{"id":"6cb1cfa6-6384-4d9e-a924-66e68dc6937e","arxiv_id":"2502.07714","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A peak flux density cut at predicted SKA-Mid sensitivities selects samples that should be about 50 percent gravitationally lensed HI galaxies at redshifts 0.8 to 3.","lead":"Gravitational lensing brightens distant neutral hydrogen galaxies, so this paper calculates where lensed HI sources outnumber ordinary ones as a function of peak flux density in future SKA-Mid surveys. A simple flux cut that selects about half lensed systems would give a cheap, new route to high-redshift gas-rich galaxies.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equality-point redshifts and yields hinge on the ALFALFA W50–M_HI relation (Eq. 6) applied to z=0–3; if high-z HI kinematics or line-profile shape differ, the 5σ intersections and the 50% efficiency claim shift.","rationale":"The paper is a careful forecasting exercise: the formalism follows established magnification-bias calculations (Perrotta et al. 2002; Negrello et al. 2007) and the authors explicitly list the main assumptions. The '50% efficiency' at the equality point is a definitional property, not an empirical discovery, so the real content is whether the equality point falls at the SKA-Mid 5σ limits. That location is controlled almost entirely by the conversion between HI mass and peak flux density at each redshift, i.e., Eq. (9) built from Eq. (6). This is the weakest link because it is a local empirical fit extrapolated over 0<z<3 with no propagated scatter and no high-z check. I therefore agree with the reader's identification. I would also ask the authors to fix the sign inconsistency between Eq. (5) and Eq. (9): as printed, Eq. (5) has a factor (1+z) in the numerator while Eq. (9) effectively uses (1+z)^{-1}; the standard formula (Meyer et al. 2017, cited in the paper) supports Eq. (9), so Eq. (5) is likely a typo, but this should be stated. That issue is secondary: if the code used Eq. (9), the headline numbers stand; the load-bearing scientific risk remains the W50–M_HI extrapolation. The proposed TNG50/high-z test would settle whether the 5σ intersections are stable. Given the forecast nature, CONDITIONAL is the right verdict, and my analysis does not change it.","tokens_in":16562,"tokens_out":18867,"duration_ms":179253,"concrete_test":"Recompute the source-count equality points and Table 1 yields after replacing Eq. (6) with the W50–M_HI relation measured from mock HI discs at z≈1–2 in a cosmological simulation (e.g., TNG50) or, if available, from high-z CO Tully–Fisher kinematics. If the equality flux at any of the three survey 5σ limits shifts by more than ~0.15 dex, the headline redshifts and yields depend on an untested local calibration; report the resulting range of z_eq and N_L.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.2 maps observed peak flux to HI mass using a mean W50–M_HI relation fitted to ALFALFA galaxies at z<0.06, then applies it at all z≤3 via Eq. (9). This is the sole link between the lensed/unlensed mass functions and the peak-flux threshold that defines the source-count equality points. Two unquantified effects make this link fragile. First, the fit uses only the mean W50 per mass bin, while Figure 3 shows roughly ±0.2 dex scatter; Eq. (4) treats W50 as single-valued at each mass, so scatter will smear the sharp N(>S) cutoff and move the equality flux. Second, evolution of disc sizes and turbulence at z~1–3, acknowledged in §3.1 and §4.1, changes W50 at fixed M_HI and also changes μmax through the disc-size relation. A 0.2 dex change in W50 shifts the inferred S_peak for a given mass by ~0.2 dex; Figure 6 indicates the equality flux changes by roughly 0.5 dex per unit redshift, so this corresponds to Δz~0.3–0.4, comparable to the separation between the Medium Wide, Medium Deep, and Deep sensitivity limits. Consequently the specific redshifts z≈0.83, 1.3, 2.6 in Table 1 and the 50% efficiency claim are not robust until the W50–M_HI relation and its scatter are tested at higher redshift or the results are shown insensitive to plausible variations.