Radial velocity homogeneous analysis of M dwarfs observed with HARPS. II. Detection limits and planetary occurrence statistics

C. Lovis; D. Segransan; F. Bouchy; G. Chaverot; G. Gaisne; G. Lo Curto; L. Mignon; M. Mayor; N. Astudillo-Defru; N. C. Santos

REVIEW 3 major objections 6 minor 2 cited by

Radial velocity homogeneous analysis of M dwarfs observed with HARPS. II. Detection limits and planetary occurrence statistics

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read After 20 years of HARPS monitoring of 197 nearby M dwarfs, this paper reports that low-mass planets with periods under 10 days occur at a rate of about 120 percent per star, and that temperate-zone planets occur around 45 percent of M…

desk verdict The new HARPS M-dwarf occurrence rates are the most careful RV measurement to date, but the flagship 120% short-period low-mass rate is more fragile than its quoted error bars because it depends on inverse-weighting a few detections at very low local detectability. read the letter →

arxiv 2502.06553 v1 pith:7YVU5M3K submitted 2025-02-10 astro-ph.EP astro-ph.SR

L. Mignon , X. Delfosse , N. Meunier , G. Chaverot , R. Burn , X. Bonfils , F. Bouchy , N. Astudillo-Defru

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G. Lo Curto G. Gaisne S. Udry T. Forveille D. Segransan C. Lovis N. C. Santos M. Mayor

This is my paper · ORCID

classification astro-ph.EPastro-ph.SR

keywords MdwarfplanetsradialvelocitysurveyexoplanetoccurrenceratesdetectionlimitstemperatezoneHARPSmultiplicityplanetformation

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 uses 20 years of HARPS radial-velocity measurements of 197 nearby M dwarfs to count how common planets are around the most numerous stars in the Solar neighbourhood. It claims that low-mass planets with periods under 10 days are the norm: an average of 120 percent, or about 1.2 planets per star, for projected masses between 0.75 and 3 Earth masses. It also derives a 45.3 percent occurrence rate for planets in the temperate (potentially habitable) zone, and finds that wide-orbit giant planets are rare and, in this sample, confined to the more massive M dwarfs. The numbers matter because they turn a two-decade observing campaign into a census that planet-formation models and future observing programs can be checked against.

What carries the argument

The load-bearing object is the stack of 197 per-star statistical detection limits, called the detectability map. For each star, the residual radial-velocity series is shuffled 1000 times to get the noise-only GLS periodogram power distribution; a sinusoidal signal of a given period is then injected at 12 phases and its amplitude raised until the 1 percent false-alarm power threshold is reached, giving a limiting projected mass. The statistical (median-phase) limits are stacked to give, for every mass and period, the fraction of stars on which such a planet would have been detected; that fraction $\alpha(m_i,p_i)$ enters the occurrence estimator $f_{jk} = (1/N) \sum \alpha^{-1}$, and a multiplicity coefficient $\mathrm{mult} = \mathrm{mult}_{\mathrm{obs}} + 1 - \langle\alpha\rangle$ extends the binomial error bars beyond 100 percent. This converts a set of non-detections into a quantitative completeness correction, which is what turns 10 detected low-mass planets into a 120 percent rate.

What would settle it

Recompute the detection limits after adding a correlated (red) noise component whose amplitude and timescale are matched to the stars' activity indicators; if the 1 percent false-alarm mass limits at periods under 10 days rise substantially, say by more than 30 percent, for the stars hosting the low-mass detections, the 120 percent occurrence rate is overestimated. An independent check would be a transit survey with known completeness that counts Earth-radius planets with periods below 10 days around about 100 nearby M dwarfs and compares the completeness-corrected number per star with 1.2.

Watch

Extended reading notes

Core claim

The central claim is that planet occurrence around M dwarfs is dominated by low-mass, short-period worlds. Using the 197 residual radial-velocity time series treated as clean of detectable signals, the paper builds a mass-period detectability map, weights each confirmed detection by the inverse of its local detectability, and obtains 120.1 percent (+24.8, -23.6) for planets with projected mass below 3.2 Earth masses and periods between 1.6 and 10 days; the corresponding system occurrence is 80 percent, with a local multiplicity of 1.6. For the temperate zone, defined by the conservative runaway-greenhouse and maximum-greenhouse boundaries, four planets fall inside and give 45.3 percent (+20.2, -16.0). In the giant-planet regime, the paper places an upper limit of 0.5 percent on hot Jupiters at short periods and finds 3.0 percent for planets above about 316 Earth masses at periods of 1000 to 10000 days, all orbiting the most massive M dwarfs in the sample.

