{"id":"489b71ca-b2cc-4098-93bb-1e0a6409f354","arxiv_id":"2508.19126","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A proof-of-concept showing that large-scale 21-cm power spectrum and bispectrum, plus an independent measurement of the cosmic HI density, can constrain the parameters of the HI mass-halo mass relation at z=1.","lead":"This paper tests whether large-scale 21-cm intensity mapping can reveal how neutral hydrogen is distributed inside dark matter haloes. Using simulations, the authors show that combining the 21-cm power spectrum, bispectrum, and a known cosmic HI density can recover the halo-mass relation that sets this small-scale distribution.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"In-sample validation: the same semi-numeric HIHM simulations are used to create the data, calibrate the bias-HIHM mapping, and test recovery, so the good fits and 1-sigma HIHM constraints only demonstrate self-consistency; an out-of-sample mock is needed.","rationale":"We read the paper as a proof-of-concept for recovering (alpha,beta,v_c0) from large-scale 21-cm PS/BS and Omega_HI using a quadratic bias model. The internal consistency of the pipeline is real: the PS/BS fits to the fiducial simulation are good within k_ul, the error bars from 10 realizations are small, and the MCMC recovers the input HIHM parameters within ~1-sigma when Omega_HI is known to 1-5%. The analysis is honest about the simplifications (no RSD, no noise, best-case cosmic variance only). However, the proof-of-concept is weakened by the fact that the same simulation suite supplies the 'measurement', the error estimates, the bias-vs-HIHM calibration grid, and the validation sample. This makes the success of the recovery almost self-fulfilling: the functional form of the HIHM relation is known a priori from eq. (1), the same FoF halos are used throughout, and the two-parameter PT model is fitted to the same data it is later judged against. The reported 1% precision on [Omega_HI b1] is also suspicious given that cosmic variance from a 150 Mpc box with 10 realizations and diagonal errors is used; an out-of-sample test would reveal whether this precision is real. No independent estimate of b1 or b2 (e.g., from the HI-matter cross spectrum) is presented, so the adequacy of eq. (5) is not directly verified. These are exactly the conditions the reader flagged; we agree with the conditional verdict but believe the emphasis should be on the lack of out-of-sample validation. The concrete test - running the pipeline on an independent mock, or at least a cross-realization split - would settle whether the concern is fatal to the current claim or merely a caveat.","tokens_in":19375,"tokens_out":9696,"duration_ms":104867,"concrete_test":"Generate a 21-cm map with an independent forward model - e.g., a hydrodynamical simulation (IllustrisTNG or similar) or an N-body simulation with a different halo finder and a different HIHM recipe (e.g., Villaescusa-Navarro et al. 2018) - with known HIHM parameters at z=1. Apply the exact pipeline of Secs. 3-4 (same k_ul=0.32, same chi-square and MCMC) to this mock. If the recovered (alpha,beta,v_c0) do not contain the true values within the quoted 1-sigma contours, or if the best-fit [Omega_HI b1] and gamma are biased relative to direct estimates from the mock, the central claim fails outside the calibration suite. As a cheaper first pass, split the existing 10 realizations: use 5 to build the Fig. 4 interpolation and 5 as the measurement; if recovery degrades substantially, the current error bars and contours are over-optimistic.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim - that large-scale PS+BS with an independent Omega_HI can recover the three HIHM parameters - rests on the assumption that the two-parameter quadratic-bias model of eqs. (5)-(7) is an unbiased description of the simulated HI field at k <= k_ul = 0.32 Mpc^-1. The evidence offered is in-sample. The 'observed' PS and BS (Figs 1, 2, A1) come from the same N-body halo catalogues and the same HIHM prescription used to build the interpolation grid of Fig. 4 and the fiducial parameters used for the recovery test in Fig. 5. k_ul is chosen post-hoc from the same data (Sec. 3.3). Any systematic error in the forward model common to both the data and the interpolated model - e.g., unmodeled tidal bias, stochasticity, 1-loop PS corrections, RSD, noise - cancels in the chi-square fit, so the reported ~1% constraint on [Omega_HI b1] and the 1-sigma recovery of (alpha,beta,v_c0) do not validate the physical bias model. There is no independent measurement of b1 or gamma (e.g., from an HI-matter cross-spectrum) and no test on a differently generated mock. Thus the paper demonstrates a self-consistent inversion of its own simulation, not yet that the method is robust to the simplifying assumptions listed in Sec. 5.