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a statistical method for selecting gravitationally lensed neutral-hydrogen (HI) galaxies in future SKA-Mid spectral-line surveys. The authors compute the distortion of the HI mass function produced by strong lensing magnification bias, using a Schechter-function HIMF fitted to ALFALFA, a Sheth-Tormen halo mass function, and singular isothermal sphere lenses. They convert HI mass to peak flux density using an ALFALFA-based W50-M_HI relation, and define 'source count equality points' where the integrated counts of lensed sources exceed those of unlensed sources. For the proposed Medium Wide, Medium Deep, and Deep surveys, they find that these equality points fall at the 5-sigma sensitivity limits at z≈0.83, 1.3, and 2.6, with lensed surface densities of roughly 0.05, 0.6, and 3 sources per square degree, respectively. They argue that a simple peak-flux-density cut should select samples that are about 50% lensed, with yields of order 20, 12, and 3 candidates for the three surveys (before redshift-dependent field-of-view scaling for the Deep survey).","tokens_in":16839,"tokens_out":6619,"duration_ms":58073,"significance":"If the underlying assumptions hold, the paper offers a practical, observationally simple route to assembling samples of lensed HI galaxies, with predictions that are falsifiable by SKA-Mid. The formal machinery is standard and the parameter choices are stated transparently, including the W50-M_HI extrapolation and the non-evolving HIMF assumption; the authors also compare their results with earlier work by Serjeant (2014) and Deane et al. (2015). The main value is in sharpening the proposal that magnification bias can be exploited for HI lens selection, and in giving concrete survey-specific thresholds. However, the central predictions are sensitive to two external relations—the W50-M_HI scaling and the redshift evolution of the HIMF—neither of which is currently tested at the redshifts of interest. The paper would be substantially strengthened by a quantitative sensitivity analysis around those relations.","major_comments":[{"comment":"The W50-M_HI relation is fitted to ALFALFA galaxies at z<0.06 and then applied over 0<z<3. The paper itself notes this limitation in Section 3.2, but it does not propagate the scatter seen in Figure 3 (roughly ±0.2 dex) into the source counts. Since Eq. (9) is the sole mapping from M_HI to peak flux density, a 0.2 dex change in W50 shifts the inferred S_peak by about 0.2 dex. According to Figure 6, the equality flux changes by roughly 0.5 dex per unit redshift, so a 0.2 dex W50 offset corresponds to a shift of order Δz≈0.3–0.4, comparable to the separation between the three survey equality redshifts (0.83, 1.3, 2.6). The claimed equality redshifts and the 50% efficiency statement are therefore not robust until either the W50-M_HI relation is tested at higher redshift or the sensitivity of the results to plausible W50 evolution and scatter is quantified.","section":"Section 3.2, Eq. (6) and Eq. (9)"},{"comment":"The calculation assumes a non-evolving HIMF, yet Section 4.1 cites conflicting evidence: Bera et al. (2022) find a decrease in high-mass galaxies from z=0 to z=0.35, while Chowdhury et al. (2024) find an increase of a factor 4–5 to z≈1. The paper discusses the qualitative direction of the effect but stops short of a quantitative test. Because the equality flux and the lensed surface densities depend directly on the Schechter parameters M*, φ*, and α, a sensitivity calculation varying these parameters within the ranges suggested by the cited literature is needed to support the statement in Section 4.1 that the estimates are 'on the conservative side.' Without such a calculation, the central predictions rest on an untested assumption that the authors themselves identify as potentially important.","section":"Section 2 and Section 4.1"},{"comment":"There is an internal inconsistency between the Deep survey yield in Table 1 and in the text. Table 1 gives N_L(Total)=2–9 for the Deep survey, which follows from multiplying the surface density by the nominal 1 deg^2 area. However, Section 4 states that at z≈2.6 the field of view expands to approximately 13.6 deg^2 and predicts a sample of 27–122 lensed candidates, a factor of about 13.6 larger. Since Table 1 is the summary of predicted yields, the discrepancy must be resolved: either the table should list the field-of-view-scaled totals, or the text should clarify why the scaling is not applied.","section":"Table 1 and Section 4 (Deep survey)"},{"comment":"The peak-flux relation is derived under a boxcar line profile, but the paper does not quantify the effect of more realistic double-horned profiles. While the authors note that the two peaks may merge at coarse velocity resolution, the threshold S_peak in Eq. (9) is used directly to define the survey detection limit. A brief test with a double-Gaussian or double-horn profile would help establish whether the equality-point fluxes shift by more than the survey sensitivity intervals.","section":"Section 3.2"}],"minor_comments":[{"comment":"In the paragraph discussing the Medium