Load-bearing premise

That each residual radial-velocity series is white noise after subtracting the modeled long-term trends, Keplerian signals, and rotation harmonics; if stellar activity or undetected planets leave correlated or inflated noise, the shuffled-periodogram detection limits are too optimistic and every occurrence rate built on them shifts.

Editorial extensions

If this is right

Most nearby M dwarfs should harbor at least one planet below roughly 3 Earth masses with an orbit shorter than 10 days; the 120 percent rate means such systems outnumber stars.
Roughly one in two M dwarfs has a temperate-zone planet under the conservative boundary definitions used here, making M dwarfs promising targets for atmosphere follow-up.
Hot Jupiters around M dwarfs are rarer than around Sun-like stars, with an upper limit of 0.5 percent at short periods.
Wide-orbit giant planets are rare, at a few percent, and in this sample appear only around M stars more massive than about 0.35 solar masses, so the giant-planet population depends on stellar mass.
The rates are consistent with the CARMENES survey when the same local-detectability weighting is applied, and discrepancies with earlier HARPS-N figures trace back to the calculation method rather than to the sample.

Reading between the lines

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

If the close-in, low-mass rate holds, then any complete and unbiased survey of nearby M dwarfs should frequently find transiting planets; the detection map implies that targeted searches of the least-massive M dwarfs will give the highest absolute yield of low-mass planets.
The paper's local-weighting correction, applied to earlier FGK surveys that used average detectability, could lower reported short-period occurrence rates for Sun-like stars and thereby change the apparent magnitude of the stellar-mass dependence.
The absence of wide-orbit giants around the less massive M dwarfs, combined with the paper's own caution that long-term trends were subtracted, suggests the true dichotomy may be even stronger than the reported 3 percent at 1000 to 10000 days, because those trends could hide additional massive companions.
The temperate-zone rate depends on the adopted effective temperatures for individual stars, with Proxima b and GJ 3323 c being sensitive cases; better stellar parameters and 3D climate-model inner edges could shift the 45.3 percent figure.

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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

Plainly, this is the best RV occurrence measurement for M dwarfs we have. It uses 197 HARPS stars, up to 20 years of data, and a detectability map built from the residuals of the companion paper. The new results are a 120% occurrence rate for sub-3 Earth-mass planets inside 10 days, a 45.3% temperate-zone rate, and the first useful RV constraints in the 1000-10000 day period range. The sample roughly doubles Bonfils et al. (2013) and the weighting scheme is an improvement: each planet counts as the inverse of its local detectability, not a domain average, and multiplicity enters the statistical bounds.

The paper earns credit for honesty. Section 7 is a genuine limitations section: activity residuals that might not be white noise, eight incomplete systems with known planets that are below the detection limits, the non-independence of draws in the binomial model, the monitoring bias in the wide-orbit giant sample, and the sensitivity of the temperate-zone result to the adopted effective temperatures. The comparison with Sabotta et al. (2021) and Pinamonti et al. (2022) is useful and mostly convincing; they track the discrepancies to the weighting method and even catch a stellar-mass misclassification in Sabotta.

The stress test is right, and it lands on the flagship number. In the 0.3-3.2 Earth-mass, 1.6-10 day bin, 10 detections give 120% with an average inverse weight near 24 per detection. The quoted ±25% error bars are binomial bounds built from Neff and a multiplicity factor; they do not include uncertainty in the detectability map itself. The map assumes white noise after subtracting the modeled signals, uses circular injections, and depends on the activity corrections from paper I. A factor-of-two change in α for one high-weight planet shifts the rate by tens of percentage points. The paper propagates mass errors (Sect. 7.1.4) but never perturbs the α map. That is load-bearing.

