}_{-0.014}$ and $e_c = 0.062^{+0.017}_{-0.014}$. The two models fit the current timing data almost equally well ($\Delta$BIC $= -1.3$), so the paper's main forward prediction is the secondary eclipse timing offset: essentially zero minutes for the damped state versus roughly $-117$ minutes for the undamped state. An observed offset larger than about 10–15 minutes would confirm that tidal damping has not yet circularized the orbit and would make LP 791-18 d a much stronger volcanic candidate.

Load-bearing premise

The load-bearing premise is that tidal damping has already reduced the planets' free eccentricities to near zero, so the observed eccentricity equals only the small forced value; if tidal dissipation is actually weak ($Q' \gtrsim 10^4$) or the system was recently disturbed, the data equally allow $e_d \approx 0.056$ and a tidal heat flux orders of magnitude larger.

Editorial extensions

If this is right

  • If the tidally damped solution is correct, LP 791-18 d's orbit is effectively circular and its tidal heat flux, while small, is still large enough to matter for silicate melting and planetary evolution, consistent with the earlier Io-like interpretation.
  • If the undamped solution is correct, the tidal heat flux is comparable to the insolation flux, the interior temperature rises by roughly 145 K, and LP 791-18 d becomes a much more compelling target for volcanic outgassing, similar to L 98-59 d.
  • JWST secondary eclipse timing can decide between the two: a measured eclipse offset of more than about 10–15 minutes rules out the tidally damped state and constrains the tidal quality factor $Q'$.
  • The improved mass constraint, $M_d = 0.91 \pm 0.19\,M_\oplus$, places LP 791-18 d on an Earth-like rock-iron composition track and confirms it has at most a modest hydrogen envelope of roughly 2–2.5% by mass.

Reading between the lines

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

  • The same parameterization bias identified here may affect other TTV studies that report small non-zero eccentricities near the detection threshold; re-running those fits with $\sqrt{e}$-type parameters could revise eccentricity estimates without any new data.
  • If JWST returns an intermediate eclipse offset, it would map $e\cos\omega$ continuously and, combined with the TTV mass constraint, could turn LP 791-18 d into a calibrated probe of terrestrial tidal dissipation across $Q'$ values.
  • The age of the system is a hidden lever: if LP 791-18 is older than roughly 1 Gyr, retaining a free eccentricity would require even larger $Q'$ values (weaker dissipation) or a recent dynamical disturbance such as a stellar flyby, a scenario the paper mentions only in passing.
  • Should the eclipse timing confirm the damped state, the TTVs' inability to sense $e \lesssim 0.01$ means the forced eccentricity of about 0.0015 remains the relevant value for tidal heating, leaving the volcanic-outgassing question to atmospheric observations rather than dynamics.
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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

3 major / 5 minor

Summary. The paper presents three new Palomar/WIRC diffuser-assisted transit observations of LP 791-18 c, with timing precisions of 6, 4, and 3 seconds, and combines them with the published P23 transit-timing dataset. The authors fit the combined TTV data with TTVFast, first reproducing P23's results, then switching from the ecos(ω)/esin(ω) parameterization to a √e cos(ω)/√e sin(ω) parameterization with and without a tidally damped free-eccentricity prior. Under the damped prior they find M_d = 0.91 ± 0.19 M⊕ and eccentricities consistent with zero (e_d = 0.0011^{+0.0010}_{-0.0008}); under a uniform eccentricity prior they find M_d = 0.98^{+0.29}_{-0.25} M⊕ and e_d = 0.056^{+0.015}_{-0.014}. They use these results to revise tidal heating estimates and to predict JWST secondary-eclipse timing offsets that can discriminate between the damped and undamped states.

Significance. If the results hold, the paper delivers a significantly improved mass constraint for a temperate Earth-sized planet, identifies a bias in the previously reported P23 eccentricities, and produces a concrete, testable JWST prediction that separates two very different tidal-heating scenarios. The analysis is generally careful: the authors validate their TTV model by reproducing P23's solution, use a well-tested n-body code, check that an e=0 model fits within the timing precision, and are transparent about the two eccentricity priors. However, the headline mass-precision improvement is conditional on a prior that the data do not actually prefer, so the significance statement must be framed with that caveat. The extraneous inserted text in the manuscript is a separate but serious issue.

