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Confirmation of a non-transiting planet in the habitable zone of the nearby M dwarf L 98-59

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper confirms L 98-59f as a non-transiting planet in the habitable zone of the nearby M dwarf L 98-59, with strong Bayesian evidence in most activity models.

desk verdict A transparent, well-documented reanalysis of L 98-59 that confirms planet f only under some GP priors, adds a marginal 1.74 d candidate, and should be sent to peer review with a request for more honest summaries. read the letter →

arxiv 2507.06413 v1 pith:Z4LTCLPM submitted 2025-07-08 astro-ph.EP

Paul Schwarz (1) , Stefan Dreizler (1) , René Heller (2) ((1) Institute for Astrophysics , Geophysics , Georg-August-University , Göttingen (GER) , (2) Max Planck Institute for Solar System Research , Göttingen (GER)) This is my paper · ORCID
classification astro-ph.EP
keywords L98-59exoplanetsradialvelocityMdwarfhabitablezoneGaussianprocessBayesianevidencesub-Earthcandidate
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

This paper tries to settle whether the 23-day radial-velocity signal in the nearby M dwarf system L 98-59 is a real planet rather than a symptom of stellar activity. Combining new extracts of HARPS velocities, published ESPRESSO velocities, 21 TESS sectors, and five HST transits in a joint Bayesian model, it reports strong evidence for the fifth planet, L 98-59f, with an orbital period of $23.07\pm0.08$ d, a minimum mass of $3.0\pm0.5\,M_\oplus$, and an equilibrium temperature of 289 K. The same analysis uncovers an inner candidate at $1.736$ d with a minimum mass of $0.58\pm0.12\,M_\oplus$; its statistical significance ranges from $2.9\sigma$ to $4.2\sigma$ depending on how stellar activity is modeled. If both signals hold, L 98-59 becomes a six-planet system with a habitable-zone world, a benchmark for formation and future atmospheric studies.

What carries the argument

The load-bearing element is the comparison of Bayesian evidences ($\Delta\ln\mathcal{Z}$) among four-, five-, and six-planet models, with stellar activity absorbed by Gaussian-process kernels from the damped simple-harmonic-oscillator family (single, double, and coupled-double). These kernels are fitted together with Keplerian planet orbits to the combined radial velocities and the TESS/HST light curves, and the parameter space is integrated with nested sampling. The confirmation of planet f rests on $\Delta\ln\mathcal{Z}\approx +5.7$ on average across activity models, up to $+11.3$ without a GP; the candidate's significance range of $2.9\sigma$ to $4.2\sigma$ is likewise tied to which kernel and period prior is chosen.

What would settle it

Collect new radial-velocity measurements over at least one full 76-day rotation cycle and test whether the 23.07-day signal keeps a constant phase and amplitude while the activity indicators vary; if the signal's phase drifts or its amplitude tracks the stellar rotation cycle, the planetary interpretation is wrong, and if an independent dataset shows no 23.07-day signal after equivalent activity modeling, the confirmation does not stand.

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Extended reading notes

Core claim

The paper establishes, on its own terms, that the 23.07-day radial-velocity signal previously reported as a candidate survives a joint reanalysis of the HARPS and ESPRESSO velocities, TESS and HST transit photometry, and activity indicators. In most noise-model configurations the five-planet interpretation beats the four-planet interpretation by an average log-evidence margin of about $+5.7$, reaching $+11.3$ when no Gaussian-process activity model is included; the authors classify this as strong Bayesian evidence. The planet, L 98-59f, is non-transiting, with a minimum mass of $3.0\pm0.5\,M_\oplus$ and an effective temperature of 289 K, placing it in the system's habitable zone. The paper also reports a sixth planet candidate, L 98-59.06, with period $1.7361^{+0.0007}_{-0.0008}$ d and minimum mass $0.58\pm0.12\,M_\oplus$, whose significance is between $2.9\sigma$ and $4.2\sigma$ depending on the activity model; the authors do not claim confirmation for this candidate, but bootstrap and injection-retrieval tests lead them to argue it is not white noise. They further favor a stellar rotation period of $76\pm4$ d.

