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Resolving the Super-Earth/Gas Giant Connection in Stellar Mass and Metallicity

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

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Pith's one-line read Around M-dwarfs below about 0.55 solar masses, inner super-Earths do not raise the odds of an outer gas giant, even for metal-rich hosts.

desk verdict The M-dwarf null result is solid, but the K-dwarf transition claim depends on one fragile field-rate bin and the abstract overstates it. read the letter →

arxiv 2502.01748 v1 pith:2DHUYDMF submitted 2025-02-03 astro-ph.EP astro-ph.GAastro-ph.SR

Marta L. Bryan , Eve J. Lee This is my paper · ORCID
classification astro-ph.EPastro-ph.GAastro-ph.SR
keywords super-EarthsgasgiantsM-dwarfsexoplanetoccurrenceratesstellarmetallicityplanetformationradialvelocitysurveysdiskmassbudget
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

Does the link between inner super-Earths and outer gas giants that shows up around metal-rich Sun-like stars also exist around M-dwarfs? Using 85 M-dwarf systems that host inner super-Earths, the paper finds that the gas-giant frequency in these systems matches the field occurrence rate for M-dwarfs, so the two planet populations form independently at these low stellar masses. The result holds even for metal-rich hosts, where the super-Earth–gas-giant correlation is normally strongest. Combining this sample with the earlier FGK sample, the paper locates the onset of the positive correlation at K-dwarfs and shows it strengthens toward F stars. This mass–metallicity map matters because it ties the inner-outer planet connection to the disk mass budget, which declines toward lower-mass stars.

What carries the argument

The argument runs on the conditional-probability identity $P(\mathrm{GG}|\mathrm{SE}) = P(\mathrm{GG})\,P(\mathrm{SE}|\mathrm{GG})/P(\mathrm{SE})$, so a positive super-Earth–gas-giant correlation is equivalent to $P(\mathrm{SE}) < P(\mathrm{SE}|\mathrm{GG})$. Each system's sensitivity to outer gas giants is quantified by injecting 50 simulated planets into every cell of a $50\times50$ mass–semi-major-axis grid, fitting one-planet models to the public radial-velocity data, and scoring detection with a Bayesian information criterion ($\Delta\mathrm{BIC}>10$); these completeness maps are summed to give effective system counts for a Beta-binomial occurrence estimate. The same injection-recovery machinery is applied to the comparison sample to get the field gas-giant rate $P(\mathrm{GG})$. On the theory side, the paper uses the disk-mass-budget model of Chachan & Lee (2023) to estimate $P(\mathrm{SE}|\mathrm{GG})$ as the fraction of disks with 2–3 times the mass needed to nucleate a $15\,M_\oplus$ core at 2000 days, and shows that this fraction drops below $P(\mathrm{SE})$ at low stellar masses.

What would settle it

A uniform radial-velocity survey of several hundred M-dwarfs between 0.3 and 0.55 solar masses, split by metallicity and by the presence of inner super-Earths, could settle the claim: if metal-rich super-Earth hosts show a gas-giant rate significantly above the field rate (for instance a >3 sigma excess), the disappearance of the correlation below 0.55 solar masses would be refuted.

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Extended reading notes

Core claim

The paper's central claim is that the positive correlation between inner super-Earths and outer gas giants disappears for host stars below roughly 0.55 solar masses, even when only metal-rich hosts are considered. For M-dwarfs with inner super-Earths, the conditional gas-giant occurrence rate is $P(\mathrm{GG}|\mathrm{SE}) = 9.4\%$ for metal-rich hosts and $<3.1\%$ for metal-poor hosts, while the field rates from the comparison sample are $10.3\%$ and $<2.6\%$, respectively; the two sets of numbers agree within their uncertainties, indicating no correlation. When the M-dwarf sample is combined with the FGK sample, the positive correlation first appears among metal-rich K-dwarfs and grows with stellar mass, reaching about $2.8\sigma$ for the most massive stars. The paper explains the mass dependence through the disk mass budget: disks around lower-mass stars rarely have enough mass to form an outer gas giant and inner super-Earths simultaneously.

Load-bearing premise

The conclusion rests on the Rosenthal et al. (2021) survey being an unbiased measure of the field gas-giant frequency around M-dwarfs after each system's sensitivity is collapsed to an average completeness; if that sample is not representative of M-dwarfs generally, or if the average-completeness correction misstates individual sensitivities, the no-correlation result and the mass–metallicity map would not follow.

