{"id":"213f8b62-a3bb-4018-9fd9-6faa150beb7b","arxiv_id":"2411.17312","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"For 24 rotating disks at z about 2, specific angular momentum scales with stellar mass as j_star proportional to M_star^0.25, significantly shallower than the local beta of about 0.67.","lead":"This paper measures the specific angular momentum of 41 star-forming galaxies at redshift 1.5 to 2.5 using adaptive-optics and seeing-limited integral field spectroscopy combined with HST photometry. It finds that the stellar mass-angular momentum relation has a shallower slope than the commonly assumed value, which would change how we think galaxies build up their spin over cosmic time.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline '3σ' significance is computed against a pure-disk local slope of β=2/3; the paper's own §6.2 cites β=0.52±0.04 for selection-matched local rotating disks, making the difference only ~1.7σ and undermining the claim of a statistically significant difference.","rationale":"The paper is careful and transparent: it uses multi-resolution kinematic modelling with CONDOR, integrates radial mass and velocity profiles (Eq. 5), compares against the R&F approximation and pixel-by-pixel methods, and explicitly identifies its own limitations. Those strengths justify not rejecting the work. However, the most load-bearing element of the central claim is the assertion of a statistically significant difference from the local Fall relation, and that assertion is fragile on two grounds. First, the comparison baseline is mismatched: a pure-disk/fixed-B/T slope of 2/3 is not the correct null for a sample selected with a broad rotating-disk criterion, and the paper's own Section 6.2 quotes β=0.52±0.04 for the matched local population, reducing the difference to roughly 1.7σ. Second, Section 6.2 shows that doubling the adopted j_star uncertainties changes β to 0.53±0.38, so the fitted slope is not stable under plausible systematic errors. The unquantified radial M/L-gradient bias flagged in Section 6.1.2 could act in the same direction, but it is not needed to demonstrate that the 3σ claim is overstated. The reader's weakest assumption was the M/L-gradient proxy; I partially agree, since that is the main threat to the measured slope itself, but the selection-matched baseline concern is more directly decisive for the headline significance and is fully acknowledged inside the manuscript. A conditional-accept posture remains appropriate: the underlying data and method are sound enough to publish once the significance claim is corrected and the M/L-gradient systematics are either quantified or explicitly removed from the headline conclusions. This read therefore keeps the reader's CONDITIONAL verdict unchanged.","tokens_in":60080,"tokens_out":8591,"duration_ms":83321,"concrete_test":"Recompute the formal significance of β=0.25±0.15 against the selection-matched local slope β=0.52±0.04 from Romanowsky & Fall (2012) Table 2 for all rotating systems satisfying the paper's broad RD criteria, using a two-sided Gaussian test. If |Δβ|/(σ_highz²+σ_local²)^(1/2) ≈ 1.7 (p ≳ 0.08), the abstract's 'approximately 3σ' and 'statistically significant difference' statements are unsupported and must be re-framed against the appropriate local baseline.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract's central claim is that β=0.25±0.15 'deviates by approximately 3σ from the commonly adopted local value β=0.67, indicating a statistically significant difference.' That significance is evaluated against a local slope appropriate for pure disks at fixed bulge-to-total ratio, not against the broad category of rotating disks that the 24 high-z systems comprise. Section 6.2 states the comparison explicitly: for all rotating systems meeting this paper's RD definition, Romanowsky & Fall (2012) find β=0.52±0.04, and 'the tension ... is not as large as initially suggested.' Against that selection-matched baseline, Δβ=0.27 with combined uncertainty roughly 0.155, i.e. about 1.7σ, not 3σ. Section 6.2 also notes that doubling the j_star uncertainties changes the best-fit slope to 0.53±0.38, so the fitted value itself is not robust to plausible systematic error. The separate unquantified M/L-gradient bias discussed in §6.1.2 would, if present, flatten the measured slope further; but the headline significance is already unsupported before that systematic is considered. The shallow-slope measurement may still be physically interesting, but the 'statistically significant