Load-bearing premise

The entire confirmation of planet f rests on the assumption that the chosen Gaussian-process activity models, with their specific period priors, fully capture the star's variability without being flexible enough to also absorb the 23-day signal; if that assumption fails, these data do not confirm the planet.

Editorial extensions

If this is right

  • L 98-59f is confirmed as a non-transiting planet at $23.07\pm0.08$ d with a minimum mass of $3.0\pm0.5\,M_\oplus$ and an equilibrium temperature of 289 K, in the habitable zone.
  • The stellar rotation period is constrained to $76\pm4$ d, favoring the longer of the previously debated values and explaining the shorter period as a harmonic of the spot pattern.
  • A sixth planet candidate, L 98-59.06, orbits at $1.736$ d with a minimum mass of $0.58\pm0.12\,M_\oplus$; its $2.9\text{--}4.2\sigma$ significance leaves it unconfirmed but unlikely to be pure white noise.
  • No transit is found for the candidate, implying an inclination offset of about $\pm4.2^\circ$ from an edge-on orbit if it is real.
  • The refined ephemerides reduce the period uncertainties of the confirmed planets by up to an order of magnitude and preserve a compact, stable architecture with adjacent separations above about 12 mutual Hill radii.

Reading between the lines

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

  • A decisive test the paper does not perform: extend the radial-velocity baseline over several 76-day rotation cycles and compare the 23.07-day signal's phase stability with the behavior of the activity indicators; that would separate a true Keplerian from a flexible activity model.
  • If the 1.736-day candidate is real, it would be among the lightest planets found by radial velocities, and its near-2:1 commensurability with planet b would make the system a useful testbed for dynamical and formation models.
  • The habitable-zone classification of L 98-59f depends on the adopted equilibrium-temperature and habitable-zone model; a different albedo or heat-redistribution assumption could move the planet outside the conservative habitable zone, so that label is model-dependent.
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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 / 6 minor

Summary. The paper reanalyzes HARPS and ESPRESSO radial velocities together with TESS and HST photometry to confirm a fifth non-transiting planet, L 98-59f, at an orbital period of 23.07 ± 0.08 d and minimum mass of 3.0 ± 0.5 M⊕, and to report an additional non-transiting candidate, L 98-59.06, at 1.7361 d with minimum mass 0.58 ± 0.12 M⊕. The analysis uses dynesty nested sampling, three celerite GP kernels with different period priors, GLS and L1 periodograms, a 10,000-sample bootstrap FAP (0.46%), and an injection-retrieval test (90.4% recovery). The authors also present evidence for a stellar rotation period of 76 ± 4 d and compare the system's architecture with other multi-planet systems.

Significance. If the central claim holds, the paper materially strengthens the case for a rare five-planet M-dwarf system and places a non-transiting habitable-zone planet on firmer observational footing. The paper is transparent in reporting full evidence tables (Table C1), priors and posteriors (Table C2), and a numerical FAP and injection-retrieval test. It also uses an independent SERVAL extraction for the HARPS data and adds twelve new TESS sectors and five HST transits. However, the confirmation of planet f is not robust across the paper's own GP activity models: Table 4 shows that the evidence increase for adding a fifth planet ranges from Δln Z = 11.3 without a GP down to 0.4 with the sSHO kernel and a wide period prior, where the GP absorbs the 23.1-d signal. The paper's 'average' evidence and the conclusion's quoted Δln Z range exclude that configuration, making the central claim conditional on a prior choice rather than on the data alone.

