{"id":"f374c849-03db-45a2-bc4a-537591787843","arxiv_id":"2505.10706","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Accreting primordial black holes with masses of 1 to 100 solar masses are constrained to less than about 0.1 to 0.7 percent of dark matter by the unresolved cosmic X-ray background, with consistent limits from the Lyman-Werner background.","lead":"This paper calculates how much light primordial black holes (PBHs) would give off as they swallow gas in the early universe, across X-rays, ultraviolet, and radio. It finds that PBHs can make up at most about 0.1 to 0.7 percent of dark matter in the 1 to 100 solar mass range, or they would overproduce the observed X-ray background.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 1 M_sun f_PBH limit is not robust: removing LHAF/eADAF sub-regimes relaxes it by 4–40x, and the abstract (0.03) and §3.2 (0.3) disagree on the relaxed value.","rationale":"The reader's weakest assumption is correct and is the load-bearing point. I sharpen it: the dominant uncertainty is not Bondi accretion per se but the LHAF sub-regime that Equation (13) plus the density profiles select. The paper demonstrates order-of-magnitude sensitivity to this choice but does not propagate it into the quoted limits, and the abstract and Section 3.2 give inconsistent relaxed values (3e-2 vs 3e-1). This does not refute the paper—PBHs are still excluded as the dominant DM component under all variants—but it does mean the precise f_PBH values (0.007, 0.0008, etc.) are not robust. A targeted radiation-hydro simulation would settle whether the LHAF luminosity is realized. The original conditional verdict remains appropriate.","tokens_in":36420,"tokens_out":7803,"duration_ms":76240,"concrete_test":"Run radiation-hydrodynamic zoom-in simulations of a 1 M_sun PBH in a ~10^5 M_sun, z~25 molecular-cooling minihalo (extending Liu et al. 2022), measuring the accretion rate and emergent 0.5–2 keV luminosity; compare with the LHAF prediction from Eq. (13) and §2.2.3. If the simulated luminosity is more than ~3x below the LHAF value, recompute f_PBH,max for 1 M_sun; a shift above 0.01 would invalidate the headline 0.7% bound and would confirm that the constraints are not robust to accretion modeling.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central numerical claim—f_PBH<=0.007 for 1 M_sun and ~6e-4 for 10–100 M_sun—rests on the accretion model in §2.2.1–2.2.3. Equation (13) adopts Bondi-Hoyle-Lyttleton accretion with the virial velocity as the characteristic velocity and gas densities from the halo profiles; the resulting ṁ then selects eADAF/ADAF/LHAF/thin-disk regimes. For the low-mass halos (M_h<10^6 M_sun) that dominate the emission, 1 M_sun PBHs fall predominantly in the LHAF window (0.1α^2<ṁ<0.07α), whose inverse-Compton and bremsstrahlung spectra dominate the soft X-ray background. LHAF radiative efficiency for stellar-mass BHs in minihalos is an uncalibrated analytical extrapolation with fixed α=0.1, δ=0.3, β=10/11; no observational anchor is provided. The paper's own 'Standard ADAF (no sub-regimes)' variation removes LHAF/eADAF and relaxes the 1 M_sun X-ray limit to f_PBH<3e-1 under the Makino+1998 profile and f_PBH<2e-2 under the simple isothermal profile (§3.2, Fig. 6). Both values exceed the headline 7e-3. This sensitivity is understated in the abstract, which reports relaxation 'to 3e-2'. The internal inconsistency between the abstract and §3.2 means the model dependence is not quantified; because the headline bound is below the relaxed bounds, the central claim is contingent on the unvalidated LHAF prescription. Additional simplifications—omission of the Bondi λ factor, use of virial velocity, no feedback/outflow or magnetic-field suppression—all bias the calculation toward higher luminosity and tighter limits.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript models the contributions of accreting primordial black holes (PBHs) to the cosmic X-ray background, Lyman-Werner background, and cosmic radio background, and derives upper limits on the PBH dark matter fraction f_PBH for monochromatic masses between 1 and 100 solar masses. The accretion model includes eADAF, standard ADAF, LHAF, and thin-disk regimes, with emission from PBHs in DM halos and the IGM. The baseline analysis yields f_PBH <= 7e-3 for 1 M_sun, 6e-4 for 10 M_sun, 6e-4 for 33 M_sun, and 7e-4 for 100 M_sun, and concludes that PBHs cannot explain the CRB excess or the EDGES signal. The paper also tests variations in halo density profiles, velocity prescriptions, halo mass functions, and ADAF subregimes, finding that removing LHAF and eADAF substantially relaxes the 1 M_sun constraint.","tokens_in":36864,"tokens_out":8358,"duration_ms":82534,"significance":"If