Minor but real: no code or derived data are shipped, so the map and the weighting cannot be independently re-run. The temperate-zone rate rests on four planets, one of which sits on the boundary, and the authors show how Teff choices move it from 45% to 50% or in or out of the zone. That is acknowledged, but it means the precision of that number is overstated.

For the field, this is the new reference RV occurrence measurement. The qualitative picture—lots of short-period low-mass planets, rare hot Jupiters, a possible stellar-mass dichotomy for wide-orbit giants—is consistent with CARMENES and TESS work and will hold. The specific percentages should be used with more caution than the abstract suggests.

Send it to peer review. A good referee will ask for a sensitivity analysis that varies the detectability map (white-noise assumption, eccentricity, activity residuals) and recomputes the rates, plus public data products. If that analysis comes out stable, this becomes a standard citation; if not, the error bars need to be revisited.

Referee Report

3 major / 6 minor

Summary. The paper derives planetary occurrence rates for M dwarfs from 197 HARPS radial-velocity time series previously analyzed in Mignon et al. (2024). Residual time series, assumed to be free of detectable signals, are used to build a detectability map via GLS injection-recovery, and occurrence rates are computed by inverse-detectability weighting of the detected planets, with binomial confidence bounds modified by a local multiplicity coefficient. The main results are a 120% occurrence rate for planets below 3.2 Earth masses with periods shorter than 10 days, a 45.3% temperate-zone occurrence rate, low rates for giant planets with a preference for long-period giants around more massive M dwarfs, and comparisons with previous RV and transit surveys and with population synthesis models.

Significance. If the headline numbers are correct, the paper provides the most precise RV-based M-dwarf occurrence rates to date and strengthens the evidence that close-in low-mass planets are common around M dwarfs. The study has clear value in its homogeneous 197-target sample, its explicit treatment of multiplicity, its extension to long orbital periods using two decades of HARPS data, and its normalized-insolation temperate-zone map. The inverse-detectability weighting is a sensible improvement over domain-averaged methods, and the results are empirical rather than circular. However, the uncertainty budget attached to the headline rates is not yet reliable, and the paper's own limitation sections identify effects that feed directly into the detectability map.

major comments (3)

[§4.3, Table 2] The quoted 1σ intervals in Eqs. (3a,b) do not estimate the variance of the inverse-probability-weighted estimator in Eq. (1). For the headline bin (0.3–3.2 M⊕, 1.6–10 d), Table 2 reports f=120.1% with nd=10, Neff'=8, and Neff=14; the implied Σ α^{-1} is about 237, i.e., an average inverse weight of about 24 per detection. Detections with local α near 2–4% therefore each contribute tens of percentage points, and the binomial interval built from Neff and mult does not capture this concentration. The effective sample size of the weighted sum, (Σw)^2/Σw^2, is likely far below 14. The paper should present a bootstrap or analytic variance estimate for the weighted estimator and a sensitivity test in which α is perturbed by, say, a factor of two before recomputing rates; as written, the precision implied by 120.1+24.8/−23.6% is not supported by the estimator's actual variance.
[§3.1, §7.1.1, §7.1.2, §7.1.4] The detectability map is built under the assumption that each residual time series is a realization of white noise after removal of all modeled signals. The paper itself documents that 23 series were corrected for rotation or activity signals and that 8 of the 31 planetary systems are incomplete relative to the NASA Exoplanet Archive. Both effects can leave correlated or inflated residuals, which directly biases α. Since Eq. (1) places α in the denominator, an overestimate of α by a factor of two for one or two high-weight detections changes the headline rate by tens of percentage points. Section 7.1.4 propagates only Gaussian mass uncertainties and never perturbs the α map itself. Please add a systematic robustness check—for example, recomputing the map using conservative rather than statistical limits, adding a jitter term, or rescaling α by plausible factors—and report the resulting range on the 120% and 45.3% rates.
[§6.2, §6.3] The temperate-zone rate of 45.3% is based on four planets whose membership in the temperate zone is highly sensitive to the adopted stellar effective temperatures. Section 6.3 documents hand-selected values (e.g., 2810 K for Proxima, 3650 K for GJ 667C) and boundary-sensitive objects such as GJ 3323 c. An alternative Teff choice for GJ 667C c moves the rate to 49.6+13/−19%, and a different Proxima Teff would remove Proxima b from the zone. Because Teff uncertainties are not propagated, the stated 45.3+20/−16% should be presented as a conditional estimate with a systematic range rather than as a standalone measured occurrence rate.