difference' claim, as stated, does not follow from the analysis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents measurements of the specific stellar angular momentum j* for 41 star-forming galaxies at 1.5<z<2.5, based on HST near-IR surface brightness profiles and multi-resolution (AO plus natural seeing) IFS kinematics from KMOS, SINFONI, and OSIRIS. A sample of 24 rotating disks is used to fit the Fall relation j* ∝ M*^β, yielding β = 0.25 ± 0.15. The authors compare this with the local pure-disk slope β = 0.67, claim a roughly 3σ difference, and argue that previous steeper high-redshift slopes are driven by inclusion of irregular systems and by use of the R&F approximation j~ ≈ k_n v_s r_eff. They also derive angular-momentum retention factors f_j = j*/j_h using abundance matching and an assumed halo spin parameter, reporting high f_j at low halo masses. The analysis is careful in several respects: the multi-resolution kinematic modeling, Monte Carlo resampling, detailed PSF treatment, and direct radial integration of j* are strengths, and the authors explicitly flag several systematics, including the M/L-gradient issue and the construction-dependent nature of the f_j analysis.","tokens_in":60377,"tokens_out":7999,"duration_ms":70514,"significance":"If the measurement is robust, a shallow Fall-relation slope at z≈2 would be an important constraint on angular momentum acquisition and feedback at cosmic noon, and it would be broadly consistent with the IllustrisTNG-based prediction of Du et al. (2022). The paper's strengths are the unique AO+NS multi-resolution modeling, the radial-integration method rather than the global R&F approximation, the public release of the CONDOR modeling code, and the systematic comparison of methods and samples. However, the headline statistical claim is not currently supported: the paper's own §6.2 shows that against the selection-matched local baseline (β = 0.52 ± 0.04 for all rotating systems meeting their RD definition) the difference is only about 1.7σ, and the same section shows that doubling the j* uncertainties changes the slope to β = 0.53 ± 0.38. The unquantified M/L-gradient bias discussed in §6.1.2 could flatten the measured slope further. The measurement remains interesting, but the significance and error budget need to be revised before the central claim is established.","major_comments":[{"comment":"The abstract claims that β = 0.25 ± 0.15 'deviates by approximately 3σ from the commonly adopted local value β = 0.67, indicating a statistically significant difference.' This significance is computed against the pure-disk slope of 2/3, but the sample is intentionally defined with a broad rotating-disk criterion. The paper itself acknowledges in §6.2 that for all rotating systems at z≈0 meeting this RD definition, the local slope is β = 0.52 ± 0.04 (Romanowsky & Fall 2012). Against that selection-matched baseline the difference is Δβ = 0.27 with a combined uncertainty of roughly 0.155, i.e., about 1.7σ, not 3σ. The headline significance is therefore unsupported as stated, independent of additional systematic biases. Please revise the abstract and §5.2 to compare against the appropriate local baseline and soften the significance claim accordingly.","section":"Abstract and §5.2"},{"comment":"The mass-to-light-ratio gradient systematic is load-bearing for the central result. The fiducial j* measurement (Eq. 5, §4.2) assumes a radially constant stellar M/L and uses the H-band surface brightness as the mass profile. Section 6.1.2 states that stellar light profiles tend to be shallower than underlying mass profiles and that the resulting overestimation of M* at large radii and low masses 'could play a significant role in driving the high j★ for galaxies in the low-mass end,' which would flatten the fitted slope. This effect is not quantified or propagated into the quoted β = 0.25 ± 0.15. Please provide a quantitative estimate, for example by adopting a plausible radially varying M/L from spatially resolved SED fitting or by re-fitting after a conservative correction of the mass profiles, and include the resulting shift in β in the error budget or in the significance statement.","section":"§6.1.2"},{"comment":"The robustness test reported in §6.2 shows that doubling the j* uncertainties changes the best-fit slope from β = 0.25 ± 0.15 to β = 0.53 ± 0.38. This demonstrates that the measured slope is not robust to a plausible level of systematic error in the individual j* measurements. Because the abstract and conclusions