Editorial extensions

If this is right

  • Around M-dwarfs below roughly $0.55\,M_\odot$, gas giants occur in super-Earth systems at the field rate, so inner and outer planets form independently at these masses.
  • The positive super-Earth–gas-giant correlation turns on in metal-rich K-dwarfs and grows with stellar mass, weakest for M-dwarfs and strongest for F stars.
  • Dynamically hot gas giants ($e > 0.2$) strengthen the correlation at all stellar masses, while distant giants ($>3\,\mathrm{AU}$) strengthen it only around G and F stars.
  • The correlation switches from single-gas-giant systems around K-dwarfs to multi-gas-giant systems around stars above $1\,M_\odot$, tracking the larger disk mass budget.
  • Below roughly $0.5\,M_\odot$, the disk mass budget rarely suffices to make both an outer giant and inner super-Earths, explaining the observed cutoff.

Reading between the lines

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

  • If the mass cutoff holds, occurrence-rate models for M-dwarf super-Earths can treat outer gas giants as an independent population; a survey targeting habitable-zone super-Earths around M-dwarfs need not correct for a formation bias from outer giants.
  • The framework predicts that around ultra-cool dwarfs below roughly $0.3\,M_\odot$, the fraction of disks able to form both populations should drop even further, possibly turning the correlation negative; a targeted RV survey of such stars could test this quantitatively.
  • The paper's disk-mass explanation and the alternative that disks are intrinsically more compact around low-mass stars are not cleanly separated by current data; measuring disk sizes with high-resolution sub-millimeter imaging across stellar mass would distinguish them.
  • The eccentricity dependence suggests a dynamical-processing channel that the authors do not fully explore: if gas giants in super-Earth systems are preferentially eccentric, the link may partly reflect gravitational stirring or scattering rather than shared formation conditions.
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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. This paper investigates whether the previously established positive correlation between inner super-Earths and outer gas giants persists for low-mass host stars. The authors assemble a sample of 85 M-dwarf systems hosting inner super-Earths, compute individual injection-recovery completeness maps from public RV data, and compare the gas giant occurrence rate around super-Earth hosts with the field rate from the Rosenthal et al. (2021) survey using beta-binomial statistics. They find no significant super-Earth/gas giant correlation for M-dwarfs, even when limiting to metal-rich hosts. Combining their M-dwarf sample with the FGK sample from Bryan & Lee (2024), they claim that the positive correlation appears in metal-rich K-dwarfs and grows stronger with increasing stellar mass, and they interpret this mass dependence through a disk mass budget argument.

Significance. The M-dwarf null result is a genuinely important empirical constraint: if confirmed, it shows that the super-Earth/gas giant correlation disappears below roughly 0.55 solar masses even in metal-rich environments, sharpening the conditions under which the two planet populations form together. The paper's strengths include a carefully documented heterogeneous sample, transparent injection-recovery completeness calculations for every system, a clear statistical framework, and the use of two independent field comparison samples. The proposed disk-mass interpretation is plausible and clearly labeled as approximate, but it is not an independent confirmation of the observed trend. The headline mass-metallicity map is currently weakened by the sensitivity of the K-dwarf transition to the choice of field comparison sample.