minor comments (6)

[Abstract and §5.1] The abstract gives the low-mass range as 0.75 to 3 Earth masses, while Table 2 and Section 5.1 use 0.3 to 3.2 M⊕; please harmonize the mass boundaries.
[§5.2 and Table 3] The text states that no occurrence rate is calculated for M∗>0.35 in the <3.2 M⊕ bin, but Table 3 lists f=100+153/−36% for that bin; the text and table should be reconciled.
[§5.2 and Table 3] The text says the M∗<0.35 low-mass rate is based on 11 detections among 11 accessible stars, whereas Table 3 reports nd=10; please make the count consistent.
[§6.1, Eq. (4)] Equation (4) defines Seff = L/d^2 without specifying units; please state that d is in au and L in L⊙, and clarify the normalization convention.
[Table A.2] The GJ 317 c row appears to have an incomplete mass entry ('1.4 420 M⊕'); please correct the formatting and confirm the value.
[Throughout] A language pass would catch typos such as 'exemple', 'limititation', and 'occurence' that appear in the current text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the occurrence rates are inverse-detectability-weighted empirical counts anchored to independent surveys, not reductions of the detectability map to itself.

full rationale

The paper's derivation chain is transparent and non-circular. Paper I supplies residual RV time series; Section 3.1 converts them into per-star GLS detection limits through an explicit injection-recovery procedure; Section 3.2 stacks these into a detectability map; Section 4.1 defines the occurrence rate as f_jk = (1/N) * sum_i alpha(m_i,p_i)^{-1} over actual detections. The detectability alpha enters as a weight, not as the predicted quantity; the occurrence rate is not defined by alpha alone but by the detections counted in each domain. The multiplicity correction (Eq. 2) is an explicitly stated model for missed planets and is used only for the binomial uncertainty bounds (Eqs. 3a,b), not to manufacture the central value. The paper repeatedly validates against independent surveys (Sabotta et al. 2021; Pinamonti et al. 2022; Bonfils et al. 2013a; Dressing & Charbonneau 2015; Bergsten et al. 2023), so the headline rates are not forced by self-citation. The reliance on paper I residuals is a data provenance dependency, not a circular inference: those residuals are the input measurements, and no equation in the paper reduces the output to the input by construction. The white-noise assumption and the sensitivity of alpha to calibration are statistical robustness concerns (correctly flagged in Sect. 7), not circularity. No step exhibits self-definition, fitted-input-as-prediction, or a load-bearing self-citation chain.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

No new physical entities are introduced. The central numbers depend on several hand-chosen thresholds and modeling assumptions, which are listed above; the largest sensitivity is to the white-noise assumption and to effective-temperature choices for temperate-zone membership.

free parameters (5)

Statistical detection limit threshold = 1% false-alarm probability
Detection limits are defined at the 1% FAP level after 1000 shuffles; changing this threshold changes the detectability map and all occurrence weights (Sect. 3.1).
Minimum observation count for sample inclusion = 10 nights
Sample selection threshold; Sect. 5.4 shows occurrence rates shift when the threshold is raised to 30, 50, or 100 nights.
Stellar-mass split for subsamples = 0.35 solar masses
Hand-chosen boundary between partially and fully convective M dwarfs; the giant-planet dichotomy is derived from this split (Sect. 5.2).
Effective temperatures for temperate-zone boundaries = e.g. 2810 K for Proxima
TZ membership of Proxima b and GJ 3323 c depends on which literature Teff is adopted; the paper selects values and reports sensitivity (Sect. 6.3).
Mass-period domain boundaries = P bins 1.6/10/100/1000/10000 d; mass bins 0.3/3.2/31.6/316/3162 Earth masses
Occurrence rates are computed per chosen bin; widths and edges affect the quoted percentages and upper limits (Sect. 4).