Deep survey, the text says 'the proposed Medium Wide survey will cover an area of 20 deg^2'; this should read 'Medium Deep survey.'","section":"Section 4"},{"comment":"The MeerKAT UHF-band is quoted as '~580–1000GHz'; the unit should be MHz.","section":"Section 4.3"},{"comment":"There is a typo in the sentence describing the Sheth-Tormen mass function: 'can be be described' should be 'can be described.'","section":"Section 2"},{"comment":"The fitting procedure uses the mean log W50 in each log M_HI bin, but the paper does not report the bin widths or the number of galaxies per bin, and it does not discuss how selection effects or inclination corrections might bias the fitted relation. A few details here would help readers assess the extrapolation to high redshift.","section":"Figure 3 and Eq. (6)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and presents a useful, falsifiable prediction. The main concern is that the headline numbers (equality redshifts, 50% efficiency) are not yet demonstrated to be robust to the W50-M_HI extrapolation and HIMF evolution, both of which the authors acknowledge. I would encourage the editor to request a revision that adds a quantitative sensitivity analysis rather than rejecting the manuscript, because the proposed method is simple and potentially valuable even if the precise redshifts shift."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid, honest forecasting paper. It applies the known magnification-bias selection method to HI 21-cm lensing, updating Serjeant (2014) to the rebaselined SKA-Mid surveys and deriving concrete peak-flux-density thresholds and yields. The formalism is standard, the parameters are stated, and the authors are candid about the two big assumptions: a non-evolving HIMF and a local ALFALFA scaling relation pushed to z=3. Credit where due: the comparison with Serjeant and with Deane et al. (2015) is careful, and the discussion of HIMF evolution uncertainty is balanced.\n\nThe main soft spot is the load-bearing W50–M_HI relation. The paper uses the mean relation and ignores the ~0.2 dex scatter visible in Figure 3, and it does not propagate that scatter into the counts. The stress-test concern is fair: a 0.2 dex shift in W50 moves the inferred S_peak by a similar amount, and since the equality flux changes roughly 0.5 dex per unit redshift in Figure 6, that corresponds to Δz~0.3–0.4—comparable to the separation between the Medium Wide, Medium Deep, and Deep sensitivities. So the headline redshifts (0.83, 1.3, 2.6) and the yield table should be read as illustrative until the authors either test sensitivity to W50 scatter or find higher-redshift constraints. The paper flags the assumption but never quantifies its impact; that is the main thing a referee should push on.\n\nTwo smaller mechanical issues. Equation (5) has (1+z) in the numerator, which conflicts with the standard HI mass formula and with Equation (9), which only works if (1+z) is in the denominator. This looks like a typo, but it is confusing. Second, the Deep survey yield is stated as 27–122 in the text using the redshift-scaled field of view, but Table 1 and the conclusion say 2–9. That internal inconsistency needs fixing.\n\nAlso, the 50% efficiency is definitional—the equality point is where lensed and unlensed counts cross—so it is not an empirical result. That is fine, but it should not be oversold as a performance claim.\n\nThe central argument holds up: a simple peak flux cut can select samples that are roughly half lensed at practical sensitivities, with modest yields (tens of candidates). This is a useful planning tool, not transformative. I would send it to peer review, with requests to propagate the W50 scatter, reconcile the Deep survey numbers, and fix the Eq. (5) typo. I'd likely cite it as the current reference for HI lens selection in SKA-Mid surveys.","headline":"A sound, useful forecast for HI lens selection in SKA-Mid surveys, but the specific equality-point redshifts rest on the local ALFALFA W50–M_HI relation extrapolated to z~3 without propagated scatter or evolution, so treat the numbers as directional, not precise.","tokens_in":17438,"tokens_out":6577,"would_cite":true,"duration_ms":53117,"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":"One flux cut yields 50% lensed HI galaxy candidates","keywords":["gravitational lensing","HI 21-cm line","neutral hydrogen","SKA-Mid","magnification bias","source counts","high-redshift galaxies","spectral line surveys"],"falsifier":"Measure the W50–M_HI relation at z ≈ 1–3 using resolved or lensed HI observations; if the mean W50 at fixed HI mass deviates from log(W50/km/s) = 