quote only the statistical uncertainty, the precision of the central claim is overstated. The systematic contribution to the uncertainty in β should be propagated into the quoted value, or the significance of the shallow slope should be attenuated accordingly.","section":"§6.2"}],"minor_comments":[{"comment":"The text says the fit to the clumpy systems shows a 'negative vertical offset from the less clumpy sample of Δα∼0.2,' but the quoted normalizations and Figure 12 (α = 3.07 ± 0.07 for the high-C sample vs α = 2.88 ± 0.10 for the low-C sample) show a positive offset. The sign should be corrected to be consistent with Figure 12 and with the conclusions bullet.","section":"§5.4"},{"comment":"The conclusions bullet on the method of measuring j* attributes β ≈ 0.26 ± 0.14 and β ≈ 0.64 ± 0.2 to the mock-galaxy experiment in §6.1.2, but that experiment reports β = 0.36 ± 0.06 for Eq. 5 and β = 0.57 ± 0.05 for the R&F approximation. The values quoted in the conclusions are the real-data fits from Table 4; please distinguish between the mock-derived and data-derived slopes.","section":"§7"},{"comment":"The caption of Figure 11 gives the best-fit slope as β = 0.25 ± 0.14, while the abstract, §5.2, and Table 3 quote β = 0.25 ± 0.15. Please make the quoted uncertainty consistent throughout.","section":"Figure 11"},{"comment":"The summary figures in Appendix B list z = 1.29 for the OSIRIS subsample (e.g., COSMOS-110446, COSMOS-171407, COSMOS-130477, COSMOS-127977, UDS-124101, COSMOS-128904), whereas Table 1 lists their redshifts as 1.46–1.62. Please correct the captions to match the sample table.","section":"Appendix B"}],"recommendation":"major_revision","confidential_remarks":"The data analysis is careful and the data set is valuable, but the headline significance claim is overstated relative to the paper's own §6.2, and two unquantified systematics—the M/L-gradient bias and the doubling-of-uncertainties robustness test—directly affect the central slope measurement. These issues are fixable within the scope of the paper, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new thing here is that they measure the stellar mass–specific angular momentum relation at 1.5<z<2.5 by radially integrating rotation curves weighted by the stellar light profile, combining AO and seeing-limited IFS with HST photometry. For 24 disks they get a free slope of β=0.25±0.15, much shallower than the local 2/3. They also show you get steeper slopes if you include irregulars (β=0.48±0.21) or use the R&F approximation (β=0.61±0.21). That is a genuine contribution and the method is careful: multi-resolution modelling, Monte Carlo errors, mock-galaxy tests, and they are transparent about most limitations.\n\nThe soft spot is the significance claim. The abstract says ~3σ from β=0.67, but against the selection-matched local rotating-disk slope of β=0.52±0.04 (Romanowsky & Fall 2012, as they themselves cite in Section 6.2) the difference is only ~1.7σ. Doubling the j* uncertainties shifts the fit to β=0.53±0.38. They also flag in Section 6.1.2 that M/L gradients could flatten the slope, because stellar light profiles are shallower than mass profiles, and that effect is not propagated into the quoted error. With 24 disks and a limited mass range, the fitted slope is fragile.\n\nThe 'statistically significant difference' headline is not supported. But the measurement itself is plausible and the method comparison is valuable. I would send this to a serious referee and expect a revision that either quantifies the M/L gradient or softens the claims. Good reading-group material for how method choices drive high-z scaling relations.","headline":"Careful measurement of a shallow Fall-relation slope at z~2, but the '3σ' headline relies on the wrong local baseline and unquantified M/L gradients; still worth refereeing.","tokens_in":60973,"tokens_out":2695,"would_cite":true,"duration_ms":26450,"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 paper finds that star-forming disk galaxies at z≈2 follow a Fall relation j_star ∝ M_star^{0.25}, about 3 sigma shallower than the local slope of 0.67.","keywords":["angular momentum","Fall relation","high-redshift galaxies","disk galaxies","galaxy kinematics","integral field spectroscopy","adaptive optics","cosmic noon"],"falsifier":"Measure spatially resolved stellar mass maps for the same 24 disks, for example by fitting spectral energy distributions to deep rest-optical and near-infrared photometry, and recompute j_star by replacing the H-band light profile