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a proof-of-concept study at z=1 aimed at constraining the HI mass-halo mass (HIHM) relation from large-scale 21-cm intensity mapping. Using ten realizations of a [150.08 Mpc]^3 N-body simulation populated with HI via the Padmanabhan et al. (2017) HIHM prescription, the authors measure the 21-cm power spectrum (PS) and bispectrum (BS). They model these with a quadratic local bias expansion (Eqs. 6 and 7) containing two free parameters, [Ω_HI b1] and γ=b2/b1, restrict the fit to k≤k_ul=0.32 Mpc^{-1}, and obtain (0.90±0.01)×10^{-3} and γ=-0.42±0.04. They then build an interpolation grid for Ω_HI, b1, and γ as functions of the HIHM parameters (α,β,v_c0) and, adding an external Ω_HI prior of 1% or 5% relative accuracy, recover the fiducial HIHM parameters within 1σ (Table 2, Fig. 5). The paper is explicitly framed as preliminary and acknowledges that RSD and system noise are ignored.","tokens_in":19753,"tokens_out":4524,"duration_ms":48882,"significance":"If the method were validated independently, it would be valuable: it connects easily accessible large-scale 21-cm statistics to the small-scale halo--HI connection, a quantity that is otherwise difficult to probe at z≈1. The paper is largely transparent about its simplifications, presents a broad exploration of bispectrum triangle shapes, and gives a concrete proposal for breaking the degeneracy between amplitude and bias by adding an Ω_HI prior. The theoretical bias model is standard, and the interpolation strategy is a reasonable first step. However, the current evidence is a self-consistency check rather than an independent validation: the same simulation suite generates the data, calibrates the bias model, builds the interpolation grid, and provides the fiducial values for recovery. The quoted precision should therefore be interpreted as an idealized upper bound on what could be achieved, not as a demonstrated robustness of the method.","major_comments":[{"comment":"The central validation is in-sample. The 'measured' PS/BS, the best-fit bias parameters, the interpolation grid of Fig. 4, and the fiducial values used in the recovery test of Fig. 5 all come from the same simulation suite and the same HIHM prescription. Any systematic error common to the data and the interpolated model—e.g., unmodeled tidal bias, stochasticity, 1-loop corrections, or resolution effects—cancels in the χ^2 fit. The reported ~1% constraint on [Ω_HI b1] and the 1σ recovery of (α,β,v_c0) therefore demonstrate internal consistency, not that the method is robust. An out-of-sample test is needed: generate 'observed' data from a different HIHM parameter set, a different simulation code, or a differently built mock, and then apply the interpolation grid to recover the input; alternatively, use cross-validation by holding out part of the parameter grid.","section":"§3.3, §4, Figs. 1-5"},{"comment":"The model of Eqs. (5)-(7) is a tree-level quadratic bias model, and k_ul=0.32 Mpc^{-1} is chosen post hoc 'by trial and error' from the same data. There is no evidence that the model is unbiased throughout k≤k_ul; the good agreement shown in Figs. 1, 2, and A1 may again reflect shared systematics. The paper should report the reduced χ^2 and residuals and test the sensitivity of [Ω_HI b1] and γ to k_ul. In addition, Eq. (10) uses only diagonal errors: it ignores correlations between PS and BS bins and between different triangle configurations, which is likely to be significant given that the error bars are estimated from only ten realizations. With such small errors (Fig. 1), the off-diagonal covariance could substantially change the quoted uncertainties.","section":"§3.3, Eq. (10)"},{"comment":"The mapping from (Ω_HI,b1,γ) to (α,β,v_c0) is constructed by interpolating values measured from the same simulation suite, and its invertibility is tested only around one fiducial point. The left panel of Fig. 5 shows that the 95% contour for α is not closed within the prior range, so the claim that the three HIHM parameters are 'possible to estimate' is not generally established. Moreover, the external Ω_HI constraints are imposed at 1% and 5% accuracy without propagating a realistic measurement; because Ω_HI is also computed from the same simulation volume, the prior is partly derived from the same data. The authors should first present the constraints in (Ω_HI,b1,γ) space and then map them through the grid, explicitly demonstrating which parameter combinations are and are not degenerate.","section":"§4, Fig. 5, Table 2"},{"comment":"RSD and noise are acknowledged as