{"id":"89ad34a1-2bcc-403b-b9da-96d46f9a0ddf","arxiv_id":"2501.11686","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Centimeter-wavelength VLA observations of 21 Taurus disks show ubiquitous free-free emission and a steepening of dust spectral indices, indicating much of the inner disk is optically thick at millimeter wavelengths.","lead":"Astronomers measured radio waves from 21 planet-forming disks in Taurus and found a faint glow from ionized gas plus dust at centimeter wavelengths. The results suggest the inner 40 au of many disks hide their dust at millimeter wavelengths, shaping how disk masses are measured.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (1)'s single dust power law is the same assumption the paper's main conclusion denies; if the dust SED breaks near 3 mm, both the free-free/accretion correlation and the cm spectral indices are biased.","rationale":"The reader's conditional verdict already identifies the two-power-law decomposition as the weakest assumption, and I agree that this is the most load-bearing point. I mark agreement as partial because the reader locates the possible steepening between 1 and 2 cm, whereas the paper's own physical conclusion is a break around 3 mm; the single-power-law form in Eq. (1) excludes that break a priori, which is a structure-level mismatch rather than only a long-wavelength extrapolation risk. I single this out over other plausible concerns (source exclusion, non-contemporaneous accretion rates, small sample, unresolved images) because it is the one systematic that couples directly to both headline claims: the free-free/accretion correlation and the 2.3-to-2.8 index shift. The manuscript is transparent about the data and the fitting, and Section 4.2 explicitly states the bias direction, so this is an addressable model-dependence rather than an internal error. The proposed broken-power-law refit is a direct control using already published photometry; it should settle whether the central results survive once the model permits the spectral break that the paper's interpretation demands. Since the reader already conditioned acceptance on this class of concern, my stress-test does not move the verdict.","tokens_in":57818,"tokens_out":7076,"duration_ms":82653,"concrete_test":"Refit all 21 SEDs with a dust component that is a broken power law with a break at 3 mm (90 GHz): S_dust(ν)=S0(ν/225 GHz)^αmm for ν≥90 GHz and S_dust(ν)=S0(90/225)^(αmm−αcm)(ν/90 GHz)^αcm below it, keeping the same gas term and priors as in Eq. (1). Then recompute (i) the 2 cm free-free values and their Pearson r against log Ṁacc, and (ii) the median α(3 mm-1 cm). If both stay within the quoted 1σ uncertainties of r=0.66±0.17 and 2.8±0.3, the single-power-law form is not decisive; if they move outside those ranges, the headline results are conditional on the assumed no-break dust spectrum.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.2 fits each SED with Eq. (1): one power law for dust from 0.85 mm to 2 cm and one for ionized gas, with αgas in [-1,2] and αdust in [2,4]. The paper then concludes from this decomposition that dust is optically thick at mm wavelengths (median α≈2.3) and optically thin at cm wavelengths (median α≈2.8), i.e., that the dust spectrum steepens around 3 mm. A single power law cannot represent both regimes; it will sit between them. At 1-2 cm, where modeled free-free contributes roughly 65% of the total, any overprediction of the dust component is compensated by a downward-biased gas amplitude. The authors explicitly acknowledge this risk in Section 4.2: the procedure may underestimate free-free emission and overestimate dust emission between 1 and 2 cm if the intrinsic dust spectrum is steepening. This is not a minor local caveat, because the free-free/accretion correlation (Fig. 2) and the centimeter dust indices (Fig. 3) are both computed from the same decomposition. A break near 3 mm, which is precisely what the paper's physical interpretation implies, would therefore shift both headline results in the same direction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents new VLA photometry at 7 mm to 6 cm for 21 Taurus disks selected from the ALMA surveys of Long et al. (2018, 2019), merged with archival ALMA, CARMA, IRAM, SCUBA, and CSO data into SEDs spanning 0.85 mm to 6 cm. Each SED is fit in Sec. 3.2 (Eq. 1) with a two-power-law model: a dust component (S_dust0 at 225 GHz, alpha_dust in [2,4]) plus an ionized-gas component (S_gas0 at 15 GHz, alpha_gas in [-1,2]). From this decomposition the paper claims (i) ubiquitous free-free