with the mass profile. If the slope moves from β≈0.25 toward β≈0.5–0.7, the shallow-slope claim is falsified; if the slope stays near 0.25, the claim survives.","tokens_in":59895,"feed_emoji":"🌀","tokens_out":9621,"duration_ms":83519,"temperature":0.7,"pith_summary":"Star-forming disk galaxies near the peak of cosmic star formation at z≈2 appear to spin up much more slowly as they grow in stellar mass than local spirals do. The paper measures the specific angular momentum (angular momentum per unit stellar mass) of 24 rotating disks among 41 galaxies at 1.5<z<2.5, using near-infrared HST photometry for mass profiles and both high-resolution adaptive-optics and ordinary seeing-limited spectroscopy for rotation. It finds a Fall-relation slope β=0.25±0.15, about 3 sigma below the local β≈0.67. The paper argues that two previously used shortcuts—including irregular or non-disk systems and approximating j_star with global quantities—each steepen the measured slope to roughly 0.5–0.6, so the shallow slope reflects the disk population measured with resolved radial profiles. If correct, angular momentum acquisition at cosmic noon was much less mass-dependent than today, with low-mass halos retaining unusually high angular momentum.","feed_headline":"Galaxy spins grow far slower than mass at z~2","feed_subtitle":"Resolved radial measurements put the Fall-relation slope at 0.25, versus 0.67 today.","key_machinery":"The load-bearing quantity is the specific angular momentum j_star = J/M, computed by azimuthally averaging the deprojected H-band surface brightness profile Σ(r_i) (assumed proportional to stellar mass with a constant mass-to-light ratio) and multiplying by a model rotation curve ṽ(r_i) from a joint fit to adaptive-optics and seeing-limited Hα kinematics: j_star = (2π Σ $r_i^{2}$ Σ(r_i) ṽ(r_i)) / (2π Σ r_i Σ(r_i)). This radial integration replaces the global Romanowsky–Fall approximation j̃_star ≈ k_n v_s r_eff, which depends on a single Sérsic fit and a single rotation velocity, and which the paper shows is biased for clumpy, compact, or poorly fitted galaxies. The same machinery yields the rotating-disk versus irregular classification and, together with halo masses from abundance matching, the angular momentum retention factors f_j.","core_discovery":"The central claim is that the stellar mass–specific angular momentum relation for rotating disk galaxies at 1.5<z<2.5 is much shallower than the local one: j_star ∝ $M_star^{{0.25±0.15}}$, compared with the commonly adopted β≈0.67 (2/3). The difference is significant at about 3 $\\sigma$, and a fixed-slope fit with β=2/3 is statistically rejected for these data. The paper attributes the steeper slopes reported by earlier high-redshift studies to two systematic choices: classifying low-mass irregular systems as disks, which adds low-j_star points at low mass, and using the Romanowsky–Fall approximation j̃_star ≈ k_n v_s r_eff instead of integrating resolved radial mass and velocity profiles. Applying those same choices to this sample reproduces steeper slopes of β=0.48±0.21 and β=0.61±0.21 respectively. The paper also derives angular momentum retention factors f_j = j_star/j_h that decline with halo mass, with values above unity in low-mass halos, which it interprets as evidence of efficient angular momentum transport in gas-rich systems and loss of low-angular-momentum gas through feedback-driven outflows.","pith_inferences":["If the shallow slope is real, galaxy formation models must produce low-mass z≈2 disks with j_star comparable to their host halos; a direct test would compare molecular gas kinematics from millimetre interferometry in low-mass galaxies to see whether the gas also carries high angular momentum.","The method comparison implies that published high-redshift Fall-relation slopes based on the R&F approximation may need to be re-derived with radial integration; existing seeing-limited surveys may already contain the photometry needed for such a re-analysis.","The f_j>1 values at low mass may indicate that abundance-matching halo masses are too low for those systems rather than that stellar disks truly exceed halo angular momentum; independent halo mass estimates from weak lensing or satellite dynamics would separate these possibilities.","If radial mass-to-light gradients are present, the true slope could differ from 0.25; in particular, stellar mass profiles steeper than the H-band light would lower the low-mass j_star values and steepen the relation, a testable prediction for spatially resolved