major comments (3)
  1. [Abstract and §5] The headline claim 'We reduce the mass uncertainty by more than a factor of two (M_d = 0.91 ± 0.19 M⊕)' is obtained under the tidally damped free-eccentricity prior described in §3.2. The uniform-eccentricity fit in §3.3 yields M_d = 0.98^{+0.29}_{-0.25} M⊕, only a ~1.5× improvement over P23's width, and the BIC comparison there gives ΔBIC = −1.3, i.e., the data slightly favor the undamped model. As stated, the abstract and summary overstate what is robustly measured. Please qualify the claim (e.g., 'under the tidally damped-state prior') and report both mass constraints prominently.
  2. [Full text, between §5 and Acknowledgments] The manuscript contains a large extraneous passage beginning 'Volcanism on Exoplanets 9' that includes equations numbered (13) and (14), a discussion of HST observations of L 98-59, and parameter values (M1 = 2.2 M⊕, P2 = 7.45 d) that have nothing to do with LP 791-18. This appears to be an accidentally included fragment from another paper (likely Seligman et al. 2023). It must be removed; as submitted, the manuscript is not a coherent paper.
  3. [§3.1] The statement that 'the originally reported values from P23 were an artifact of the chosen e and ω parameterization' is only established for fits that also impose the tidally damped free-eccentricity prior. Under the uniform eccentricity prior, the updated fit still returns e_d = 0.056^{+0.015}_{-0.014} and e_c = 0.062^{+0.017}_{-0.014} (Table 2, §3.3), so the non-zero eccentricities are not purely a parameterization artifact. Please restrict the 'artifact' claim to the damped case, as §5 does.
minor comments (5)
  1. [§1] Introductory paragraph contains a duplicated word: 'with amplitudes of ~2.5 min and ~0.5 min for for planets c and d, respectively'.
  2. [§3.1] The sentence 'As originally noted by Ford (2006), fitting for esin(ω) and esin(ω) results...' should read 'fitting for ecos(ω) and esin(ω)'.
  3. [Table 2] The damped-fit period for LP 791-18 c is printed as '4.9899100+0.0000012−0.0000014'; this should be formatted with a reasonable number of decimal places (e.g., 4.98991 ± 0.0000013).
  4. [Figure 6 caption] The caption says 'using 104 draws from the period, e, and ω distributions'; this should be 10^4 draws to be unambiguous.
  5. [§6 Acknowledgments] The software list credits 'Claude 3.5 Sonnet' without specifying its role; if an AI assistant was used for code or text, please state its contribution explicitly, and if not, remove it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central mass constraint is data-driven and the prior-dependence is transparently disclosed.

full rationale

The updated mass constraint is derived from new Palomar/WIRC transit timings fit with the TTVFast n-body model, and the reported posteriors (damped: M_d = 0.91 ± 0.19 M⊕; undamped: M_d = 0.98+0.29−0.25 M⊕) are likelihood results rather than quantities defined in terms of the eccentricity prior by construction. The tidally damped eccentricity prior is an explicitly stated assumption inherited from P23 and re-implemented by the authors with independent 6-month REBOUND simulations in §3.1, so it is not a self-citation used as proof. The paper also reports the non-damped fit and quotes ΔBIC = -1.3, acknowledging that the data do not prefer the damped model (§3.3). The claim that P23's small nonzero eccentricities were a parameterization artifact is supported by an internal re-fit using √e cos(ω) and √e sin(ω), not by citation alone. The JWST secondary-eclipse timing forecast is a standard propagation of fitted (e, ω, P) through ∆t = 2P ecosω/π; it is a genuine prediction for future observations, not a fitted input relabeled as a prediction. Self-citations—Greklek-McKeon et al. (2023) for the transit modeling framework, Peterson et al. (2023) for data and the physical prior, and Puranam & Batygin (2018) for the tidal circularization timescale—are methodological or are re-derived in this work, and none is load-bearing for the central mass claim. The prior sensitivity of the headline factor-of-two precision gain is a real statistical caveat, but it is disclosed in the body of the paper and does not constitute logical circularity.

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

The TTV fit contains standard dynamical model parameters; the only assumption that materially changes the scientific conclusion is the damped eccentricity prior. No new physical entities are introduced.

free parameters (4)
  • Planet mass ratio M_d/M* (converted to M_d) = 0.91 ± 0.19 M⊕ (damped), 0.98 +0.30/-0.25 M⊕ (undamped)
    Primary target of the TTV fit; the mass uncertainty is reduced by more than a factor of two with the new WIRC timings.
  • Planet mass ratio M_c/M* = 7.16 ± 0.65 M⊕ (damped), 8.87 +1.43/-1.46 M⊕ (undamped)
    Mass of the perturbing sub-Neptune, fitted jointly in the TTV model.
  • Eccentricity e_d = 0.0011 +0.0010/-0.0008 (damped), 0.056 +0.015/-0.014 (undamped)
    Constraints on planet d's eccentricity; the value depends strongly on the eccentricity prior.
  • Eccentricity e_c = 0.0001 ± 0.0001 (damped), 0.062 +0.017/-0.014 (undamped)
    Eccentricity of planet c from the same TTV fit.
assumptions (4)
  • domain assumption Planet b is neglected in the TTV model because its predicted effect on transit times is less than one second, independent of planet masses.
    Section 3: 'we did not include planet b in the TTV analysis because the predicted amplitude of its TTVs and its predicted impact on the TTVs of planets c and d are less than one second, independent of the planet masses.' If this assumption fails, the inferred masses could shift.
  • domain assumption Planets d and c are edge-on with negligible mutual inclination, so inclinations can be fixed to 90 degrees and the longitude of ascending node set arbitrarily.
    Section 3: 'we fixed the planetary orbital inclinations to 90 degrees, since the transit fits indicate that planets d and c have a low mutual inclination and are very close to edge-on.' A non-negligible mutual inclination would break this simplification.
  • ad hoc to paper Tidally damped free eccentricity prior: free eccentricities of d and c are Gaussian centered at zero with sigma 0.001 and 0.0001 respectively.
    Section 3.2 imposes this prior from P23's REBOUND simulations. The eccentricity posterior in the damped case essentially reflects this prior; the undamped fit gives e_d = 0.056.
  • domain assumption Stellar mass and radius from P23 are correct.
    Section 2.2: 'We adopted stellar parameters from P23.' These convert fitted mass ratios to physical masses and radii.