emission whose 2 cm flux correlates with the mass accretion rate (Pearson r = 0.66 +/- 0.17) and is independent of ALMA outer-disk morphology; (ii) dust spectral indices that change from a median of about 2.3 at 0.89-3 mm to about 2.8 at 3 mm-1 cm and 2.7 at 1-2 cm, interpreted as the optically thick-to-thin transition and implying an optically thick inner region up to 40 au; (iii) similar 1.3 mm-2 cm flux ratios between compact and sub-structured disks once a 40 au aperture is used; and (iv) an opacity-dominated uncertainty on centimeter-wavelength disk masses. HP Tau is excluded from the SED fitting, and DQ Tau requires fixing alpha_gas to 0.6.","tokens_in":58079,"tokens_out":25553,"duration_ms":266712,"significance":"If the results hold, this is a substantial observational step: it provides the largest homogeneous sample of ordinary Class II disks in Taurus with 1-2 cm photometry, extends the free-free/accretion connection reported by Rota et al. (2024) for transition disks to the typical disk population, and yields a statistical set of centimeter dust spectral indices in a regime previously dominated by individual-object studies. The paper's strengths are its new VLA dataset with documented self-calibration, the complete per-source photometry and fit tables (Tables A.1, A.2), the transparent flagging of non-standard cases (HP Tau, DQ Tau), the model-free robustness check of the accretion correlation against the total 2 cm flux, and the explicit statement that the central claims are falsifiable with resolved cm observations (ngVLA, SKA-mid, ALMA Band 1). The principal weakness is that the two-power-law decomposition underpinning both headline results is not quantitatively validated against plausible curvature in the dust SED, a limitation the authors themselves acknowledge in Sec. 4.2; this is fixable within the manuscript's scope.","major_comments":[{"comment":"The decomposition in Eq. (1) is the load-bearing step for both headline results, and its central assumption conflicts with the paper's main conclusion. The model assumes a single dust power law from 0.85 mm to 2 cm, while the paper claims that the dust spectrum changes from alpha ≈ 2.3 to ≈ 2.8 across exactly this range. A single power law cannot represent both regimes, and the authors concede in §4.2 that if the intrinsic dust spectrum is steepening, the procedure underestimates free-free and overestimates dust emission between 1 and 2 cm. Because the Fig. 2 free-free fluxes and the Fig. 3 free-free-subtracted cm indices both come from this same fit, this is not a local caveat. Note that the bias is not uniformly unfavorable: overestimated dust at 1-2 cm would make the inferred 3 mm-1 cm index a lower limit, so the claimed break would be strengthened rather than weakened by curvature; however, the effect on the free-free normalization, and hence on Fig. 2, is unquantified and could vary source by source. I request: (i) per-source residuals and a goodness-of-fit statistic for the current fits; (ii) an explicit validation of the decomposition, e.g., an injection-recovery test in which synthetic SEDs containing a 2.3-to-2.8 dust break are fitted with Eq. (1), reporting the resulting bias in S_gas0 and in the derived cm indices, or, alternatively, a fit with a broken power law for the dust; and (iii) a statement of how the two summary conclusions shift under that bias. Without (ii), the r = 0.66 correlation and the alpha_cm = 2.8 values remain products of the assumed model.","section":"§3.2 (Eq. 1); §4.2"},{"comment":"The 'pronounced change' from millimeter to centimeter indices is not tested as a paired difference. The errors quoted in Fig. 3 (±0.3, ±0.4) are sample dispersions, not errors on the mean; with 19-21 objects the mean error is roughly an order of magnitude smaller, but the same objects contribute to alpha(1.3-3 mm) and alpha(3 mm-1 cm), so an unpaired comparison can inflate apparent significance. Please report the per-source difference Δα = α_cm - α_mm and its distribution with a paired test (e.g., Wilcoxon signed-rank or a bootstrap on the mean difference), and state how many sources enter each average (not all 21 have 3 mm photometry, per §2.3). In addition, the alpha_2cm average of 2.7 ± 0.4 is computed after excluding six sources whose index error exceeds 1.0; please state how many sources remain and verify that the exclusion does not bias the mean (e.g., whether the excluded sources are preferentially the faintest at 2 cm). Finally, Fig. 3 should visually distinguish which indices are direct photometric ratios (alpha at 