{"id":"209b0fba-c1b5-4bf3-a531-80afd7c20bc5","arxiv_id":"2412.11921","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Accounting for radiative feedback and formation-time effects, accretion grows primordial black holes by at most a few percent in the radiation era and negligibly in the baryonic Park-Ricotti model, while the Bondi model with dark-matter halos allows orders-of-magnitude growth only for high…","lead":"Primordial black holes (PBHs) may or may not grow substantially by swallowing gas in the early universe. This paper compares two accretion models and finds that large growth is only possible under a specific, optimistic set of assumptions, while a model with radiation feedback predicts almost no growth.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"PR suppression claim hinges on the arbitrary c_in_s=25 c_s scaling; a physically motivated constant sound speed may reverse the negligible-growth conclusion.","rationale":"The reader identified the extrapolation of the Park-Ricotti radiative-feedback prescription as the weakest assumption; my concern is the sharpest version of that assumption. The paper's central contrast between the BHL and PR models is what makes its conclusion novel: without the PR suppression, the BHL plus DM-halo scenario predicts several orders of magnitude growth for Mi >= 100 M_sun, which would be relevant for SMBH seeds. The PR suppression in the linear regime comes almost entirely from the 1/(c_in_s)^5 scaling, so the numerical value of c_in_s is not a minor nuisance parameter but the deciding factor. The paper's own sensitivity check, varying c_in_s by a factor of five changes the accreted mass by roughly five orders of magnitude, demonstrates that the headline statement is not stable under the quoted uncertainty. I therefore do not claim the paper is wrong; I claim its central 'negligible PR growth' result is conditional on a c_in_s choice that may overestimate the temperature of the ionized bubble in the high-redshift cosmological fluid. The proposed test is straightforward and would settle the question using the authors' own framework, because all other ingredients are fixed. If the test shows PR growth remains negligible for a constant c_in_s around 10-15 km/s, the paper's qualitative conclusion survives; if not, the conclusion needs to be reframed as highly parameter-dependent. The conditional verdict remains appropriate, so I do not change it.","tokens_in":26676,"tokens_out":9579,"duration_ms":86317,"concrete_test":"Recompute the right panel of Fig. 12 using c_in_s = 10 km/s and c_in_s = 15 km/s (constant) instead of c_in_s = 25 c_s, and also with c_in_s = 25 c_s restricted to z <= 1100 while using BHL for z > 1100. If for Mi >= 100 M_sun with DM halos the accreted-mass fraction Delta M/M_i rises above order unity in any of these variants, the PR-negligibility conclusion is an artifact of the feedback-sound-speed choice.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central conclusion that PR feedback makes baryonic growth negligible is driven by the fixed ratio c_in_s = 25 c_s introduced in Sec. 4. The Park-Ricotti calibration was performed for local IMBHs accreting from gas with c_s of order a few km/s, where 25 c_s ~ 25 km/s is a plausible photoionized sound speed. In the cosmological application, Eq. (3.7) gives c_s ≈ 6 km/s at z ≈ 1000, so c_in_s = 150 km/s; at z ≈ 100 it is about 48 km/s. These values are far above the roughly 10-20 km/s expected for photoionized gas, and because the linear-regime PR accretion rate in Eq. (4.7) scales as (c_in_s)^{-5}, this choice suppresses the early-universe accretion rate by factors of roughly 10^2 to 10^5 relative to a constant c_in_s = 10-15 km/s. The authors explicitly find that varying c_in_s from 10 to 50 km/s changes the accreted mass by about five orders of magnitude (Sec. 4.1), yet Fig. 12 fixes only 25 c_s and never displays the alternative curves. A smaller, physically motivated c_in_s, or one that is roughly constant in redshift as photoionization equilibrium suggests, could make PR growth non-negligible for Mi >= 100 M_sun, undermining the headline claim that PR mass evolution is negligible.