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arxiv: 2603.01534 · v2 · submitted 2026-03-02 · 🌌 astro-ph.EP

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The Intrinsic Multiplicity Distribution of Exoplanets Revealed from the Radial Velocity Method. II. Constraints on Giant Planet Multiplicity from Different Surveys

Jiayin Li , Wei Zhu
Authors on Pith no claims yet

Pith reviewed 2026-05-15 17:11 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords giant planetsexoplanet multiplicityradial velocityplanet formationHARPSCalifornia Legacy SurveySun-like starsoccurrence rates
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The pith

Giant planet multiplicity around Sun-like stars falls short of planet-planet scattering predictions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper derives the intrinsic multiplicity distribution of giant planets from two cleaned radial velocity surveys. It reports that about 8 percent of Sun-like stars host exactly one giant planet within 10 au, with 2 to 7 percent hosting two and even smaller fractions hosting three or more. The low rate of multiples differs from theoretical models based on planet-planet scatterings, which produce too many systems with several giants. The difference between the two surveys is attributed to their distinct stellar metallicity distributions, and the results constrain formation pathways by showing that most giant planets occur singly.

Core claim

From the HARPS sample, (7.8±1.4%, 2.3±1.2%, 0.5+0.8-0.3%) of Sun-like stars have one, two, or three giant planets within 10 au; the California Legacy Survey yields (7.3±2.8%, 7.2±2.3%, <1.3%, 1.0+1.0-0.6%) for one through four. After correcting for detection completeness, the total fraction of stars with at least one giant planet is 10.6±1.2% and 15.8±2.1% respectively, and this distribution is inconsistent with most planet-planet scattering models, which predict too many multi-giant systems.

What carries the argument

The intrinsic multiplicity distribution recovered by applying detection completeness corrections to cleaned radial velocity survey samples of giant planets above Saturn mass.

If this is right

  • Scattering is disfavored as the dominant process shaping giant planet systems after formation.
  • Most giant planets form and remain in single-planet configurations rather than packed multiples.
  • Metallicity primarily affects overall occurrence rates rather than the shape of the multiplicity distribution.
  • Theoretical models must be revised to produce mostly isolated giant planets within 10 au.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The pattern supports core-accretion formation with limited subsequent dynamical stirring for most systems.
  • Extending the same completeness-corrected approach to sub-Saturn planets could test whether the single-planet dominance holds at lower masses.
  • Independent constraints from transit or direct-imaging surveys on outer giants would provide a cross-check on the 10 au cutoff.

Load-bearing premise

The cleaned RV survey samples represent Sun-like stars without bias once detection completeness and metallicity differences are accounted for.

What would settle it

A new volume-complete RV survey that directly counts all giant planets above Saturn mass within 10 au around Sun-like stars and finds a substantially higher fraction of multi-planet systems than the reported 2-7 percent would falsify the inferred distribution.

Figures

Figures reproduced from arXiv: 2603.01534 by Jiayin Li, Wei Zhu.

Figure 1
Figure 1. Figure 1: The distribution of 822 HARPS sample stars in the minimum mass vs. semi–major axis plane. Planets with different observed multiplicities are differentiated with different labels and colors. The contours represent the sur￾vey completeness, with lighter shades indicating higher sen￾sitivity and darker shades indicating lower sensitivity. Both based on the data from M. Mayor et al. (2011). The vertical dashed… view at source ↗
Figure 3
Figure 3. Figure 3: The distribution of the remaining 351 CLS sam￾ple stars in the minimum mass vs. semimajor axis plane after selection. The meanings of the markers, background contours, and various lines are the same as described in the caption of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: This figure shows in blue dots the planets de￾tected in the less biased CLS sample whose properties fall within our chosen parameter space. The values shown in the grid and their meanings are the same as described in the caption of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustrations of the derived intrinsic planet multiplicity distributions for the three chosen planet classes from the cleaned CLS (blue) and HARPS (orange) datasets. The maximum-likelihood solutions and 1σ–3σ confidence intervals are indicated by the colored bars with increasing transparency. np mp Fp 0.0 0.5 1.0 1.5 2.0 CLS / HARPS [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Ratios of CLS to HARPS values for average num￾ber of planets per star (¯np), average multiplicity ( ¯mp), and the fraction of stars with planets (Fp). The values are taken for the “All giant” population. Error bars indicate 1σ un￾certainties. The dashed line at unity marks equal values between the two samples. even more metal-rich environment than do cold giants, thus putting constraints on the in situ for… view at source ↗
read the original abstract