major comments (3)
  1. [Section 5, Table 1, and abstract] The claim that the positive SE/GG correlation 'emerges in metal-rich K-dwarfs and strengthens with increasing stellar mass' rests on the 2.3σ significance in the K-dwarf high-metallicity bin, where the authors compare their P(GG|SE)=27.1% with the R21 field rate P(GG)=2.8%. The authors themselves flag the R21 value as anomalously low and report that replacing it with the W20 value (12.5%) reduces the significance to 0.7σ. The abstract states the K-dwarf emergence without this caveat. Because the mass-metallicity map is the paper's central new claim, the abstract and Section 5 should present the K-dwarf transition as tentative, and ideally the field rate should be estimated from a combined R21+W20 sample or subjected to a sensitivity analysis over plausible field rates before being quoted as a resolved transition.
  2. [Section 4 vs Section 5/Table 1] The gas giant definition is inconsistent between the two halves of the paper. Section 4 computes M-dwarf occurrence rates for gas giants of 0.5–20 M_Jup and 0.1–10 AU, while Table 1 and the mass-metallicity map use the default range 0.5–20 M_Jup and 1–10 AU. This is not a purely cosmetic difference: for the high-metallicity M-dwarf bin, P(GG|SE) changes from 18.3% in Section 4 to 12.1% in Table 1, and GJ 876's two gas giants at 0.136 and 0.218 AU are counted in the former but excluded from the latter. The authors should state which definition drives the mass-metallicity transition, justify the inner boundary, and show that the claimed emergence in K-dwarfs is not an artifact of this choice.
  3. [Section 4, Eq. (1)] The effective number of systems is computed by taking the average completeness over each sample and inserting it into a beta-binomial likelihood. If individual systems have heterogeneous sensitivity, as the completeness maps indicate, the detection count follows a Poisson-binomial distribution, and collapsing to a single neff can bias both the central estimate and the posterior width. The authors should either weight each system by its own completeness in the likelihood or explicitly demonstrate that the reported rates and significances are insensitive to this approximation, especially for the M-dwarf null result and the K-dwarf transition.
minor comments (5)
  1. [Section 5 and Table 1] The text defines the highest mass bin as '>1.5 M☉', while Table 1 uses '>1.05 M☉'; the abstract also says the mass range is 0.3–1.5 M☉. These boundary values should be harmonized.
  2. [Section 4] The upper limits are quoted as 1σ limits (e.g., P(GG|SE, [Fe/H]≤0) < 3.1%) without stating the convention at first use; please define the confidence level for all upper limits in one place.
  3. [Table 2] In the 0.3–0.65 M☉ rows, the entries for 'Multi GG' and 'Single GG' are identical for both the B&L and R21 samples; please check whether this is a typo or a definitional artifact and clarify in the table note.
  4. [Section 7] The sentence reporting the median and standard deviation of the orbital distances of outer giants is difficult to parse; please rephrase to list the values per mass bin unambiguously.
  5. [Figures 2 and 3] The captions should explicitly state the semi-major axis range used in each panel, since Figure 2 corresponds to the 0.1–10 AU definition while Table 1 uses 1–10 AU.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: measured occurrence rates are independent of the post-hoc disk-budget interpretation.

full rationale

The core comparison in this paper is between two measured occurrence rates, P(GG|SE), computed from the 85 M-dwarf super-Earth sample via injection-recovery completeness maps, and the field P(GG) computed from the R21 (and W20) samples with the same sensitivity procedure; neither quantity is defined in terms of the other, and the Bayes-rule identity used in Section 7 is a definition of what the authors mean by a positive correlation, not a derivation of the data. The FGK portion of the mass-metallicity map is taken from BL24, a prior paper by the same authors, but that prior measurement is based on public RV data and is externally falsifiable, so its reuse is ordinary data aggregation rather than circularity. The theoretical interpretation in Section 7 uses Chachan & Lee (2023) with hand-chosen parameters (15 Earth-mass core, 2-3x disk mass) and is explicitly labeled approximate; it is presented after the fact and does not enter the occurrence-rate calculation, so it cannot make the measurement circular. The paper itself flags the fragility of the K-dwarf bin (R21 P(GG)=2.8% versus W20 12.5%, 2.3 sigma dropping to 0.7 sigma), which is a robustness concern about the choice of comparison sample, not a circularity. No self-definitional, fitted-input-as-prediction, imported-uniqueness, or ansatz-smuggling step is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central observational claim rests on the R21 field comparison and the completeness correction, which are domain assumptions rather than measured quantities. The theoretical interpretation introduces several hand-chosen model parameters, but these do not feed back into the occurrence rate measurements.

free parameters (3)
  • Critical core mass for gas giant formation = 15 Earth masses (chosen)
    Chosen in Section 7 to ensure runaway gas accretion within 1 Myr; using 10 Earth masses shifts P(SE|GG) up but does not change the qualitative result.
  • Disk mass requirement factor for P(SE|GG) = 2-3 times single-giant mass
    Chosen in Section 7 so the disk has enough mass for 1-2 outer giants and multiple inner super-Earths; this choice makes the inequality hold down to about 0.5 solar masses.
  • Turbulent alpha and accretion rate in disk model = alpha_t = 1e-3, Mdot_star = 1e-8 solar masses/yr
    Representative values used in the Figure 4 calculation, stated in Section 7; authors note similar results at higher fragmentation velocities.
assumptions (4)
  • domain assumption The R21 sample provides an unbiased estimate of the field gas giant occurrence rate around M-dwarfs after completeness correction.
    Used as the baseline P(GG) in Section 4 to test for correlation; if the R21 M-dwarf sample is biased in metallicity or RV sensitivity, the no-correlation conclusion changes.
  • domain assumption The injection-recovery sensitivity maps correctly capture each system's completeness to gas giants in 0.5-20 Jupiter masses and 0.1-10 AU.
    Sections 3 and 4 use these maps to compute the effective number of systems; the method averages completeness over the grid, which approximates each system's sensitivity.
  • domain assumption Stellar masses and metallicities from the literature are accurate to the quoted uncertainties.
    Sample selection and metallicity binning in Sections 2 and 5 rely on these values; errors on [Fe/H] are assumed 0.1 dex when unavailable.
  • domain assumption Disk mass scales with stellar mass per Manara et al. 2023, and the pebble accretion model of Chachan & Lee 2023 applies.
    This is the basis of the theoretical interpretation in Section 7 that connects the observed mass trend to disk mass budget.