the central constraints are correct, this paper provides one of the strongest exclusion limits on stellar-mass PBHs as dark matter, competitive with microlensing and CMB accretion bounds, and it demonstrates complementarity between X-ray, Lyman-Werner, and radio constraints. The manuscript is unusually transparent: the analytic framework is specified in enough detail to re-implement, the fixed microphysical parameters are acknowledged, and a systematic sensitivity analysis is included. The main weakness is that the headline limits depend sensitively on an unvalidated LHAF prescription, and the reported model dependence is internally inconsistent between the abstract and Section 3.2. With those issues addressed, the paper would be a valuable contribution to the PBH literature.","major_comments":[{"comment":"The abstract and Section 3.2 disagree on the relaxed 1 M_sun limit. In Section 3.2, the 'Standard ADAF (no subregimes)' variation relaxes the X-ray constraint from f_PBH < 1e-2 to f_PBH < 3e-1 for the Makino+1998 profile and to f_PBH < 2e-2 for the simple isothermal profile, while the abstract reports '3e-2'. The factor ~15 spread between the two profiles is not reflected in Section 4, which describes the relaxation as 'up to an order of magnitude'. Since the baseline constraint is f_PBH <= 7e-3, this is a factor 4-40 model dependence that is understated. Please unify the numbers, state the full range, and reframe the headline constraints as conditional on the adopted LHAF prescription.","section":"Section 3.2, Fig. 6, Abstract, Section 4"},{"comment":"The LHAF regime, which dominates the soft X-ray emission that sets the headline limits, is an analytical extrapolation that is not directly calibrated for stellar-mass BHs in low-mass minihalos. Fixed microphysical parameters (alpha=0.1, delta=0.3, beta=10/11) are adopted without variation, and the accretion rate in Eq. (13) omits the Bondi factor while using the virial velocity as the characteristic velocity, both of which bias the calculation toward higher luminosity. Because removing LHAF relaxes the 1 M_sun limit by a factor of 4-40, the central claim is contingent on an unvalidated prescription. The authors should either vary alpha, delta, and beta explicitly or state clearly that the baseline limits are upper envelope constraints under the LHAF model, and the abstract and conclusion should be adjusted accordingly.","section":"Section 2.2.3 after Eq. (16), Eq. (13), Section 3.1.1"},{"comment":"The final f_PBH limits are quoted as single central values without propagating the asymmetric uncertainties of the nsCXB measurement (9.7 +1.6/-1.8 per cent in 0.5-2 keV and 17 +5.9/-7.0 per cent in 2-10 keV), nor the JWST-related caveat in the footnote that the unresolved background may decrease. Because f_PBH scales approximately linearly with the assumed excess, the asymmetric errors translate into roughly 20-40 per cent uncertainties in the derived limits. Please quote the limits with propagated ranges, or explicitly state that the constraints are central-value comparisons that do not include observational error.","section":"Section 3.1.1 and Cappelluti et al. (2017) nsCXB data"},{"comment":"The 10 M_sun constraint is presented inconsistently: Section 3.1.1 quotes f_PBH <= 0.0008 as the refined CXB constraint, while Section 3.1.2 states that the LWB tightens this to f_PBH <= 0.0006, and the abstract uses 6e-4. This is a genuine inconsistency if the two numbers are meant to represent the same final constraint. Please label the CXB-only and multi-frequency limits separately, or standardize on a single final value in all sections.","section":"Section 3.1.1 and Section 3.1.2"}],"minor_comments":[{"comment":"The function F(c) is used in Eq. (8) and Eq. (34) but never explicitly defined; please define F(c) = ln(1+c) - c/(1+c) in the text.","section":"Eqs. (8) and (34)"},{"comment":"The phrase 'viral temperature' should be 'virial temperature'.","section":"Section 2.3 after Eq. (35)"},{"comment":"The statement that PBHs can explain up to 99 per cent of the soft X-ray excess is a band-integrated saturation value obtained by construction; please clarify that no comparison of the spectral shape inside the 0.5-2 keV band is made.","section":"Section 3.1.1"},{"comment":"The EDGES radio excess parameter A_r is quoted for specific f_PBH values; it would help the reader if the table also listed the f_PBH required to reach the lower bound A_r=1.9, to quantify the shortfall directly.","section":"Section 3.1.3 and Table 1"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper before reading it. First, it is a serious, re-implementable attempt to constrain stellar-mass PBHs as dark matter using X-ray, Lyman-Werner, and radio backgrounds together, and the qualitative conclusion—PBHs in the 1–100 M_sun range cannot be most of the DM—is robust. Second, the headline numbers are more model-dependent than the abstract lets on: the 1 M_sun limit of f_PBH ≤ 0.007 rests largely on the LHAF accretion sub-regime, and the paper's own sensitivity run without sub-regimes relaxes that limit to 0.3 (Makino+1998 profile) or 0.02 (isothermal), not the 0.03 quoted in the abstract.