0.8-1.3 mm and 1.3-3 mm) from those requiring the model subtraction (3 mm-1 cm and 1-2 cm), since the two classes have different systematic sensitivities.","section":"§3.4, Fig. 3"},{"comment":"Three issues affect the support for the free-free/accretion correlation. First, r = 0.66 ± 0.17 is a Pearson coefficient computed on model-inferred free-free fluxes whose uncertainties are large and asymmetric (Table A.1); given N = 20-21 and the modest dynamic range, a rank-based coefficient (Spearman) or an error-aware regression with bootstrap should also be reported. Second, the most extreme point of the correlation, DQ Tau, is also the one that required a manual intervention: alpha_gas is fixed to 0.6 (Table A.1) because the unconstrained fit places an unphysical 35% of the 1.33 mm emission into free-free (Appendix A). DQ Tau is a high-leverage point, so the correlation should be quoted with and without it, and the unconstrained fit should be shown. Third, the weakest free-free values are marginal detections at best (CIDA 9: S_gas0 = 0.02 +0.01/-0.02 mJy, with the posterior piling up at the zero boundary; V409 Tau: 0.02 +0.02/-0.01 mJy), so the wording 'ubiquitous presence of free-free emission' in the Abstract, §3.3, and §5 overstates these cases; the average 65% free-free fraction at 2 cm may still be robust, but per-source detections should be flagged with their significance and the 'presence in all sources' claim softened.","section":"§3.3, Fig. 2"},{"comment":"The estimate that the optically thick region extends to roughly 40 au is presented without a quantitative uncertainty. The 40 au scale is inferred from the change in the millimeter index at R_ALMA ≈ 40 au in Fig. 4, where only five disks lie below 40 au, and from the aperture experiment in Fig. 5. The flux-ratio differences (73% at 1.3 mm versus 54% at 3 mm-2 cm and 59% at the 40 au aperture) are shown without error bars, and no test establishes that they are mutually inconsistent; with 8-11 objects per morphology class the bootstrap spread could be substantial. Please add uncertainties to the ratios, report a significance test (e.g., bootstrap or permutation), and present the 40 au value as a range rather than a sharp radius, given that the unresolved VLA photometry cannot directly locate the transition.","section":"§3.5, Figs. 4-5; §4.1"}],"minor_comments":[{"comment":"The description of the CARMA 3 mm data is confusing: the text mentions 'unpublished CARMA data of 7 sources' but then says the observations cover the entire sample except CIDA 9, UZ Tau, and V409 Tau; please clarify how many of the 21 sources actually contribute the 3 mm photometry used in §3.2 and §3.4, and tabulate the IRAM and CARMA contributions separately.","section":"§2.3"},{"comment":"The fitting description omits the prior parameterization (flat in which variable?) and the implementation of the constraints (S_gas0 cannot exceed the total 2 cm flux, etc.); given that several posteriors in Table A.1 pile up at the zero boundary, the priors and basic MCMC convergence diagnostics (e.g., chain length, acceptance rate, or R-hat) should be reported.","section":"§3.2"},{"comment":"The C-band upper limits used to argue against gyro-synchrotron emission are listed but are not incorporated into the SED fits; please state explicitly how the non-detections at 6 cm enter the analysis, since the identification of the radio excess as free-free rests on the positive alpha_gas values whose individual uncertainties in Table A.1 are large.","section":"§3.1, Table A.2"},{"comment":"The red 'ISM' reference line at alpha ≈ 2.8 (i.e., an opacity index beta ≈ 0.8) needs a citation; common sub-millimeter ISM opacity indices (beta ≈ 1.5-1.7) correspond to alpha ≈ 3.5-3.7, so the provenance of this line should be specified, or the comparison drawn against the adopted value instead of an implied absolute one.","section":"Fig. 3"},{"comment":"The sentence 'This does indicate what is net loss of 1.3-mm flux in these disks but it does qualitatively suggest that is very high even for extended disks...' is garbled and should be reworded to convey the intended meaning (likely 'does not indicate a net loss' and 'that this is very high').","section":"§3.5"},{"comment":"For DQ Tau, the conclusion that the K-band flare lasted less than a few hours rests on a single same-day Ka-band measurement; please state whether any additional epochs from the 21B-267 data support this, and add a sentence to §2.2 or Table A.2 noting the epoch spread across the assembled SEDs (SCUBA 2005, CARMA 2009-2012, ALMA 2017-2019, VLA 