{"id":"6c9335db-0b0e-45f2-b653-90eeb9414ad4","arxiv_id":"2501.02215","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"The inner edge of small-planet systems scales with stellar mass as a power law with index roughly 0.6 to 1.1 after metallicity correction, best matching the pre-main-sequence dust sublimation radius.","lead":"This paper measures how the orbit of the innermost small planet in multi-planet Kepler systems depends on host star mass, finding a steeper correlation than earlier work after correcting for stellar metallicity. The authors argue this favors the dust sublimation radius of the young protoplanetary disk as the physical limit for where small planets can reside.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The metallicity-correction functional form in Eq. (7) is the load-bearing assumption; if the [Fe/H] dependence is not a log-separable power law, the headline gamma1 = 0.6-1.1 and the dust-sublimation preference are not secure.","rationale":"The reader's weakest-assumption analysis identifies Eq. (7) as the critical link, and I agree. The quantitative claim is not simply the existence of an outward shift (which survives without correction) but the specific range gamma1 = 0.6-1.1 and the conclusion that the PMS dust sublimation radius is favored. Both depend on the MLR correction and on the slope-only model comparison. The paper itself flags the ad hoc nature of Eq. (7), and the reported sensitivities ('testing various alternatives' without details) are not enough to establish robustness. I considered the LAMOST selection effect and the occurrence-rate appendix as possible alternative concerns; the selection effect is secondary because the qualitative trend is present in the selected sample and could be checked separately, and Appendix A is an explanatory toy that does not feed the main slope estimate. The proposed generalized-regression test is cheap, uses the same public catalogs, and would settle whether the separable-power-law assumption is load-bearing. A negative result would strengthen the paper; a positive result would require reinterpreting the headline as conditional on the chosen form. This is exactly the kind of addressable issue that supports the reader's CONDITIONAL verdict rather than ACCEPT or REJECT.","tokens_in":27159,"tokens_out":9020,"duration_ms":94563,"concrete_test":"On the same 166-system sample, re-fit Eq. (8) against a generalized model that adds a quadratic metallicity term and a mass-metallicity interaction, e.g. log a_in = log gamma0 + gamma1 log M + gamma2 [Fe/H] + gamma22 [Fe/H]^2 + gamma12 log M [Fe/H], and compare by cross-validated AIC/BIC for the all-multiple and mixed samples. If the generalized terms improve the fit by DeltaAIC > 2, or if gamma1 from the generalized model moves outside 0.6-1.1, the headline slope is an artifact of the assumed separable power law rather than a robust measurement.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim (Abstract, Sec. 3.3, Table 2) is that, after removing the metallicity effect, the inner edge scales as a_in ∝ M^gamma1 with gamma1 = 0.6-1.1. This value comes from the multiple linear regression log(a_in) = log(gamma0) + gamma1 log(M) + gamma2 [Fe/H] (Eq. 8). The authors explicitly state in Sec. 3.3 that this functional form 'does not have a strong theoretical or astrophysical basis.' The correction matters: for sub-Neptunes gamma1 rises from 0.38 ± 0.09 to 0.67 ± 0.17 after including [Fe/H], and for all/mixed systems it rises from 0.63/0.95 to 0.81/1.12. Because [Fe/H] correlates with M (gamma3 = 0.09-0.17, Fig. 5) and the fitted gamma2 is negative, any misfit of the assumed separable power-law form is projected directly into the corrected gamma1. The paper says alternative forms were tested but gives no quantitative results, so the reader cannot assess how much of the reported range is model choice rather than measurement. Furthermore, the theoretical comparison in Fig. 7 forces all model intercepts to the observed intercept and compares slopes only; with 1-sigma uncertainties, dust sublimation (active, alpha=1; slope 0.78) and stellar tides (0.69) are both consistent with the observed all-multiple slope 0.81 ± 0.09. Thus the mechanism conclusion is not strongly discriminated even if the slope is accepted. I note that the uncorrected correlations are also positive (gamma1 = 0.38-0.95), so the qualitative outward shift is robust; the fragile part is the quantitative range and the mechanism attribution.