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Cite this review

Pith. "Pith review of Resolving the Super-Earth/Gas Giant Connection in Stellar Mass and Metallicity." pith.science (2026). https://pith.science/paper/2DHUYDMF

@misc{pith2026250201748,
  author       = {Pith},
  title        = {Pith review of: Resolving the Super-Earth/Gas Giant Connection in Stellar Mass and Metallicity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2DHUYDMF}},
  note         = {Machine review of arXiv:2502.01748}
}
abstract

The observed correlation between inner super-Earths and outer gas giants places strong constraints on formation theories. Building on previous work, Bryan $\&$ Lee 2024 showed that there is a statistically significant positive correlation between super-Earths and outer gas giants around metal-rich FGK stars, and that this correlation disappears for metal-poor hosts. Here we consider how this connection evolves across stellar mass. Starting with our sample of 85 M-dwarfs ($<$0.6 M$_{\odot}$) hosting inner super-Earths, we calculate P(GG|SE, [Fe/H]$>$0) = 9.4 (+10.2 -3.1)$\%$ and P(GG|SE, [Fe/H]$\leq$0)$<$3.1$\%$. Compared to the field gas giant frequency calculated from the Rosenthal et al 2021 sample, we find P(GG|[Fe/H]$>$0) = 10.3 (+6.9 -3.1)$\%$, and P(GG|[Fe/H]$\leq$0)$<$2.6$\%$ for M-dwarfs. While we see a higher gas giant frequency around metal-rich M-dwarfs for both samples, we find no significant correlations between super-Earths and gas giants. Combining our 85 M-dwarf sample with our FGK sample from Bryan $\&$ Lee 2024, we resolve the SE/GG correlation in stellar mass (0.3--1.5 M$_{\odot}$) and metallicity. We show the positive correlation emerges in metal-rich K-dwarfs and strengthens with increasing stellar mass. Gas giant properties also impact the correlation -- for metal rich stars, the positive correlation is strengthened by: 1) dynamically hot gas giants for all stellar masses; 2) distant gas giants only for higher mass stars; and 3) single gas giants for K-dwarfs and multiple gas giants around more massive stars. We discuss how the stellar mass dependence of the inner-outer planet correlation can be understood from the increasing disk mass budget for higher mass stars.

Figures

Figures reproduced from arXiv: 2502.01748 by the authors.

Figure 1
Figure 1. Top left: M-dwarf mass distribution from the R21 sample. Top right: M-dwarf mass distributions from this paper. Bottom left: M-dwarf metallicity distribution from the R21 sample. Bottom right: M-dwarf metallicity distribution from this paper’s sample. For all panels, black histograms correspond to systems without gas giants, red correspond to those with gas giants. Gas giants considered are 0.5−20 MJup and < 10 AU. … view at source ↗
Figure 2
Figure 2. Top: occurrence rate of gas giants in metal￾rich M-dwarf systems. Bottom: same in metal-poor systems. Frequencies from this paper are in maroon, R21 are in black. While metal-rich M-dwarfs have a higher frequency of gas giants for both samples, there is no significant difference in occurrence rates between the samples. We find no significant correlation between super-Earths and gas giants around M￾dwarf host stars. … view at source ↗
Figure 3
Figure 3. Comparison of gas giant (0.5–20 MJup 1–10 AU) frequencies from this paper’s sample P(GG|SE), the R21 sample P(GG), and the W20 sample P(GG). Top Left: Comparison of low, middle, and high metallicity occurrence rates for early M￾dwarfs. Top right: Same comparison for K-dwarfs. Bottom Left: Same comparison for G stars. Bottom right: Same comparison for F stars. For all panels, frequencies from this paper are shown in … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Fraction of disks expected to create inner (inside 100 days) super-Earths (black) compared to the fraction of disks with enough mass to create both the outer giant and inner super-Earths bounded by thrice as much (lower edge of the red zone) and twice as much (upper ed…

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