2020-2021), since free-free variability is itself flagged as important in §4.2.","section":"§4.3, Appendix A"},{"comment":"Minor wording: 'the grain population responsible for these indices are analogous' should read 'is analogous'; also, the Summary would benefit from explicitly listing the number of sources entering each analysis (SED fits, Fig. 2, and each index in Fig. 3), since HP Tau is excluded from the fits and the correlation, and DQ Tau enters with a constrained parameter.","section":"§4.3, §5"}],"recommendation":"major_revision","confidential_remarks":"The reader's circularity concern lands, but on close reading as an unquantified systematic rather than a fatal flaw. The millimeter indices (alpha_1mm, alpha_3mm) are direct photometric ratios that barely involve the model, and the bias direction from dust curvature would make the inferred cm indices lower limits, which actually supports the claimed break. The free-free/accretion correlation has a partial model-free check (total 2 cm flux), but the manual alpha_gas fix for DQ Tau and the exclusion of HP Tau should be sensitivity-tested, and the 'ubiquitous' wording should be softened for the two weakest sources. The decisive missing piece is a quantitative validation of the two-power-law decomposition (injection-recovery or a broken-power-law alternative); if the authors provide it, this is a solid A&A paper. Worth noting editorially: two in-prep dependencies (Rota et al. in prep. for the interpretation of Fig. 2, and Blair et al. in prep. for the CARMA photometry used here) mean part of the evidence base is not yet public; I would ask the authors to ensure the CARMA fluxes are available or independently documented in the revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. This is a useful, honest observational paper. It provides the first sample-level VLA characterization of ordinary Taurus disks at 1-2 cm, moving beyond the usual exceptional objects. The two-component SED decomposition is transparent, the MCMC uncertainties are reported, and the paper is upfront about what it cannot do without resolved centimeter images.\n\nThe genuinely new results are the free-free/accretion correlation in non-transition disks (with a check against total 2 cm flux, which is not model-dependent), the sample of centimeter dust spectral indices, and the comparison with disk extent suggesting optically thick emission up to ~40 au. The trend between millimeter and centimeter indices is a plausible and interesting observation, and the paper connects it to existing evidence for optically thick inner disks from ALMA surveys.\n\nThe main soft spot is exactly what the stress-test note says. Eq. (1) fits a single dust power law from 0.85 mm to 2 cm, while the physical interpretation is that the dust spectrum breaks near 3 mm. A single power law cannot represent both the optically thick and thin regimes; it will average between them. At 1-2 cm, where free-free is ~65% of the total, any curvature in the dust SED will push the fit toward underestimating free-free and overestimating dust. Both the free-free/accretion correlation and the centimeter indices come from that decomposition, so the bias would affect both headline results in the same direction. The authors explicitly acknowledge this in Section 4.2, which is to their credit, but it does mean the least model-dependent claims (the correlation with total 2 cm flux, the mm indices) are the strongest, and the model-dependent ones (the 40 au optically thick region) are more conditional.\n\nOther soft spots are minor and mostly disclosed: DQ Tau needs a constrained gas spectral index, HP Tau is excluded from the correlation, and several 1-2 cm indices have errors larger than 1.0 and are dropped. None of these undermine the sample-level picture.\n\nI would send this to a referee. The dataset is valuable, the analysis is reproducible in principle (though no code or calibrated products are shipped), and the limitations are stated rather than hidden. The right referee will push on the spectral break and ask for a robustness test with a broken power law or a free-free-subtraction alternative. For readers working on disk centimeter emission or dust growth, this will be a standard reference.","headline":"A solid, honest sample-level VLA study of ordinary Taurus disks at 1-2 cm; the two-power-law SED decomposition is the main soft spot and the paper says so itself, but it deserves refereeing.","tokens_in":58704,"tokens_out":3306,"would_cite":true,"duration_ms":34665,"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":"Centimeter