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper measures the correlation between the inner edge of multi-planet systems and stellar mass using Kepler DR25, Gaia (Berger et al. 2020), and LAMOST metallicities (PAST II). Restricting to small planets in multi-transiting systems, it fits a single power law a_in ∝ M^γ1, then a multiple linear regression that adds a metallicity term 10^{γ2 [Fe/H]}. The reported metallicity-corrected exponent is γ1 = 0.6–1.1 across all multiple systems, super-Earths, sub-Neptunes, and mixed systems. The paper argues that transit selection bias does not induce the correlation, that the occurrence-rate method used by earlier work underestimates γ1, and that comparison with theoretical models favors the pre-main-sequence dust sublimation radius as the physical mechanism setting the inner edge of small planets, in contrast to hot Jupiters.","tokens_in":27677,"tokens_out":4344,"duration_ms":44401,"significance":"If the measurement is robust, it sharpens an important observational constraint on the inner-edge–stellar-mass relation and reconciles the discrepancy with occurrence-rate-based estimates (γ1 ≈ 0.3) by attributing it to methodological bias. The paper is careful in several respects: uncertainties are propagated by resampling stellar parameters, p-values are computed with permutation tests, the transit-selection effect is examined in dedicated simulations, and the authors explicitly acknowledge the ad hoc nature of the metallicity-correction form. The final physical conclusion, however, rests on a model comparison that is only weakly discriminating, and the headline exponent depends on a functional form whose robustness is asserted rather than demonstrated.","major_comments":[{"comment":"The headline result γ1 = 0.6–1.1 depends on the assumed log-separable metallicity term 10^{γ2 [Fe/H]} in Eq. (7)/(8). The text itself states that this form 'does not have a strong theoretical or astrophysical basis.' Since [Fe/H] correlates with log M (γ3 = 0.09–0.17 in Fig. 5) and γ2 is fitted negative, any misspecification of the metallicity dependence (e.g., a nonlinear or non-separable [Fe/H] effect) will be projected directly into the corrected γ1. The paper says alternative forms were tested but gives no quantitative results. Please report the alternative fits (e.g., quadratic [Fe/H], interaction terms, or binned analyses) and show whether γ1 remains in the quoted range; otherwise the 0.6–1.1 interval is a property of the assumed model rather than a measured range.","section":"Sec. 3.3, Eq. (8)"},{"comment":"The theoretical comparison fixes all model intercepts to the observed intercept and compares only slopes. With the reported 1σ uncertainties, active dust sublimation (α = 1, slope 0.78) and stellar tides (0.69) are both within 1σ of the all-multiple MLR slope 0.81 ± 0.09, and passive sublimation (k = 2, 1.0) is within 2σ. The statement that the pre-main-sequence dust sublimation radius 'best matches' the data is therefore not a quantitatively supported discrimination. Please provide a formal model comparison (e.g., likelihood or information-criterion based, with the intercept as a free parameter, or with the observed scatter included) and state which mechanisms are rejected at what confidence.","section":"Sec. 4.1 and Fig. 7"},{"comment":"The analysis uses only the 166 LAMOST-matched multi-planet systems from the larger Kepler multis sample. Requiring a metallicity measurement can introduce selection effects in stellar mass and metallicity, and the paper does not test whether the LAMOST subsample is representative of all Kepler multis. Please compare the mass, radius, and period distributions and the uncorrected γ1 of the LAMOST subsample versus the full Kepler multis sample, or apply a weighting/selection correction. This is needed to support the claim that the measured correlation is intrinsic rather than a property of the metallicity-matched subset.","section":"Sec. 2.1 and Table 1"},{"comment":"The appendix's quantitative claim that occurrence rates bias γ1 down to ≈0.36 from an intrinsic value of 1.0 relies on the identification f_occ ∝ a_occ = mean(a_n) in Eq. (A.3) and on adopting N_L = 3, N_H = 2 from Yang et al. (2020). The step f_occ ∝ a_occ is not derived from the occurrence-rate equations of Mulders et al. (2015) that are quoted in Eqs. (A.1)–(A.2); in particular, the star-count N* and the planet-multiplicity N are conflated. Please either derive this relation carefully from the occurrence-rate definition or reframe the appendix as an illustrative toy estimate rather than the explanation for the discrepancy with previous work.","section":"Appendix A, Eqs. (A.1)–(A.10)"}],"minor_comments":[{"comment":"The sub-Neptune panel reports p = 0.2177, so the statement in the text that 'a correlation ... can be observed' for sub-Neptunes should be explicitly qualified as not statistically significant at the usual threshold; the subsequent power-simulation discussion is helpful and should