\n\nWhat's actually new: the regime-dependent accretion model (eADAF/ADAF/LHAF/thin disk) applied consistently to three backgrounds, and the claim that the Lyman-Werner background gives limits comparable to X-ray, contrary to Liu et al. (2022). The model is specified in enough detail to re-implement, and the comparison against microlensing, CMB accretion, and Galactic center bounds is thorough. The paper does well to test variations in density profiles and velocity prescriptions; most variations move things by factors of a few.\n\nThe soft spots are real but manageable. The internal inconsistency between the abstract and §3.2 on the relaxed limit needs fixing—it is not merely cosmetic, because it shows the headline bound is contingent on one uncalibrated prescription. Relatedly, the f_PBH limits are quoted without error bars; the nsCXB measurement has asymmetric errors, and alpha, beta, delta are fixed at fiducial values. A simple propagation would let the reader see how much of the constraint is physics versus assumption. The accusation of a coding bug in Liu et al. (2022) is asserted, not demonstrated; the paper needs either a direct comparison with that code or a more careful framing of the difference. Finally, the Bondi-Hoyle treatment with virial velocity omits the Bondi factor and feedback/outflow suppression, which biases toward higher luminosity and tighter limits.\n\nNone of this sinks the main result: the order-of-magnitude exclusion of f_PBH ~ 1 in the stellar-mass window is consistent with previous bounds and internally coherent. But the precise values (0.007, 0.0006) should be treated as indicative, not precise.\n\nThis paper is for the PBH/early-universe crowd. It deserves a serious referee and, after revision, could be a useful reference. I would send it out for review, with the request that the authors reconcile the abstract with §3.2, add error propagation (even rough), and substantiate or soften the Liu et al. criticism.","headline":"The multi-frequency framework is solid and the qualitative exclusion of stellar-mass PBHs as all the DM holds, but the headline 1 M_sun limit is much softer if LHAF is excluded, and the paper understates that sensitivity.","tokens_in":37420,"tokens_out":3439,"would_cite":true,"duration_ms":30348,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["95.35.+d","97.60.Lf","98.70.Vc"],"model":"deepseek-v4-flash","headline":"Stellar-mass primordial black holes can make up at most about 0.7 percent of dark matter before their accretion radiation overproduces the cosmic X-ray background.","keywords":["primordial black holes","dark matter","cosmic X-ray background","Lyman-Werner background","cosmic radio background","Bondi-Hoyle-Lyttleton accretion","advection-dominated accretion flow","early universe"],"falsifier":"High-resolution radiation-hydrodynamic simulations of a single stellar-mass PBH accreting in a $10^4$–$10^6\\,M_\\odot$ high-redshift halo, with gas heating, outflows, and magnetic fields, would settle the central assumption: if simulated X-ray luminosities fall systematically below the Bondi-based values used here, the reported caps are too strong by roughly that factor. A deep X-ray survey that resolved most of the non-source CXB into ordinary sources would instead shrink the room for PBH emission.","tokens_in":36204,"feed_emoji":"🕳️","tokens_out":14479,"duration_ms":126127,"temperature":0.7,"pith_summary":"This paper sets out to test whether stellar-mass primordial black holes—objects that could have formed from density fluctuations in the early universe—can make up a meaningful share of dark matter. It argues that they cannot, provided their gas accretion is described by the Bondi-Hoyle-Lyttleton model with the halo gas densities and virial velocities used here: a 1 solar-mass PBH population would exceed the unresolved cosmic X-ray background once it reaches $7\\times10^{-3}$ of the dark matter, and populations of 10, 33, and 100 solar masses are capped at $8\\times10^{-4}$, $6\\times10^{-4}$, and $7\\times10^{-4}$. At those same allowed levels, PBHs could still explain up to 99, 93, 80, and 91 per cent of the unresolved soft X-ray background, so they remain a possible contributor to that excess. The paper also