future work, but they are not just presentational caveats: they enter the derivation of the model predictions. In redshift space the PS and BS acquire anisotropic and additional nonlinear contributions that can bias b1 and γ even at k≤0.32 Mpc^{-1}. Given that the paper's stated goal is to show the method can estimate the HIHM relation from 21-cm measurements, the current noiseless, real-space test should be described as an idealized feasibility study rather than as a demonstration that observational 21-cm data can recover the HIHM parameters.","section":"§5, Abstract"}],"minor_comments":[{"comment":"There is a contradiction in the allowed triangle-shape constraint: §3.1 states that the allowed region satisfies 2 μ t ≥ 1, while Appendix A states the constraint as 2 μ t ≤ 1. Please correct the typo and ensure the figure description is consistent.","section":"Appendix A vs §3.1"},{"comment":"The χ^2 in Eq. (10) does not specify how many k-bins and how many (μ,t) configurations are included, nor how σ_P and σ_B are estimated from the ten realizations. Adding the number of data points and the resulting degrees of freedom would help the reader judge the goodness of fit.","section":"§3.3, Eq. (10)"},{"comment":"The right vertical axes labeled 'M_cut(×10^{10} M_⊙)' are difficult to parse. Please clarify the units or use a logarithmic axis, since a large part of the parameter space corresponds to very low Ω_HI.","section":"Fig. 4"},{"comment":"The abstract says 'we show that it is possible to estimate the three parameters' of the HIHM relation. In light of the idealized, in-sample nature of the test, I suggest softening to 'demonstrate in an idealized simulation' or 'show in principle'.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable proof of concept, and the authors are candid about RSD/noise being deferred. The main issue is the in-sample validation and the post hoc choice of k_ul; this is fixable by adding an out-of-sample mock test, reporting full covariances, and softening the abstract/conclusions. I do not see a fundamental flaw in the methodology, but the central claim as currently worded is stronger than the evidence supports. Also please check the μ-t constraint typo before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does a clean job of demonstrating, in simulation, that large-scale 21-cm power spectrum and bispectrum measurements, combined with an independent Omega_HI determination, can recover the three parameters of the HIHM relation. That specific inversion is new, as far as I know, and the perturbation-theory framework is standard and carefully applied. The bispectrum analysis covers all triangle shapes, and the interpolation grid of bias parameters against HIHM parameters is a useful practical tool. The limitations—no RSD, no noise, cosmic variance only—are stated plainly in the abstract and Section 5, which I appreciate.\n\nThe soft spots are the ones the stress-test note flags. The validation is in-sample: the 'measured' PS and BS are generated from the same HIHM prescription and the same halo catalogues used to build the interpolation grid and to set the k_ul = 0.32 Mpc^-1 cut. The good chi-square and the successful recovery of fiducial HIHM parameters therefore demonstrate self-consistency, not robustness to modeling error. If the quadratic-bias model misses something (tidal bias, stochasticity, RSD, or noise), that error cancels between the mock data and the interpolated model. The paper acknowledges RSD and noise as future work, which is honest, but the lack of any out-of-sample mock means the quoted 1-sigma constraints should be treated as lower bounds. The k_ul choice is also post-hoc, and the Omega_HI prior is the Padmanabhan value, which is about twice the Chowdhury et al. stacking value; the paper notes this but does not test sensitivity to it.\n\nNone of this is fatal for a proof of concept. The central logic holds: the large-scale PS and BS constrain two combinations of bias and abundance, and adding Omega_HI breaks the degeneracy. The paper delivers exactly that demonstration.