Compared to the commonly used planet occurrence rates, the multiplicity distribution of planets can be more useful in constraining the formation and evolution pathways of planetary systems. This work follows an earlier work of Zhu (2022) and derive the intrinsic multiplicity distribution of giant planets (with masses above Saturn mass) from two independent radial velocity (RV) surveys. In particular, we find that $(7.8\pm1.4\%, 2.3\pm1.2\%, 0.5^{+0.8}_{-0.3}\%)$ of Sun-like stars in the HARPS sample have $(1, 2, 3)$ giant planets within 10\,au, whereas $(7.3\pm2.8\%, 7.2\pm2.3\%, <1.3\%, 1.0^{+1.0}_{-0.6}\%)$ of Sun-like stars in the California Legacy Survey (CLS) have $(1, 2, 3, 4)$ giant planets within 10\,au. Here we have further cleaned the CLS sample and removed planet detections that were not discovered in the survey mode. The total fraction of Sun-like stars with at least one giant planet within 10\,au from the two samples are $10.6\pm1.2\%$ and $15.8\pm2.1\%$, respectively, and the difference may be accounted for by their different metallicity distributions. We briefly discuss the theoretical implications of our results. In particular, the inferred giant planet multiplicity distribution is inconsistent with most of the proposed theoretical models involving planet--planet scatterings, which predict too many multi-giant systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript derives the intrinsic multiplicity distribution of giant planets (masses above Saturn mass) within 10 au from two independent radial velocity surveys (HARPS and the cleaned California Legacy Survey). It reports specific fractions of Sun-like stars hosting 1, 2, 3 (and 4 for CLS) such planets, with totals of 10.6±1.2% and 15.8±2.1% respectively, attributing sample differences to metallicity distributions, and concludes that the low multiplicity is inconsistent with most planet-planet scattering models, which overpredict multi-giant systems.

Significance. If the completeness corrections and sample cleaning prove robust, the quantitative multiplicity fractions provide stronger constraints on giant planet formation and evolution than occurrence rates alone, as they directly test predictions from scattering scenarios. The use of two independent surveys and explicit uncertainty reporting adds value for theoretical comparisons, though the result hinges on unverified aspects of the inversion method.

major comments (2)
  1. [Abstract and methods] Abstract and methods section: the reported fractions (e.g., HARPS 7.8±1.4% single, 2.3±1.2% double) are presented as the outcome of fitting observed detections to an intrinsic distribution, but no explicit equations, likelihood function, or step-by-step completeness modeling are shown to demonstrate how detection biases for 2+ planet systems within 10 au (including metallicity effects) are inverted without circularity.
  2. [CLS sample description] CLS sample description: the cleaning step that removes non-survey-mode detections is load-bearing for the claim of low multi-giant fractions (7.3% single, 7.2% double), yet no quantitative test is provided on whether the cleaned sample remains representative of Sun-like stars or whether completeness for higher-multiplicity systems is systematically underestimated due to unmodeled interactions or noise.
minor comments (1)
  1. The abstract would benefit from a one-sentence outline of the statistical method used to recover the intrinsic distribution from the surveys.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight areas where the methods and sample validation can be clarified, which will strengthen the manuscript. We address each major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: [Abstract and methods] Abstract and methods section: the reported fractions (e.g., HARPS 7.8±1.4% single, 2.3±1.2% double) are presented as the outcome of fitting observed detections to an intrinsic distribution, but no explicit equations, likelihood function, or step-by-step completeness modeling are shown to demonstrate how detection biases for 2+ planet systems within 10 au (including metallicity effects) are inverted without circularity.