be connected directly to this p-value.","section":"Sec. 3.1, Fig. 3"},{"comment":"The normalization in Eq. (11), P_max = R*(max)/a_in(min), uses the maximum of one quantity and the minimum of another; clarify that this is indeed the intended maximum over the sample and that the resulting P_transit is bounded by unity in the simulation.","section":"Sec. 3.4, Fig. 6"},{"comment":"The caption says the systems are ordered 'from left to right' by increasing stellar mass, but the horizontal axis labels and tick marks are unclear in the figure as printed; please make the ordering explicable without reference to the caption alone.","section":"Appendix A, Fig. A.2"},{"comment":"In the paragraph after Eq. (8), the statement that alternative functional forms 'do not have a strong theoretical or astrophysical basis' is used to justify the chosen form; this is fine, but the same paragraph should contain the quantitative robustness check requested in the major comments, not only a caveat.","section":"Sec. 3.3"}],"recommendation":"major_revision","confidential_remarks":"The paper has a solid empirical core: the positive uncorrected slopes, the permutation tests, and the selection-bias simulations are credible, and the qualitative conclusion that the inner edge moves outward with stellar mass is robust. The main risk is that the headline range and the mechanism claim are oversold relative to the robustness of the metallicity correction and the discriminating power of the model comparison. I believe the authors can address this with added robustness tests and a more cautious interpretation; I would not recommend rejection, but the current version needs major revision before acceptance. I also note that Appendix A's occurrence-rate calculation, while presented as the explanation for the discrepancy with Mulders et al. (2015), is too schematic to carry that weight in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid observational paper with an honest presentation of a new measurement—inner edge of Kepler multis as a function of stellar mass, corrected for metallicity. The result: gamma1 ~ 0.6-1.1, steeper than Mulders et al. (2015). The paper does the statistical homework: sample selection is documented, permutation p-values, resampling for uncertainties, and a transit-geometry bias simulation that yields no induced correlation. That bias check is a real plus.\n\nThe soft spot is the metallicity correction. The adopted functional form, a_in = gamma0 M^gamma1 10^(gamma2 [Fe/H]), is explicitly stated to lack a strong theoretical basis. The authors tested alternatives but don't report numbers, so the reader can't judge how much of the gamma1 = 0.6-1.1 range is model choice. Given that [Fe/H] correlates with M and gamma2 is negative, any mis-specification leaks directly into the mass slope. That's a legitimate concern, but not a fatal one: the uncorrected slopes are already positive (0.38-0.95), so the qualitative outward shift is robust.\n\nThe mechanism conclusion is weaker than the abstract suggests. In Fig. 7, all model intercepts are forced to the observed value and slopes are compared; stellar tides (0.69) sits within 1 sigma of the all-multiple slope (0.81 +/- 0.09). Dust sublimation is favored but not strongly discriminated. The sub-Neptune subsample alone doesn't carry the trend (p = 0.22 uncorrected, N = 33); the mixed-multiple systems drive the signal. Appendix A's occurrence-rate toy model is cute but rests on a debatable definition of the occurrence edge (a_occ = mean a) and should be treated as illustrative, not quantitative.\n\nThese are all fixable with more sensitivity analysis and a clearer statement of what the data can and cannot discriminate. This is a paper I'd want to see in the literature; it gives a cleaner measurement of a correlation that has been discussed for a decade and it makes the selection-bias checks public. I'd send it to a referee, asking specifically for (a) quantitative robustness tests of the metallicity functional form, and (b) a model comparison that doesn't freeze the intercepts.","headline":"A careful measurement of the inner-edge–mass correlation in Kepler multis, with a steeper slope after metallicity correction; the slope is robust in direction, but the exact value and the dust-sublimation preference rest on an ad hoc functional form and a weak model comparison.","tokens_in":28221,"tokens_out":2612,"would_cite":true,"duration_ms":24266,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The innermost orbits of small planets are set by the dust sublimation radius of the protoplanetary disk, not by stellar magnetism.","keywords":["exoplanets","inner edge","stellar mass relation","metallicity correction","dust sublimation radius","Kepler