assumptions (7)

domain assumption Residual radial-velocity series are white noise after subtracting all detected signals.
Stated in Sect. 3.1; activity residuals and missed planets can create correlated noise, biasing detection limits. Sect. 7.1.1 acknowledges incomplete activity cleaning.
domain assumption Injection of circular orbits recovers planets up to eccentricity 0.5.
Sect. 3.1 relies on Cumming and Dragomir (2010); higher-eccentricity planets would be underestimated, though most detected planets have e below 0.45.
domain assumption The statistical median-phase detection limit, not the conservative limit, is the correct population sensitivity.
Sect. 3.1 assumes most systems are not observed at the worst phase; if this fails, occurrence rates are underestimated.
domain assumption Binomial sampling with replacement and an average multiplicity gives valid 1-sigma bounds.
Sect. 4.3 and Sect. 7.1.3 note that detections of additional planets are not fully independent, so the bounds are approximate.
domain assumption The Kopparapu temperate-zone model for a 1-Earth-mass, Earth-composition planet applies to the detected planets.
Sect. 6.1 and 6.2; the model is valid only for 0.1-10 Earth masses and terrestrial composition, while some TZ planets have minimum masses near 6-10 Earth masses.
domain assumption The 197 HARPS targets are representative of the overall M-dwarf population.
Targets were selected by program availability, distance, declination, and at least 10 nights; Sect. 5.4 documents that observation-count cuts alter occurrence rates.
domain assumption Adopted stellar masses and luminosities are accurate enough for mass and insolation conversions.
Sects. 2.1 and 6.1 use empirical mass-luminosity relations and TESS or Boltzmann luminosities; errors propagate into planet masses and temperate-zone boundaries.

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Cite this review

Pith. "Pith review of Radial velocity homogeneous analysis of M dwarfs observed with HARPS. II. Detection limits and planetary occurrence statistics." pith.science (2026). https://pith.science/paper/7YVU5M3K

@misc{pith2026250206553,
  author       = {Pith},
  title        = {Pith review of: Radial velocity homogeneous analysis of M dwarfs observed with HARPS. II. Detection limits and planetary occurrence statistics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7YVU5M3K}},
  note         = {Machine review of arXiv:2502.06553}
}

read the original abstract

We re-determine planetary occurrences around M dwarfs using 20 years of observations from HARPS on 197 targets. The first aim of this study is to propose more precise occurrence rates using the large volume of the sample but also variations to previous calculations, particularly by considering multiplicity, which is now an integral part of planetary occurrence calculations. The second aim is to exploit the extreme longevity of HARPS to determine occurrence rates in the unexplored domain of very long periods. This work relies entirely on the 197 radial velocity time series obtained and analysed in our previous study. By considering they are cleaned of any detectable signal, we convert them into detection limits. We use these 197 limits to produce a detectability map and combine it with confirmed planet detections to establish our occurrence rates. Finally, we also convert the detection limits from orbital period to insolation in order to construct an occurrence statistics for the temperate zone. We find a strong prevalence of low-mass planets around M dwarfs, with an occurrence rate of 120% for planets with a mass between 0.75 and 3 Me. In addition, we compute an occurrence rate of 45.3% +20-16% for temperate zone planets around M dwarfs. We obtain an occurrence rate of a few percent for giant planets with wide separations. In our sample these giant planets with wide separations are only detected around the most massive M dwarfs.

Figures

Figures reproduced from arXiv: 2502.06553 by the authors.

**Figure 2.** Iso-frequency map obtained by stacking the 197 statis [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Planetary occurrence statistic. Colours in the background refer to the detection limit map, from the non-reachable region [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Planetary occurrence statistics obtained on the sub [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Planetary occurrence statistics obtained on the sub [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Comparison of occurrence rates obtained as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: GJ 163 statistical mass limit as a function of insolation. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 9.** Figure 9: Occurrence of low-mass planets around FGK stars based [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Occurrence rates of theoretically calculated planets by [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

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Forward citations

Cited by 2 Pith papers

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Revisiting TOI-4438 and TOI-442 planetary systems with new observations from SPIRou and TESS
astro-ph.EP 2026-07 accept novelty 6.0 of 10

Refined masses and radii for TOI-4438 b and TOI-442 b, stellar rotation periods from magnetic variability, and a single-transit planet candidate around TOI-4438.
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Pith tools

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