0.298 log(M_HI/M_sun) − 0.63 by more than the local scatter, the predicted equality points will not hold. Alternatively, apply the Deep survey selection at log(S_peak/Jy) ≈ −5.35 and image the candidates: a lensed fraction clearly below 50% would falsify the central claim.","tokens_in":16285,"feed_emoji":"📡","tokens_out":10188,"duration_ms":78145,"temperature":0.7,"pith_summary":"This paper argues that strong gravitational lensing distorts the observed neutral-hydrogen (HI) mass function enough to create a clean statistical selection: a peak flux density cut that isolates lensed, HI-rich galaxies in upcoming SKA-Mid spectral line surveys. At the 5σ sensitivity limits of the proposed Medium Wide, Medium Deep, and Deep surveys, the 'source count equality points'—where lensed integrated counts first exceed unlensed counts—fall at redshifts z ≈ 0.83, 1.3, and 2.6, with lensed surface densities around 0.05, 0.6, and 3 sources per square degree. A single flux-density cut at these points should return samples that are about 50% lensed candidates, with no multiwavelength information required. The payoff would be direct 21-cm detections of HI at redshifts and masses that are otherwise inaccessible, plus a new baryonic tracer for selecting foreground dark matter haloes.","feed_headline":"One flux cut yields 50% lensed HI galaxy candidates","feed_subtitle":"At SKA-Mid's 5-sigma limits, lensed counts overtake unlensed at z=0.8-2.6, giving 0.05-3 sources per square degree.","key_machinery":"The load-bearing object is the lensed HI mass function, Φ'(M_HI, z_S) = ∫_{μ_min}^{μ_max} dμ p(μ, z_S) Φ(M_HI/μ, z_S), where Φ is the local ALFALFA Schechter mass function, p(μ, z_S) is the magnification probability from a Sheth-Tormen halo population with singular isothermal sphere density profiles, μ_min = 2, and μ_max ∈ [10, 30]. The counts are converted to observable units through a HI mass–peak flux density relation built from the ALFALFA W50–M_HI fit log(W50/km/s) = 0.298 log(M_HI/M_sun) − 0.63 and a boxcar line profile. The 'source count equality point'—where the lensed integrated count curve N(>S_peak) first rises above the unlensed curve—is the selection threshold, and the comparison set is the estimated 5σ sensitivity of each proposed SKA-Mid survey.","core_discovery":"The central claim is that gravitational lensing's effect on the observed HI mass function yields a practical, threshold-based way to find lensed HI galaxies in the SKA-Mid era. By computing the integrated counts of lensed and unlensed HI sources as functions of peak flux density, the authors identify 'source count equality points' where the two counts cross. For the proposed surveys these points land at the 5σ sensitivity limits: z ≈ 0.83 for Medium Wide (400 $deg^{2}$), z ≈ 1.3 for Medium Deep (20 $deg^{2}$), and z ≈ 2.6 for Deep (1 $deg^{2}$, with field of view stretching to ~13.6 $deg^{2}$ at that redshift). At those thresholds the lensed surface densities are roughly 0.05, 0.6, and 3 per square degree, corresponding to average sample sizes of about 20, 12, and 3 candidates in each survey. The paper further claims that, at these thresholds, a simple peak flux density cut gives a 50% lensed fraction, with the unlensed half being massive foreground HI galaxies that can be identified and removed with multiwavelength data such as LSST.","pith_inferences":["A consequence the authors leave implicit is that the equality-point technique does not require optical preselection, so it can serve as a low-latency search channel that flags candidate lensed HI systems before any imaging follow-up.","Because lensed HI selects foreground haloes via an extended, low-surface-brightness baryonic tracer rather than starlight, it may probe a different part of halo concentration parameter space than optical lens searches; the paper motivates this but does not quantify the gain.","The same argument could be pushed beyond z ≈ 3 or applied to other spectral lines, such as CO or OH megamasers, provided the relevant line-width–luminosity relation can be calibrated at the target redshifts.","An end-to-end simulation of the Deep survey with a ray-traced mock lightcone would be a direct test of whether the analytically derived equality points survive real noise, RFI, and source confusion in the data cubes."],"forward_implications":["A single peak flux density cut in SKA-Mid surveys should yield candidate lensed HI samples of roughly 20 (Medium Wide), 12 (Medium Deep), and 3 (Deep) sources, each about 50% lensed.","The predicted lensed surface densities for the Medium Deep and Deep surveys (0.2–9 per square degree) exceed the 0.13 per square