finds that the allowed fractions are consistent with Lyman-Werner background limits, but are two to four orders of magnitude too small to explain the ARCADE 2 radio excess or the EDGES 21-cm absorption signal. The result matters because it turns three independent cosmic radiation backgrounds into mutually consistent upper limits on PBH dark matter.","feed_headline":"Primordial black holes capped at 0.7 percent of dark matter","feed_subtitle":"X-ray and Lyman-Werner backgrounds cap stellar-mass PBHs near one percent of dark matter and rule them out for EDGES.","key_machinery":"The load-bearing object is the Bondi-Hoyle-Lyttleton accretion rate, $\\dot M=4\\pi G^2M^2 n\\mu m_p/\\tilde v^3$, where $n$ is the local gas density and $\\tilde v$ combines the gas sound speed with the relative velocity. The emission spectrum is chosen by the Eddington-scaled rate $\\dot m$: a thin disk for $\\dot m\\gtrsim0.07\\alpha$, then LHAF, standard ADAF, and eADAF (advection-dominated accretion flows, in which most viscously generated heat is carried into the hole rather than radiated) at progressively lower rates. The paper feeds this accretion model with gas densities from a simple isothermal profile, a hydrostatic-equilibrium halo gas profile, and a rescaled simulation halo profile, using the halo virial velocity as the characteristic velocity, and integrates over a halo mass function modified by PBH isocurvature perturbations. This turns a chosen PBH dark-matter fraction into predicted X-ray, Lyman-Werner, and radio backgrounds that can be compared with observed excesses.","core_discovery":"On its own terms, the paper's central discovery is that accreting stellar-mass PBHs inside low-mass dark-matter halos would have already left a clear imprint in the unresolved X-ray sky. Using a four-regime accretion model (eADAF, standard ADAF, LHAF, and thin disk) and halo gas densities from three profiles, the paper finds that matching the observed non-source soft X-ray background requires $f_{\\rm PBH}\\le 7\\times10^{-3}$ for $M_{\\rm PBH}=1\\,M_\\odot$ and $f_{\\rm PBH}\\le 8\\times10^{-4}$, $6\\times10^{-4}$, $7\\times10^{-4}$ for 10, 33, and 100 $M_\\odot$, respectively; at these levels PBHs account for up to 99, 93, 80, and 91 per cent of that background. The Lyman-Werner background gives independent limits of the same order, tightening the 10 $M_\\odot$ case to $6\\times10^{-4}$. The radio background adds a negative result: even with all dark matter in PBHs, the predicted $z=0$ radio brightness is below the observed excess, and reaching the EDGES-required radio enhancement $1.9<A_r<418$ needs fractions the X-ray and Lyman-Werner constraints already exclude.","pith_inferences":["Because the caps are set by how much of the non-source X-ray background remains unresolved, future deep X-ray surveys that resolve more of that background into ordinary galaxies and AGNs would push the allowed PBH fraction downward, not upward.","For extended mass functions, the monochromatic caps should not be read as literal bounds; the same machinery would spread emission across masses, and the tightest squeeze is likely to sit near 10–100 $M_\\odot$ where the caps are deepest.","If the EDGES absorption is confirmed as a genuine radio-background excess, this paper's logic predicts the source is not stellar-mass PBHs, which focuses the search on astrophysical emitters or non-PBH particles.","The same accretion-plus-background pipeline could be turned around to test PBH seeding of high-redshift supermassive black holes: any seeding model that requires a large PBH fraction in this mass window would now have to beat these X-ray and Lyman-Werner caps."],"forward_implications":["PBHs in the 1–100 solar-mass window cannot be the dominant form of dark matter; the caps are $7\\times10^{-3}$ at 1 $M_\\odot$ and $6$–$7\\times10^{-4}$ at 10–100 $M_\\odot$.","Allowed PBH populations can still account for most of the unresolved soft X-ray background—99, 93, 80, and 91 per cent for 1, 10, 33, and 100 $M_\\odot$—but only about a third of the hard X-ray background.","The Lyman-Werner background independently excludes fractions above roughly the same thresholds, so the allowed PBHs do not dissociate enough molecular hydrogen to delay early star formation.","PBHs do not explain the ARCADE 2 excess or the EDGES 21-cm absorption; producing the EDGES-required radio enhancement would need fractions two to four orders of magnitude above the X-ray caps, and the $z=0$ excess also remains above PBH predictions.","The constraints are sensitive to accretion physics: omitting the ADAF sub-regimes relaxes the 1 $M_\\odot$ cap from $7\\times10^{-3}$ to $3\\times10^{-2}$, leaving an order of magnitude of room in that