observations of 21 Taurus disks show the dust spectral index rising from about 2.3 at millimeter wavelengths to about 2.8 in the centimeter regime, implying that the inner 40 au of these disks is optically thick at ALMA…","keywords":["protoplanetary disks","centimeter emission","free-free emission","dust spectral index","optical depth","Taurus star-forming region","accretion rate","very large array"],"falsifier":"Resolve a few of these disks at 1 cm and 2 cm with ngVLA and map the free-free component directly; if the true dust spectral index between 3 mm and 1 cm is close to the millimeter value of about 2.3 rather than 2.8, the evidence for a 40 au optically thick inner region would disappear, and if the free-free/accretion correlation vanishes when free-free is measured from resolved images rather than from the model, the proposed accretion link would be refuted.","tokens_in":57605,"feed_emoji":"📡","tokens_out":6285,"duration_ms":63032,"temperature":0.7,"pith_summary":"Using new VLA observations of 21 ordinary planet-forming disks in Taurus, the paper establishes two things. First, the dust spectral index jumps from a median of about 2.3 at millimeter wavelengths to about 2.8 between 3 mm and 1 cm, after subtracting a ubiquitous free-free component; this change implies that the inner disk, up to 40 au, is optically thick at ALMA wavelengths and becomes optically thin only beyond 3 mm. Second, the inferred free-free emission correlates with mass accretion rate (r = 0.66 ± 0.17) and is unaffected by outer disk morphology, tying the ionized gas to inner-disk accretion and outflow processes. The results matter because they show that common disks hide their inner solid reservoir at millimeter wavelengths, and that centimeter observations offer a way to measure dust and gas components separately.","feed_headline":"Centimeter data expose opaque inner zone of planet-forming disks","feed_subtitle":"Spectral index jump from 2.3 to 2.8 hints the inner 40 au is opaque; free-free radio emission tracks accretion.","key_machinery":"The central tool is a two-component spectral energy distribution fit: $S_{\\nu}^{\\mathrm{total}} = S_0^{\\mathrm{gas}}(\\nu/15\\,\\mathrm{GHz})^{\\alpha_{\\mathrm{gas}}} + S_0^{\\mathrm{dust}}(\\nu/225\\,\\mathrm{GHz})^{\\alpha_{\\mathrm{dust}}}$. The fit separates the unresolved 0.85 mm–6 cm photometry into a flat free-free power law ($\\alpha_{\\mathrm{gas}}\\in[-1,2]$) and a steep dust power law ($\\alpha_{\\mathrm{dust}}\\in[2,4]$). Subtracting the gas component yields dust spectral indices at 3 mm–1 cm and 1–2 cm, which are then compared with ALMA disk radii to locate the optically thick region.","core_discovery":"The paper finds that the dust spectral index of planet-forming disks in Taurus changes sharply from a median of about 2.3 at millimeter wavelengths to about 2.8 between 3 mm and 1 cm, after subtracting a free-free component inferred from a two-power-law fit to photometry spanning 0.85 mm to 6 cm. The authors interpret this change as evidence that a large portion of the inner disk, up to 40 au, is optically thick at ALMA wavelengths and becomes optically thin only beyond 3 mm. They also find that the inferred free-free emission correlates with mass accretion rate (r = 0.66 ± 0.17) and is independent of outer disk morphology, suggesting that the ionized gas is tied to accretion and outflow activity in the inner disk rather than to large-scale disk structure.","pith_inferences":["Implicitly, the correlation between free-free emission and accretion rate suggests that centimeter continuum could become a straightforward accretion diagnostic for Class II disks, independent of the usual UV and optical veiling assumptions.","If the centimeter dust index is indeed about 2.8 everywhere, the grain population responsible for the emission may be strikingly uniform, hinting at a common growth ceiling; resolved imaging will test whether the emission actually originates in the same radial zone.","A testable extension is to apply the same two-power-law decomposition to VLA observations of another star-forming region, such as Lupus or Chamaeleon, to see whether the 40 au optically thick scale and the accretion correlation persist outside Taurus."],"forward_implications":["If the inner 40 au of typical disks is optically thick at ALMA wavelengths, dust masses derived from millimeter fluxes are systematically underestimated, especially for compact disks where this region dominates the emission.","The centimeter index being uniform across disks of different sizes and morphologies