stellar mass maps."],"forward_implications":["The Fall-relation slope at z≈2 for disk galaxies is β=0.25±0.15, about 3 sigma below the local value, so specific angular momentum grows only weakly with stellar mass during cosmic noon.","Combining the R&F approximation with a sample that includes irregulars yields β≈0.77, matching the commonly adopted 2/3; previous high-redshift slopes therefore likely overestimate the true slope.","A fixed-slope fit with β=2/3 to the disks is statistically rejected (p≈4×10^-10), so analyses that assume 2/3 at z>1 miss real evolution.","Low-mass halos show angular momentum retention factors f_j>1 that decline with mass, implying efficient angular momentum transport and preferential loss of low-angular-momentum gas in low-mass galaxies.","The slope evolution seen here, shallow at z≈2 and steepening toward 0.67 at z=0, matches the trend seen in cosmological simulations, suggesting the local relation was largely assembled at z<1."],"supporting_citations":[{"why":"Defines the j̃_star ≈ k_n v_s r_eff approximation and the local 2/3-slope benchmark; this is the method the paper shows biases high-redshift slopes upward.","marker":"Romanowsky & Fall (2012)"},{"why":"High-redshift (0.8<z<2.6) 360-galaxy study that assumed a fixed slope β=2/3 using the R&F approximation; supplies the main comparison slope and normalisation.","marker":"Burkert et al. (2016)"},{"why":"z~1.5 survey with a free-slope fit β=0.53±0.1; source of part of the parent sample and an example of R&F-based slope measurements.","marker":"Gillman et al. (2020)"},{"why":"Local Fall-relation benchmark with β=0.67 for fixed bulge-to-total ratio; the reference value the z≈2 slope is compared against.","marker":"Fall & Romanowsky (2018)"},{"why":"Cosmological hydrodynamical simulation study finding a shallow slope at z=1.5 and a steeper slope at z=0; independent theoretical support for slope evolution.","marker":"Du et al. (2022)"},{"why":"Introduces the multi-resolution (AO+NS) kinematic modelling with CONDOR that this paper uses to derive rotation curves and velocity profiles.","marker":"Espejo Salcedo et al. (2022)"},{"why":"Provides the HST near-IR photometry and single-component Sérsic fits for the SINS sample; basis for the mass profiles and the R&F approximation comparison.","marker":"Tacchella et al. (2015)"},{"why":"Survey data release with adaptive-optics Hα observations for the z~2.2 subsample; supplies the AO kinematics and the v_rot comparison.","marker":"Förster Schreiber et al. (2018)"},{"why":"Redshift-dependent abundance matching relations used to assign halo masses and compute angular momentum retention factors f_j.","marker":"Moster et al. (2013)"}],"fun_headline_variants":["Galaxy spin-mass slope at z~2 is just 0.25, not 0.67","High-z galaxy disks spin up slower than mass grows","Fall relation slope at z~2 is 0.25, 3-sigma shallower","Cosmic noon galaxies: spin grows far slower than mass","Steep Fall slopes at high z traced to systematic biases"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper assumes that the near-infrared brightness of a galaxy, scaled uniformly, faithfully traces its stellar mass at every radius; if strong radial gradients in stellar population or dust exist, the measured low-mass angular momenta and the shallow slope could be artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Galaxy spin-mass slope at z~2 is just 0.25, not 0.67","High-z galaxy disks spin up slower than mass grows","Fall relation slope at z~2 is 0.25, 3-sigma shallower","Cosmic noon galaxies: spin grows far slower than mass","Steep Fall slopes at high z traced to systematic biases"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000237,"raw_usage":{"total_tokens":1670,"prompt_tokens":1268,"completion_tokens":402,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":884,"completion_tokens_details":{"reasoning_tokens":304}},"tokens_in":884,"tokens_out":402,"duration_ms":4473,"temperature":1.0,"reasoning_tokens":304,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:14:43.782556+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure spatially resolved stellar mass maps for the same 24 disks, for example by fitting spectral energy distributions to deep rest-optical and near-infrared photometry, and recompute j_star by replacing the H-band light profile with the mass profile. If the slope moves from β≈0.25 toward β≈0.5–0.7, the shallow-slope claim is falsified; if the slope stays near 0.25, the claim survives.","supporting_citations":[],"review_version":1}