\n\nWho is it for? Anyone working on 21-cm intensity mapping forecasts, HIHM models, or bias expansion methods. It deserves a serious referee. I would send it to review, with the expectation that the authors add an out-of-sample test or, at minimum, reframe the results as a self-consistency check and soften the precision claims. It is a useful method demonstration, not an observational measurement.","headline":"Solid proof-of-concept that 21-cm PS+BS can constrain HIHM parameters, but the validation is entirely in-sample; treat the quoted errors as optimistic.","tokens_in":20229,"tokens_out":1577,"would_cite":false,"duration_ms":19767,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Large-scale 21-cm intensity-mapping statistics can be used to estimate the HI distribution inside dark-matter haloes.","keywords":["21-cm intensity mapping","neutral hydrogen","HI–halo mass relation","power spectrum","bispectrum","perturbative bias","large-scale structure","cosmic variance"],"falsifier":"Run a matched simulation that includes redshift-space distortions (or a hydrodynamic simulation with a different HIHM prescription) and apply the same PS+BS fit for k≤0.32 Mpc^-1; if the recovered [Ω_HI b1] and γ move by more than the quoted 1σ errors, or the recovered (α, β, v_c0) fall outside the fiducial 68 per cent contours, the central claim fails.","tokens_in":19279,"feed_emoji":"📡","tokens_out":9926,"duration_ms":85438,"temperature":0.7,"pith_summary":"This paper asks whether the 21-cm intensity-mapping signal at large cosmological scales can measure how neutral hydrogen is distributed among dark-matter haloes at small scales—the halo–HI mass relation (HIHM). At z=1, using ten N-body simulations with haloes populated by a fiducial HIHM, the authors show that the 21-cm power spectrum and bispectrum up to k=0.32 Mpc^-1 are fit by perturbation theory with just two parameters, [Ω_HI b1] and γ=b2/b1. Combining those two measured quantities with an independent measurement of the cosmic HI density Ω_HI, they recover the three HIHM parameters (α, β, v_c0), with 1σ errors that shrink when Ω_HI is known at 1 per cent rather than 5 per cent accuracy. The point of the proof of concept is that future 21-cm surveys could estimate the HIHM relation, a direct handle on galaxy formation and interstellar-medium evolution, without resolving individual galaxies.","feed_headline":"21-cm power spectrum plus bispectrum recovers the HI–halo link","feed_subtitle":"At z=1, two bias parameters fit the large-scale signal; adding Ω_HI pins down all three HIHM parameters.","key_machinery":"The load-bearing machinery is the quadratic local bias expansion δ_HI = b1 δ + (b2/2) δ^2, paired with second-order perturbation theory for the bispectrum of a biased tracer. The power-spectrum amplitude fixes the product Ω_HI b1; the shape dependence of the bispectrum over all triangle configurations fixes γ=b2/b1; and a precomputed numerical map from the HIHM parameters (α, β, v_c0) to (Ω_HI, b1, γ) closes the chain, turning large-scale statistics into an estimate of the small-scale HI–halo connection.","core_discovery":"At scales k ≤ 0.32 Mpc^-1 the simulated 21-cm brightness-temperature power spectrum and bispectrum at z=1 are well described by a perturbative bias model with two free parameters: [Ω_HI b1] sets the amplitude of the power spectrum, and γ=b2/b1 sets the shape dependence of the bispectrum. A joint PS+BS fit gives [Ω_HI b1]=(0.90±0.01)×10^-3 and γ=-0.42±0.04, with the negative γ indicating that HI avoids the densest regions. The three HIHM parameters are mapped numerically onto (Ω_HI, b1, γ); adding an independent Ω_HI measurement closes the system and lets a Markov-chain Monte Carlo fit recover the fiducial (α=0.09, β=-0.58, v_c0=36.3 km/s) inside the 68 per cent contours. The demonstration is","pith_inferences":["Editorial: including redshift-space distortions could break the Ω_HI degeneracy, since line-of-sight anisotropy adds a velocity term that carries the growth rate; the authors list this as future work, but the same PS+BS pair might then constrain Ω_HI, b1, and γ simultaneously.","Editorial: the method should transfer to other redshifts: rerunning the pipeline at z=2–5 where Ω_HI is independently known would map the redshift evolution of the HIHM parameters and hence of the interstellar medium, a testable extension the paper does not carry out.","Editorial: the strong α–v_c0 correlation seen in the posteriors suggests that at fixed [Ω_HI b1] there is a near-degenerate family of HIHM curves; combining PS+BS from multiple redshifts or adding squeezed-limit triangles could tighten the parameter combination.","Editorial: the same approach could be used as a model discriminator—for example, comparing a two-parameter HIHM family against the three-parameter one by whether the recovered parameters remain consistent with the input across simulations."],"forward_implications":["A single 21-cm observation at z≈1 can deliver [Ω_HI b1] and γ from large scales alone, giving the two numbers needed to normalize the HI bias expansion used in cosmological analyses.","With an external Ω_HI measurement at 5 per cent accuracy, the HIHM parameters are recovered with the fiducial values inside the 68 per cent contours; improving to 1 per cent shrinks the 1σ errors by roughly 30–50 per cent.","The negative best-fit γ implies the HI distribution