degree achieved by the H-ATLAS sub-millimetre lens search.","Adding LSST optical data to identify foreground massive ellipticals should remove the unlensed HI contaminants and push the selection efficiency well above 50%.","If the HI mass function evolves with redshift as some recent measurements suggest, the lensed counts and the equality-point flux thresholds would both increase, improving the projected yields."],"supporting_citations":[{"why":"Establishes the spectral-line lensing formalism and provides the SKA-Mid sensitivity estimates that set the comparison thresholds.","marker":"Button & Deane (2024)"},{"why":"Provides the ALFALFA HI mass function parameters (α = −1.25, log M*_HI = 9.96, φ* = 4.24 × 10^-3 Mpc^-3 dex^-1) used as the intrinsic source population.","marker":"Jones et al. (2018)"},{"why":"Supplies the simulated HI-disc magnification distribution and the μ_max = 10–30 range adopted for maximum magnification.","marker":"Deane et al. (2015)"},{"why":"Originates the magnification-bias distortion of number counts for extended sources on which the HI mass function distortion is based.","marker":"Perrotta et al. (2002)"},{"why":"Supplies the dark matter halo mass function used to compute the lensing probability p(μ, z_S).","marker":"Sheth et al. (2001)"},{"why":"Defines the proposed SKA-Mid HI survey areas and sensitivity levels used throughout.","marker":"Staveley-Smith & Oosterloo (2015)"},{"why":"Underlies the 5σ sensitivity calculation for the SKA-Mid surveys.","marker":"Braun et al. (2019)"},{"why":"Provides the ALFALFA catalogue from which the W50–M_HI relation is fitted.","marker":"Haynes et al. (2018)"},{"why":"Motivates the no-evolution HI mass function assumption by bounding cosmic HI density evolution to about a factor of two out to z ~ 4.","marker":"Walter et al. (2020)"}],"fun_headline_variants":["One flux cut gives 50% lensed HI galaxies in SKA-Mid","SKA-Mid threshold: half of flux-selected HI are lensed","Flux cut selects lensed HI with 50% efficiency in SKA-Mid","Simple flux threshold yields 50% lensed HI galaxies","Flux threshold finds lensed HI at z up to 2.6"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions assume the local ALFALFA relation between HI mass and velocity width, together with a non-evolving HI mass function, remains valid out to z = 3; if high-redshift HI discs are systematically narrower, broader, or rarer than local ones, every threshold and yield estimate shifts.","fun_headline_variants_meta":{"raw":{"variants":["One flux cut gives 50% lensed HI galaxies in SKA-Mid","SKA-Mid threshold: half of flux-selected HI are lensed","Flux cut selects lensed HI with 50% efficiency in SKA-Mid","Simple flux threshold yields 50% lensed HI galaxies","Flux threshold finds lensed HI at z up to 2.6"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001492,"raw_usage":{"total_tokens":6075,"prompt_tokens":1116,"completion_tokens":4959,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":732,"completion_tokens_details":{"reasoning_tokens":4859}},"tokens_in":732,"tokens_out":4959,"duration_ms":30659,"temperature":1.0,"reasoning_tokens":4859,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T11:48:43.968485+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the W50–M_HI relation at z ≈ 1–3 using resolved or lensed HI observations; if the mean W50 at fixed HI mass deviates from log(W50/km/s) = 0.298 log(M_HI/M_sun) − 0.63 by more than the local scatter, the predicted equality points will not hold. Alternatively, apply the Deep survey selection at log(S_peak/Jy) ≈ −5.35 and image the candidates: a lensed fraction clearly below 50% would falsify the central claim.","supporting_citations":[{"cited_title":"B., Deane R","cited_arxiv_id":null,"evidence_quote":"Establishes the spectral-line lensing formalism and provides the SKA-Mid sensitivity estimates that set the comparison thresholds."},{"cited_title":"P., Obreschkow D., Heywood I., 2015, @doi [ ] 10.1093/mnrasl/slv086 , 452, L49","cited_arxiv_id":null,"evidence_quote":"Supplies the simulated HI-disc magnification distribution and the μ_max = 10–30 range adopted for maximum magnification."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Originates the magnification-bias distortion of number counts for extended sources on which the HI mass function distortion is based."},{"cited_title":"K., Mo H","cited_arxiv_id":null,"evidence_quote":"Supplies the dark matter halo mass function used to compute the lensing probability p(μ, z_S)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the proposed SKA-Mid HI survey areas and sensitivity levels used throughout."}],"review_version":1}