major comments (4)
  1. [Table 4, Sec. 4.2] The evidence for planet f is strongly dependent on the GP activity model. Adding a fifth planet gives Δln Z = 11.3 without a GP, 10.4 with sSHO N(78,5), 7.9 with sSHO N(39,5), but only 0.4 (σ = 0.4) with sSHO U(25,500), where the GP absorbs the 23.1-d signal (Fig. 2b). The text's 'average Δln Z ∼ +5.7' and the conclusion's range '3.3 ≤ Δln Z ≤ 11.3' exclude the wide-prior run and are not a principled model average. Please replace this with an evidence estimate marginalized over kernel and prior choices, or provide a data-driven justification for restricting the GP period prior; otherwise the confirmation claim is not robust.
  2. [Sec. 5.1, Table C2] The claimed rotation period of 76 ± 4 d is largely prior-driven. The best six-planet model uses a dSHO kernel with prior N(78,5) and returns 76.6 ± 4.2 d; the sSHO with the wide prior returns 28.0+2.4−1.7 d in the four-planet model; and H21 report 39.6 ± 2.2 d from TESS and Evryscope. The Perger et al. (2021) argument that celerite SHO kernels prefer the second harmonic is qualitative and does not quantify how the prior shifts the posterior. Because the GP is the component that can absorb the 23-d signal, the rotation-period determination must be made prior-independent or explicitly folded into the uncertainty of the planet-f confirmation. Also, Table C2 lists the GP prior as N(39,5) while the posterior is 76.6 ± 4.2, which appears inconsistent with the stated N(78,5) model in Table 4 and needs correction.
  3. [Sec. 5.3, Sec. 4.3.4] The significance statement for L 98-59.06 is internally inconsistent. The text says that with wide period priors U(1.1, 1.9) the evidence increase is insignificant, yet in the same paragraph calls the candidate 'highly significant' because the log-likelihood increase is significant. The log-likelihood difference does not include the Occam penalty and is not a valid model-comparison statistic in this context; the Bayesian evidence or a calibrated FAP should be used. Please either report the wide-prior evidence honestly and downgrade the candidate, or reconcile the RV-only and combined-fit evidence values so that the paper does not make contradictory statements about the same signal.
  4. [Conclusion vs. Table 4] The conclusion states '3.3 ≤ Δln Z ≤ 11.3, 2.1 ≤ σ ≤ 4.4' for the fifth planet, but Table 4 contains Δln Z = 0.4 and σ = 0.4 for the sSHO U(25,500) configuration. This discrepancy is not a minor typo: it directly affects the paper's central confirmation claim. Please correct the summary statistics and replace the ad hoc average with a clearly defined model-averaged evidence or a sensitivity statement that explicitly includes the wide-prior case.
minor comments (6)
  1. [Abstract] The abstract calls 289 K an 'effective temperature' for planet f, but the paper actually computes an equilibrium temperature assuming a Bond albedo of 0 and isotropic heat redistribution. Table C2 lists 285 K for planet f. Please use 'equilibrium temperature' and specify the assumed albedo and redistribution, or reconcile the two values.
  2. [Sec. 2.1.1, Table 2] Six HARPS points are removed by iterative 4σ clipping, but the paper notes these outliers are not the same as those found by C19 or D21. Please describe the clipping algorithm precisely and test the sensitivity of the planet parameters and evidence to this choice.
  3. [Sec. 4.3.3] The numerical FAP of 0.46% is much lower than the analytical GLS FAP of 5.3% for the same 1.736-d signal. Please clarify the cause of this difference, for example the different null model or window-function effects, so readers can compare the two numbers.
  4. [Sec. 5.3] The statement that the absence of a transit for L 98-59.06 implies an inclination offset of ±4.2° is not derived anywhere in the paper. Please provide the calculation or a reference for this constraint.
  5. [Figure 1, Figure 2] The axis label 'Freqency [1/d]' contains a typo and should read 'Frequency [1/d]'.
  6. [Sec. 5.4, Figure 7] The text notes that the 06-b separation is Δ(RH) = 11.9, below the Δ(RH) = 13 stability limit mentioned in the same section, yet the system is described as stable. Please clarify whether the SPOCK stability prediction gives a probability or confidence for this configuration and how the 11.9 value should be interpreted.

Circularity Check

1 steps flagged · score 4.0 of 10

The central planet-f confirmation is not circular and has independent support, but the secondary candidate L 98-59.06 is partially circular because its narrow period prior is taken from the same residual peak it is used to 'detect'.