    Authors: We agree that additional explicit details would improve clarity. The inversion follows the Bayesian framework of Zhu (2022), in which the observed detection counts are modeled as the intrinsic multiplicity distribution convolved with survey-specific completeness functions derived from injection-recovery tests. The likelihood is a Poisson likelihood on the binned detections, with the completeness for multi-planet systems computed by simulating the joint detectability of multiple signals (accounting for period and mass correlations). Metallicity dependence enters only through the occurrence prior, not the completeness itself, avoiding circularity. We will add the explicit likelihood expression, a flowchart of the completeness calculation, and a dedicated subsection in Methods describing these steps. revision: yes

  2. Referee: [CLS sample description] CLS sample description: the cleaning step that removes non-survey-mode detections is load-bearing for the claim of low multi-giant fractions (7.3% single, 7.2% double), yet no quantitative test is provided on whether the cleaned sample remains representative of Sun-like stars or whether completeness for higher-multiplicity systems is systematically underestimated due to unmodeled interactions or noise.

    Authors: The cleaning removes detections obtained outside the uniform survey cadence to maintain consistent selection and observing strategy. We will add a table comparing the distributions of stellar mass, metallicity, and spectral type before and after cleaning, confirming that the cleaned sample remains representative of the original Sun-like star population. For completeness, our injection tests already incorporate realistic RV noise and sampling; however, planet-planet dynamical interactions are not explicitly simulated in the recovery step. We will add a quantitative estimate of the potential bias (based on N-body simulations of a subset of systems) and include this as a systematic uncertainty in the final error budget. revision: partial

Circularity Check

1 steps flagged

Minor self-citation to Zhu (2022) method paper; central inference is data-driven fitting with no reduction by construction

specific steps
  1. self citation load bearing [Abstract]
    "This work follows an earlier work of Zhu (2022) and derive the intrinsic multiplicity distribution of giant planets (with masses above Saturn mass) from two independent radial velocity (RV) surveys."

    The core inference procedure is imported from the overlapping-author prior paper; while the current application to new samples yields independent numerical results, the self-citation is the sole justification for the fitting methodology used to obtain the reported fractions.

full rationale

The paper applies the multiplicity inference framework from the author's prior work (Zhu 2022) to cleaned HARPS and CLS RV data, fitting assumed intrinsic fractions (1-planet, 2-planet, etc.) against observed detections after applying survey-specific completeness corrections. This is standard forward modeling; the output fractions are not equivalent to any prior fitted constants or self-cited inputs by construction. The self-citation supports the method but is not load-bearing for the new numerical results or the comparison to scattering models. No self-definitional loops, fitted inputs renamed as predictions, or ansatz smuggling occur. The derivation remains self-contained against the external RV catalogs and completeness functions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on statistical inference from RV detections that assumes standard completeness models and representative samples after cleaning; no new entities are introduced.

free parameters (1)
  • multiplicity fractions per survey
    Fitted values (e.g., 7.8%, 2.3%) chosen to match observed planet counts after completeness correction.
axioms (2)
  • domain assumption RV detection completeness is known and can be inverted to recover intrinsic occurrence rates
    Invoked to convert observed detections into intrinsic multiplicity percentages.
  • domain assumption Cleaned survey samples are unbiased representatives of Sun-like stars
    Required for generalizing the fractions to the broader population.

pith-pipeline@v0.9.0 · 5611 in / 1260 out tokens · 47564 ms · 2026-05-15T17:11:11.665903+00:00 · methodology

discussion (0)

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