multi-planet systems","super-Earths","sub-Neptunes"],"falsifier":"Split the multi-planet sample into metal-poor and metal-rich bins at fixed stellar mass and refit the inner-edge slope in each bin: if the separable power-law form is right, the mass slope should be the same in both bins, while a divergent slope would falsify the correction. A complementary test would resolve the dust sublimation radius in pre-main-sequence disks around stars of known mass and compare it directly with the inner edges of the resulting planetary systems.","tokens_in":26934,"feed_emoji":"🪐","tokens_out":7830,"duration_ms":67862,"temperature":0.7,"pith_summary":"This paper tries to establish what determines the innermost orbit of small planets in compact multi-planet systems. Using Kepler multi-planet systems with Gaia-derived stellar masses and LAMOST metallicities, the authors fit the inner edge as a power law in stellar mass and, after correcting for the metallicity projection, find $\\gamma_1 \\approx 0.6$–$1.1$. Comparing that slope with theoretical predictions, the pre-main-sequence dust sublimation radius of the protoplanetary disk matches best, whereas hot Jupiters are thought to be halted by the magnetospheric truncation of the gas disk. If correct, the result means small planets and giant planets stop at different physical boundaries in their natal disks.","feed_headline":"Small planets stop where the disk dust vaporizes","feed_subtitle":"Kepler multi-planet systems show the inner edge scales with stellar mass as M^0.6–1.1, matching the dust sublimation radius.","key_machinery":"The load-bearing object is the metallicity-corrected power-law fit $a_{\\mathrm{in}} = \\gamma_0\\,(M_\\star/M_\\odot)^{\\gamma_1}\\,10^{\\gamma_2\\,[\\mathrm{Fe/H}]}$, fitted in log space by multiple linear regression. The argument also rests on defining the inner edge as the semimajor axis of the innermost planet in coplanar multi-transiting systems rather than inferring it from occurrence rates; an appendix quantifies how occurrence rates dilute the slope, giving $\\Delta\\gamma \\approx -0.64$ for a $1\\,M_\\odot$ versus $0.5\\,M_\\odot$ comparison. Theoretical slopes for dust sublimation, tidal, and co-rotation mechanisms are tabulated and compared with the measured $\\gamma_1$, with the active $\\alpha=1$ dust-sublimation model matching the all-multiple-systems slope within $1\\sigma$.","core_discovery":"The central claim is that the inner edge of systems of small planets scales with stellar mass more steeply than previously reported once stellar metallicity is controlled: for the four population samples the metallicity-corrected power-law index is $\\gamma_1 = 0.6$–$1.1$, with all multiple systems at $0.81^{+0.09}_{-0.08}$, mixed systems at $1.12^{+0.08}_{-0.07}$, super-Earth systems at $0.57^{+0.10}_{-0.11}$, and sub-Neptune systems at $0.67^{+0.17}_{-0.18}$. The authors argue that this slope agrees with the pre-main-sequence dust sublimation radius, so the innermost orbits of small planets are likely limited by the dust-destruction region of the protoplanetary disk. They further show that earlier occurrence-rate based estimates near $\\gamma_1 \\approx 1/3$ underestimated the correlation because outer planets dilute the inner-edge signal, and that transit selection bias does not produce the observed trend.","pith_inferences":["If dust sublimation sets the inner edge, then the inner edge should also respond to disk luminosity and grain size; systems with larger grains or dimmer disks should permit planets closer in, a prediction that could be tested with spatially resolved disk surveys.","The innermost-planet method used here could be applied to TESS multi-planet systems to check whether the $\\gamma_1 \\approx 0.6$–$1.1$ slope holds outside the Kepler field and is not a survey-specific artifact.","By the authors' logic, single-transiting systems, once corrected for inclination and geometric bias, should show the same intrinsic slope; measuring it would separate detection geometry from the physical truncation mechanism.","If the boundary is set in the pre-main-sequence phase, the inner edge should correlate more tightly with stellar properties than with planet mass or system age; age-dated samples could test this ordering."],"forward_implications":["For all multi-planet systems the metallicity-corrected slope is $\\gamma_1 = 0.81^{+0.09}_{-0.08}$, notably steeper than the $\\sim 1/3$ slope obtained from occurrence rates in earlier work.","Mixed systems containing both super-Earths and sub-Neptunes show the strongest mass dependence ($\\gamma_1 = 1.12^{+0.08}_{-0.07}$), suggesting that samples containing both populations are the most sensitive to stellar mass.","The measured $\\gamma_1 = 0.6$–$1.1$ range is consistent with active dust sublimation and, at the lower end, with stellar tides, while co-rotation and planetary tides are disfavored as the dominant controls.","Extrapolating the all-multiple-systems slope to A-type stars places the inner edge near $0.21$–$0.27$ AU, consistent with the observed rarity of close-in planets around A-type stars.","The comparison with hot-Jupiter results implies that different planet populations have different inner-edge regulators: dust sublimation for small planets versus magnetospheric truncation for giant planets."],"supporting_citations":[{"why":"supplies the Gaia-Kepler stellar mass catalog with ~7 percent mass uncertainties used for all host stars.","marker":"Berger et al. 2020"},{"why":"provides the PAST II LAMOST-Gaia-Kepler catalog with stellar metallicity measurements used for the correction.","marker":"Chen et al. 2021b"},{"why":"is the Kepler DR25 catalog providing the planetary orbital periods and radii.","marker":"Thompson et al. 2018"},{"why":"is the earlier occurrence-rate based study whose ~1/3 slope is the baseline the paper explains and corrects.","marker":"Mulders et al. 2015"},{"why":"derives the active dust sublimation radius scaling used for the theoretical slope comparison.","marker":"Liu et al. 2019"},{"why":"derives the passive disk sublimation radius scaling used for the theoretical slope comparison.","marker":"Dullemond et al. 2001"},{"why":"provides the stellar and planetary tidal evolution scalings used as competing theoretical models.","marker":"Jackson et al. 2009"},{"why":"supplies the hot-Jupiter result that inner edges align with magnetospheric truncation, the contrast case for the paper's conclusion.","marker":"Mendigutía et al. 2024"},{"why":"supplies the planet multiplicity versus stellar mass relation used to quantify how occurrence rates dilute the inner-edge slope.","marker":"Yang et al. 2020"}],"fun_headline_variants":["Dust sublimation radius sets inner edge for small planets","Inner edge scales with stellar mass as dust line predicts","Why small planets stop at the dust sublimation line","Kepler reveals dust-destruction zone governs small planet orbits","Dust line not magnetosphere sets small planet inner orbit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central result assumes that metallicity enters the inner-edge relation as a single power law in [Fe/H] that multiplies a mass power law, with no cross-term or break; the authors state this functional form has no strong theoretical or astrophysical basis, so if the true metallicity dependence differs, the reported slope is an artifact of the assumed model.","fun_headline_variants_meta":{"raw":{"variants":["Dust sublimation radius sets inner edge for small planets","Inner edge scales with stellar mass as dust line predicts","Why small planets stop at the dust sublimation line","Kepler reveals dust-destruction zone governs small planet orbits","Dust line not magnetosphere sets small planet inner orbit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000573,"raw_usage":{"total_tokens":2775,"prompt_tokens":1078,"completion_tokens":1697,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":694,"completion_tokens_details":{"reasoning_tokens":1617}},"tokens_in":694,"tokens_out":1697,"duration_ms":13110,"temperature":1.0,"reasoning_tokens":1617,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:15:07.236733+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Split the multi-planet sample into metal-poor and metal-rich bins at fixed stellar mass and refit the inner-edge slope in each bin: if the separable power-law form is right, the mass slope should be the same in both bins, while a divergent slope would falsify the correction. A complementary test would resolve the dust sublimation radius in pre-main-sequence disks around stars of known mass and compare it directly with the inner edges of the resulting planetary systems.","supporting_citations":[{"cited_title":"A., Huber , D., van Saders , J","cited_arxiv_id":null,"evidence_quote":"supplies the Gaia-Kepler stellar mass catalog with ~7 percent mass uncertainties used for all host stars."},{"cited_title":"D., Pascucci , I., & Apai , D","cited_arxiv_id":null,"evidence_quote":"is the earlier occurrence-rate based study whose ~1/3 slope is the baseline the paper explains and corrects."},{"cited_title":"2009, , 698, 1357","cited_arxiv_id":null,"evidence_quote":"provides the stellar and planetary tidal evolution scalings used as competing theoretical models."},{"cited_title":"2020, , 159, 164","cited_arxiv_id":null,"evidence_quote":"supplies the planet multiplicity versus stellar mass relation used to quantify how occurrence rates dilute the inner-edge slope."}],"review_version":1}