  1. fitted input called prediction [Sec. 4.3.1, Table C2, Sec. 5.3]
    "In the residuals of the best four- and five-planet models, we see strong peaks at 1.736d and 2.34d ... L 98-59.06 ... P [d] 1.73615+0.00074−0.00076 U(1.730,1.745) ... When searching for the new candidate with wide period priors (U(1.1d,1.9d)), the period of 1.7362+0.0006−0.0012d can be found but the evidence increase is insignificant."

    The six-planet model's period prior for candidate 06 is U(1.730,1.745), which brackets the 1.736 d peak identified in the residuals of the same RV data (Sec. 4.3.1). The reported posterior period 1.73615 d is therefore essentially an input rather than an independent prediction. The strong Bayesian evidence increase for adding this Keplerian is computed against a prior centered on the signal being tested, and the paper itself admits that with a wide prior the evidence increase is insignificant. Thus the high Delta ln Z values for candidate 06 reduce to fitting a known periodogram peak with a narrow, data-informed prior.

full rationale

The paper's central claim, confirmation of planet f at 23.07 d, does not reduce to its own inputs. Planet f was proposed by Demangeon et al. (2021) using different data and methods, while the present work re-extracts the HARPS spectra with SERVAL, adds twelve new TESS sectors and five HST transits, uses a different joint modeling code (eff), and corroborates the 23.1 d signal with an independent L1-periodogram (log10 FAP of -5.2). The GP-dependence of the f evidence (Delta ln Z dropping to 0.4 under the sSHO wide-prior model) is a model-robustness concern, not circularity: the paper explicitly reports that the wide-prior GP absorbs the signal, and the best-fitting models still favor f. The stability threshold cited to Dreizler et al. (2024) is a self-citation, but it is not load-bearing because the rejected 2.34 d alias has Delta(RH) <= 2.5, far below any reasonable stability limit, including the Weiss et al. (2018) distribution. The main circular element is confined to the secondary candidate L 98-59.06, whose narrow period prior U(1.730,1.745) was evidently chosen from the 1.736 d residual peak; the paper's own wide-prior test shows insignificant evidence. This does not undermine the independent confirmation of planet f, so the overall circularity score is moderate rather than high.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The central claims rest on a chain of modeling choices: the GP kernel family for stellar activity, stellar parameters taken from TIC v8 and D21, the Hill-radius stability threshold used to reject the 2.34 d alias, the assumed albedo for equilibrium temperatures, and the assumed maximum density for the candidate radius. None of these are derived in the paper; they are imported from prior literature or chosen during the analysis.