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Cite this review

Pith. "Pith review of Updated Mass, Eccentricity, and Tidal Heating Constraints for the Earth-sized Planet LP 791-18 d." pith.science (2026). https://pith.science/paper/6JW2AKA6

@misc{pith2026250118700,
  author       = {Pith},
  title        = {Pith review of: Updated Mass, Eccentricity, and Tidal Heating Constraints for the Earth-sized Planet LP 791-18 d},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6JW2AKA6}},
  note         = {Machine review of arXiv:2501.18700}
}
abstract

LP 791-18 d is a temperate Earth-sized planet orbiting a late M dwarf, surrounded by an interior super-Earth (LP 791-18 b, $R_P$ = 1.2 $R_{\oplus}$, $P=0.95$ days) and an exterior sub-Neptune (LP 791-18 c, $R_P$ = 2.5 $R_{\oplus}$, $P=4.99$ days). Dynamical interactions between LP 791-18 d and c produce transit timing variations (TTVs) that can be used to constrain the planet masses and eccentricities. These interactions can also force a non-zero eccentricity for LP 791-18 d, which raises its internal temperature through tidal heating and could drive volcanic outgassing. We present three new transit observations of LP 791-18 c with Palomar/WIRC, including the most precise TTV measurements ($<$ 6 seconds) of this planet to date. We fit these times with a TTV model to obtain updated constraints on the mass, eccentricity, and tidal heat flux of LP 791-18 d. We reduce the mass uncertainty by more than a factor of two ($M_d$ = 0.91 $\pm$ 0.19 $M_{\oplus}$). We perform an updated fit assuming tidally damped free eccentricities and find $e_d = 0.0011^{+0.0010}_{-0.0008}$ and $e_c = 0.0001 \pm 0.0001$, consistent with circular orbits. We find that the observed TTVs are not sensitive to $e \leq$ $\sim$0.01. Without a tidally damped eccentricity prior, $e_d = 0.056^{+0.015}_{-0.014}$, much higher than the eccentricity predicted by n-body simulations incorporating the effects of dynamical excitation and tidal damping. We predict the timing of upcoming JWST secondary eclipse observations for LP 791-18 d, which could tightly constrain the eccentricity and tidal quality factor of this Earth-sized exoplanet.

Figures

Figures reproduced from arXiv: 2501.18700 by the authors.

Figure 1
Figure 1. Detrended Palomar/WIRC light curves for the three transit observations of LP 791-18 c (upper panels) and residuals after the best-fit transit light curve has been subtracted (lower panels). Unbinned data are shown as grey circles, with 10 minute binned points overplotted as black circles. The best joint-fit transit models are overplotted as red lines, with red shading to indicate the 1σ uncertainties on the transit … view at source ↗
Figure 2
Figure 2. The posterior probability density distribution of planetary eccentricities for LP 791-18 d and c with a fit to the TTV data of P23 using a tidally damped-state eccentricity prior and parameterizing e and ω as √ e cos(ω) and √ e sin(ω). We obtained results consistent within 1σ to those re￾ported in P23 for all fit parameters with this damped￾state eccentricity model framework. When we repeated the TTV analysis withou… view at source ↗
Figure 3
Figure 3. TTVs from the ground-based follow-up campaign of P23 (black circles) including the high-precision Spitzer observa￾tions (gray squares), and our new Palomar/WIRC follow-up observations (orange stars), with 100 random posterior draws from our damped eccentricity TTV model (red) and free eccentricity TTV model (blue) for LP 791-18 c (top panel) and d (bottom panel). Our Palomar/WIRC timing measurements for LP 791-18 c … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Posterior distributions for the masses and eccentricities of LP 791-18 d and c from a fit to the updated set of TTV observations in the case of a tidally damped free eccentricity prior (red), and a uniform eccentricity prior (blue). If we assume that the eccentricities…
Figure 7
Figure 7. Figure 7: Mass-radius diagram for LP 791-18 d (square) and c (triangle), with updated measurements from this work (filled markers from the damped eccentricity TTV results, open markers for the free eccentricity TTV results) compared to the mass constraints from P23 (gray markers…
Figure 8
Figure 8. Figure 8: Corner plot of posteriors for TTV model parameters for LP 791-18 d and c from the damped eccentricity (red) and undamped (blue) versions of the TTV fit, made with the corner package (Foreman-Mackey 2016). Fit parameters included planet-to-star mass ratios but we have c…

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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