specific model choice."],"supporting_citations":[{"why":"It supplies the observed non-source cosmic X-ray background excess in the 0.5–2 and 2–10 keV bands that the paper uses as the target for PBH emission.","marker":"Cappelluti et al. (2017)"},{"why":"It supplies the four-regime accretion emission model (eADAF, ADAF, LHAF, thin disk) and microphysical parameters used to compute PBH luminosities.","marker":"Takhistov et al. (2022)"},{"why":"It supplies the hydrostatic halo gas density profile that, together with the simple isothermal profile, yields the baseline X-ray constraints.","marker":"Makino et al. (1998)"},{"why":"It supplies the rescaled halo density profile used as a third gas model and the earlier Lyman-Werner treatment that the paper corrects.","marker":"Liu et al. (2022)"},{"why":"It supplies the PBH-modified power spectrum and halo mass function used to distribute PBHs among halos.","marker":"Zhang et al. (2024a)"},{"why":"It provides the prior PBH background constraints and the sound-speed velocity prescription adopted as a model variation.","marker":"Ziparo et al. (2022)"},{"why":"It supplies the ARCADE 2 low-frequency radio excess that the paper shows PBHs cannot reproduce at allowed fractions.","marker":"Fixsen et al. (2011)"},{"why":"It supplies the $1.9<A_r<418$ range required to explain EDGES, which the paper uses to rule out PBH radio explanations.","marker":"Fialkov & Barkana (2019)"},{"why":"It supplies the EDGES 21-cm absorption detection whose radio-background interpretation the paper tests.","marker":"Bowman et al. (2018)"}],"fun_headline_variants":["X-ray background caps PBH dark matter at 0.7 percent","Stellar-mass PBHs restricted to under 1% of dark matter","Cosmic X-rays limit primordial black holes as dark matter","EDGES radio excess incompatible with PBH dark matter fraction","PBH dark matter constrained by X-ray and Lyman-Werner backgrounds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole argument rests on Bondi-Hoyle-Lyttleton accretion with halo virial velocity and the chosen gas density profiles faithfully describing how brightly PBHs actually shine; if real accretion is weaker because of gas heating, outflows, magnetic fields, or streaming velocities, the constraints loosen.","fun_headline_variants_meta":{"raw":{"variants":["X-ray background caps PBH dark matter at 0.7 percent","Stellar-mass PBHs restricted to under 1% of dark matter","Cosmic X-rays limit primordial black holes as dark matter","EDGES radio excess incompatible with PBH dark matter fraction","PBH dark matter constrained by X-ray and Lyman-Werner backgrounds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001027,"raw_usage":{"total_tokens":4453,"prompt_tokens":1192,"completion_tokens":3261,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":808,"completion_tokens_details":{"reasoning_tokens":3170}},"tokens_in":808,"tokens_out":3261,"duration_ms":23951,"temperature":1.0,"reasoning_tokens":3170,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:04:43.983787+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"High-resolution radiation-hydrodynamic simulations of a single stellar-mass PBH accreting in a $10^4$–$10^6\\,M_\\odot$ high-redshift halo, with gas heating, outflows, and magnetic fields, would settle the central assumption: if simulated X-ray luminosities fall systematically below the Bondi-based values used here, the reported caps are too strong by roughly that factor. A deep X-ray survey that resolved most of the non-source CXB into ordinary sources would instead shrink the room for PBH emission.","supporting_citations":[{"cited_title":"B., et al","cited_arxiv_id":null,"evidence_quote":"It supplies the four-regime accretion emission model (eADAF, ADAF, LHAF, thin disk) and microphysical parameters used to compute PBH luminosities."},{"cited_title":"1998, ApJ, 497, 555","cited_arxiv_id":null,"evidence_quote":"It supplies the hydrostatic halo gas density profile that, together with the simple isothermal profile, yields the baseline X-ray constraints."},{"cited_title":"2022, MNRAS, 517, 1086 Article number, page 21 of 23 A&A proofs:manuscript no","cited_arxiv_id":null,"evidence_quote":"It provides the prior PBH background constraints and the sound-speed velocity prescription adopted as a model variation."},{"cited_title":"J., Kogut, A., Levin, S., et al","cited_arxiv_id":null,"evidence_quote":"It supplies the ARCADE 2 low-frequency radio excess that the paper shows PBHs cannot reproduce at allowed fractions."},{"cited_title":"& Barkana, R","cited_arxiv_id":null,"evidence_quote":"It supplies the $1.9<A_r<418$ range required to explain EDGES, which the paper uses to rule out PBH radio explanations."}],"review_version":1}