at z=1 avoids the highest-density regions, meaning the large-scale bispectrum carries a measurable signal of how much HI lives in low-mass versus high-mass haloes.","Because the analytic PS and BS models match simulations on large scales, future intensity-mapping surveys can use perturbation theory rather than full simulations as the forward model for cosmological parameter estimation and non-Gaussianity constraints."],"supporting_citations":[{"why":"Supplies the HIHM relation (eq. 1) and the fiducial parameter values used to populate dark-matter haloes with HI.","marker":"Padmanabhan, Refregier & Amara (2017)"},{"why":"Provides the dark-matter-only N-body halo catalogues and simulation setup that generate the 21-cm signal.","marker":"Sarkar, Bharadwaj & Anathpindika (2016)"},{"why":"Gives the brightness-temperature mapping used to convert HI density into the 21-cm signal.","marker":"Bharadwaj & Saiyad Ali (2005)"},{"why":"Originates the second-order perturbation-theory bispectrum of a biased tracer used in eq. (7).","marker":"Fry (1984)"},{"why":"Derives the biased-tracer bispectrum model adopted for the 21-cm bispectrum.","marker":"Matarrese et al. (1997)"},{"why":"Provides the closed-form bispectrum for biased tracers with the quadratic bias term.","marker":"Scoccimarro (2000)"},{"why":"Supplies the independent Ω_HI measurement at z≈1.06 used as the third constraint.","marker":"Chowdhury et al. (2020)"},{"why":"Gives analytic expressions for the bispectrum kernels in the (μ,t) triangle-shape parameterization.","marker":"Mazumdar et al. (2020)"},{"why":"Provides the transfer function used to build the linear matter power spectrum.","marker":"Eisenstein & Hu (1999)"},{"why":"Sets the ΛCDM parameters used to compute the known quantities in the model.","marker":"Planck Collaboration et al. (2014)"}],"fun_headline_variants":["Large-scale 21-cm PS+BS recovers HI–halo link","Two bias parameters flatten HI–halo relation","PS+BS plus Ω_HI pin down HIHM at z=1","Small-scale HI mapped from large-scale 21-cm"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"Everything rests on the quadratic bias expansion δ_HI = b1 δ + (b2/2) δ^2 being an accurate description of the 21-cm signal at k ≤ 0.32 Mpc^-1, with higher-order bias, stochasticity, redshift-space distortions, and noise all negligible; if that expansion fails, the recovered HIHM parameters are biased.","fun_headline_variants_meta":{"raw":{"variants":["Large-scale 21-cm PS+BS recovers HI–halo link","Two bias parameters flatten HI–halo relation","PS+BS plus Ω_HI pin down HIHM at z=1","Small-scale HI mapped from large-scale 21-cm"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000159,"raw_usage":{"total_tokens":1146,"prompt_tokens":905,"completion_tokens":241,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":649,"completion_tokens_details":{"reasoning_tokens":166}},"tokens_in":649,"tokens_out":241,"duration_ms":2917,"temperature":1.0,"reasoning_tokens":166,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T15:54:55.720334+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a matched simulation that includes redshift-space distortions (or a hydrodynamic simulation with a different HIHM prescription) and apply the same PS+BS fit for k≤0.32 Mpc^-1; if the recovered [Ω_HI b1] and γ move by more than the quoted 1σ errors, or the recovered (α, β, v_c0) fall outside the fiducial 68 per cent contours, the central claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the dark-matter-only N-body halo catalogues and simulation setup that generate the 21-cm signal."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the brightness-temperature mapping used to convert HI density into the 21-cm signal."},{"cited_title":"N., 1984, Astrophysical Journal, Part 1 (ISSN 0004-637X), vol","cited_arxiv_id":null,"evidence_quote":"Originates the second-order perturbation-theory bispectrum of a biased tracer used in eq. (7)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the biased-tracer bispectrum model adopted for the 21-cm bispectrum."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the closed-form bispectrum for biased tracers with the quadratic bias term."},{"cited_title":"N., Sethi S., Dwarakanath K., 2020, Nature, 586, 369","cited_arxiv_id":null,"evidence_quote":"Supplies the independent Ω_HI measurement at z≈1.06 used as the third constraint."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives analytic expressions for the bispectrum kernels in the (μ,t) triangle-shape parameterization."},{"cited_title":"J., Hu W., 1999, The Astrophysical Journal, 511, 5","cited_arxiv_id":null,"evidence_quote":"Provides the transfer function used to build the linear matter power spectrum."}],"review_version":1}