implies that the grain population emitting at 1–2 cm is similar even when the outer disk structure differs greatly.","Because the free-free emission tracks accretion and ignores outer disk morphology, centimeter observations can serve as a clean probe of inner-disk accretion and outflow activity, independent of the millimeter structure.","The finding that the dust emission is still appreciable at 2 cm means that future arrays like ngVLA and SKA-mid can realistically resolve the centimeter dust component and directly measure grain growth in ordinary disks.","Mass estimates from centimeter fluxes are dominated by the choice of dust opacity for grains of at least millimeter size, so centimeter mass measurements will require better laboratory opacities rather than longer integrations."],"supporting_citations":[{"why":"Supplies the ALMA sample, the compact versus substructured disk classification, and the effective disk radii at 1.3 mm used throughout the analysis.","marker":"Long et al. (2019)"},{"why":"Provides the mass accretion rates for most of the sample, used in the free-free versus accretion correlation.","marker":"Gangi et al. (2022)"},{"why":"Established the free-free emission versus accretion rate correlation in transition disks, which this work extends to ordinary full disks.","marker":"Rota et al. (2024)"},{"why":"Earlier evidence that a significant portion of disk emission is optically thick; the paper's index-versus-radius trend is compared with this work.","marker":"Tazzari et al. (2021a)"},{"why":"Provides the opacity law $\\kappa_\\nu \\propto \\nu^\\beta$ used to convert centimeter fluxes into dust masses and to discuss opacity uncertainties.","marker":"Beckwith et al. (1990)"},{"why":"Resolved centimeter imaging of GM Aur showing how free-free and dust emission are separated in a planet-forming disk, a precedent for the SED decomposition.","marker":"Macías et al. (2018)"},{"why":"Argued from millimeter surveys that a significant portion of disk emission may be optically thick, the idea this paper more directly constrains with centimeter data.","marker":"Tripathi et al. (2017)"}],"fun_headline_variants":["Radio view of Taurus disks reveals inner opacity jump","Centimeter eyes peer into opaque heart of planet disks","Taurus disks' hidden inner 40 au revealed by radio","Spectral index jump hints at opaque planet-forming zones","Free-free radio tracks accretion in Taurus disks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The two-power-law decomposition assumes a single power-law dust spectrum from 0.85 mm to 2 cm and a flat gas power law; if the dust spectrum steepens between 1 and 2 cm, the model will underestimate free-free emission and overestimate dust emission, biasing both the free-free/accretion correlation and the centimeter dust indices.","fun_headline_variants_meta":{"raw":{"variants":["Radio view of Taurus disks reveals inner opacity jump","Centimeter eyes peer into opaque heart of planet disks","Taurus disks' hidden inner 40 au revealed by radio","Spectral index jump hints at opaque planet-forming zones","Free-free radio tracks accretion in Taurus disks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000645,"raw_usage":{"total_tokens":3009,"prompt_tokens":1034,"completion_tokens":1975,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":650,"completion_tokens_details":{"reasoning_tokens":1910}},"tokens_in":650,"tokens_out":1975,"duration_ms":15441,"temperature":1.0,"reasoning_tokens":1910,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T17:57:54.386108+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Resolve a few of these disks at 1 cm and 2 cm with ngVLA and map the free-free component directly; if the true dust spectral index between 3 mm and 1 cm is close to the millimeter value of about 2.3 rather than 2.8, the evidence for a 40 au optically thick inner region would disappear, and if the free-free/accretion correlation vanishes when free-free is measured from resolved images rather than from the model, the proposed accretion link would be refuted.","supporting_citations":[{"cited_title":"A., Meijerhof , J","cited_arxiv_id":null,"evidence_quote":"Established the free-free emission versus accretion rate correlation in transition disks, which this work extends to ordinary full disks."},{"cited_title":"M., Birnstiel , T., & Wilner , D","cited_arxiv_id":null,"evidence_quote":"Argued from millimeter surveys that a significant portion of disk emission may be optically thick, the idea this paper more directly constrains with centimeter data."}],"review_version":1}