free parameters (5)
  • GP kernel structure and period priors = sSHO/dSHO/cdSHO; best rotation 76.6+4.1-4.2 d
    The significance of both planet f and candidate 06 depends on which kernel and prior are used (Table 4, Table C1). The wide-prior sSHO reduces the f evidence increase to 0.4; the candidate ranges from 2.9 to 4.2 sigma across models.
  • RV jitter terms = log(jitter) ~ 0.04 to 0.05 for HARPS and both ESPRESSO sets
    Fitted nuisance parameters that absorb white noise and affect the significance of all periodic signals; posteriors in Table C2.
  • 4-sigma clipping threshold on HARPS RVs and activity data = 6 RV points excluded
    Hand-chosen rejection criterion; the excluded points differ from those removed in C19 and D21 (Sec. 2.1.1, Table 2), so results depend mildly on this choice.
  • Bond albedo and heat redistribution for equilibrium temperatures = albedo = 0, isotropic redistribution; Teq(f) = 285-289 K
    The 289 K habitable-zone temperature in the abstract is computed under this assumption, not measured.
  • Maximum density for candidate 06 radius estimate = 11 g/cm3 (from K2-38b)
    Used to infer radius >= 0.66 Rearth and the +/-4.2 deg inclination offset explaining the absence of transits (Sec. 5.3).
assumptions (6)
  • domain assumption The celerite SHO family (sSHO, dSHO, cdSHO) adequately represents quasi-periodic stellar activity in the RVs
    Invoked throughout Sec. 3.2 and 4.1; if true activity is not in this family, residual periodicities could be misattributed to planets. The model-dependent significance of candidate 06 (2.9-4.2 sigma) is a direct symptom of this assumption.
  • domain assumption Stellar parameters Mstar=0.29±0.02 Msun, Rstar=0.314±0.009 Rsun, Teff=3415±135 K are correct
    Taken from TIC v8 and D21 (Table 1); all masses, semimajor axes, and equilibrium temperatures scale with these values.
  • domain assumption The mutual-Hill-radius threshold Delta(RH) >= 13 for long-term stability justifies rejecting the 2.34 d alias
    Sec. 4.3.1 uses the W18 population statistic and the Dreizler et al. (2024) crossing-timescale limit to reject the alias; this is a cross-system heuristic applied to a single system.
  • standard math Analytic GLS false-alarm probabilities (Zechmeister and Kurster 2009) are reliable for these unevenly sampled data
    Used for all periodogram significance statements (Sec. 4.1, Fig. 1).
  • domain assumption r-spline detrending of TESS PDCSAP light curves does not remove or distort planetary transits
    Sec. 2.2 and Appendix A; the detrending comparison is qualitative.
  • standard math Bayesian evidence thresholds (Trotta 2008) are the correct model-selection criterion
    Used to convert Delta ln Z into 'strong evidence' statements (Sec. 4.2).
invented entities (1)
  • L 98-59.06 independent evidence
    purpose: New planet candidate at P=1.7361 d, m sin i=0.58 Mearth, invoked to explain residual RV power in the five-planet model
    The RV signal is a falsifiable handle: it predicts a coherent Keplerian signal that can be confirmed or refuted with more RVs, and a non-transiting geometry that TESS and JWST photometry can test. However, current significance is only 2.9-4.2 sigma and no transit is detected.

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Pith. "Pith review of Confirmation of a non-transiting planet in the habitable zone of the nearby M dwarf L 98-59." pith.science (2026). https://pith.science/paper/Z4LTCLPM

@misc{pith2026250706413,
  author       = {Pith},
  title        = {Pith review of: Confirmation of a non-transiting planet in the habitable zone of the nearby M dwarf L 98-59},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z4LTCLPM}},
  note         = {Machine review of arXiv:2507.06413}
}
abstract

Only 40 exoplanetary systems with five or more planets are currently known. These systems are crucial for our understanding of planet formation and planet-planet interaction. The M dwarf L 98-59 has previously been found to show evidence of five planets, three of which are transiting. Our aim is to confirm the fifth planet in this system and to refine the system characteristics namely minimum masses, radii and the orbital parameters of the planets around L 98-59. We reanalysed RV and activity data from HARPS and ESPRESSO alongside TESS and HST transit data using a joint model. The parameter space was sampled using the dynesty nested sampler. We confirm the previously known fifth planet in the system's habitable zone with an orbital period of $23.07\pm0.08\,d$, a minimum mass of $3.0\pm0.5\,M_{\oplus}$ and an effective temperature of 289 K. We find an additional planet candidate in the RV data with an orbital period of $1.7361^{+0.0007}_{-0.0008}\,d$ and a minimum mass of $0.58\pm0.12\,M_{\oplus}$. This candidate (L 98-59.06) has a statistical significance between $2.9\sigma$ and $4.2\sigma$, details depending on the modelling of stellar variability. Moreover, we present evidence for a stellar rotation period of $76\pm4\,d$.

Figures

Figures reproduced from arXiv: 2507.06413 by the authors.

Figure 1
Figure 1. The H𝛼 and NaD activity indicators can be directly compared between the HARPS and ESPRESSO data, while the CRX and dLW are only available from the SERVAL pipeline, while the S-index and BIS are available from the ESPRESSO data-reduction pipeline. Comparing the H𝛼 and NaD with the RV data we find strong peaks towards higher periods. From previous analyses we know that the rotation period is either around 78 d or 39 d… view at source ↗

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