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper revisits accretion onto primordial black holes (PBHs), separating radiation accretion in the early Universe from baryonic accretion at later times. For radiation accretion, it derives an analytic mass-growth integral and finds a maximum mass increase of about 4% for λ=0.1, considerably smaller than earlier claims of up to 40%, because the formation-time factor γ and an improved z(t) are included. For baryons, the authors compare the traditional Bondi-Hoyle-Lyttleton (BHL) model with the Park-Ricotti (PR) model, including radiative feedback, and study both isolated PBHs and PBHs surrounded by dark-matter halos, in linear and non-linear regimes, with SPIK20 and ROM07 velocity profiles. The central claims are that BHL accretion with DM halos can grow PBHs with Mi ≳ 100 M⊙ by several orders of magnitude by z ≲ 10, while PR feedback makes baryonic growth negligible; the paper emphasizes that both results are highly sensitive to the sound speed and velocity assumptions.","tokens_in":1581,"tokens_out":2005,"duration_ms":52185,"significance":"The paper is a useful, transparent mapping of the uncertainties in PBH accretion, an important ingredient for early supermassive-black-hole seed scenarios, CMB constraints, and gravitational-wave merger-rate predictions. Its strengths include an analytic treatment of radiation accretion that clearly identifies the role of the formation time, a systematic side-by-side comparison of BHL and PR models, and an explicit exploration of velocity-profile and parameter sensitivities (λ, x_e, c_in_s, DM halo profile). If the results hold, the paper would usefully temper recent claims of guaranteed large PBH growth and would sharpen the conditions under which growth is possible. The main caveat is that the headline PR result is conditional on a specific extrapolation of a feedback closure calibrated on local IMBH simulations, which the authors themselves show to be highly sensitive.","major_comments":[{"comment":"The linear-regime PR accretion rate in Eq. (4.7) scales as (c_in_s)^{-5}, and Sec. 4.1 reports that varying c_in_s in the range 10-50 km/s changes the accreted mass by about five orders of magnitude; yet Fig. 12 fixes c_in_s = 25 c_s. At z ~ 1000, where Eq. (3.7) gives c_s ≈ 6 km/s, this corresponds to c_in_s ≈ 150 km/s, far above the ~10-20 km/s photoionized sound speed relevant to the Park-Ricotti calibration, and at z ~ 100 it is still ≈ 48 km/s. Because this choice directly drives the 'negligible PR growth' conclusion, the paper should show ∆M/Mi for alternative physically motivated prescriptions (for example, constant c_in_s ≈ 10, 15, or 20 km/s, or a value tied to photoionization equilibrium) and state how the conclusion changes when c_in_s is lower. Without this, the claim that PR mass evolution is negligible is not established outside the specific 25 c_s assumption.","section":"Sec. 4, Eq. (4.7)"},{"comment":"The ROM07 accretion-efficiency formula in Eq. (3.4) is applied down to z ≲ 15, and into the non-linear regime z ≤ 10, although the text itself notes at the end of Sec. 3 that this description breaks down once structure forms. The large BHL growth shown in Fig. 12 (left panel) is driven by saturation of λ near unity after recombination together with the DM-halo enhancement; the authors state in Sec. 5 that fixing λ = 0.1 instead gives less than 60% growth. The abstract's claim that PBHs heavier than about 100 M⊙ 'can grow in mass by several orders of magnitude' should therefore be qualified as contingent on an extrapolated, high-efficiency regime, or the paper should provide a quantitative test (for example, comparing with local simulation-calibrated efficiencies) showing that the saturation is not an artifact of applying Eq. (3.4) outside its validity range.","section":"Sec. 3, Eq. (3.4)"},{"comment":"The PR model is inherited from simulations of intermediate-mass black holes accreting from a local, relatively dense medium (Refs. [63-65]) and is applied here to PBHs accreting from the cosmological fluid at redshifts up to z ~ 10^4, where the density, ionization state, Hubble flow, and radiative-transfer conditions differ substantially from the calibration environment. The additional assumption that the DM halo does not affect the ionized-region density and velocity profiles is stated but not tested; at low redshift the effective Bondi radius for massive halos can approach the size of the ionized region, weakening the 'sufficiently smaller' criterion. A dedicated sensitivity test that relaxes the PR closure (for instance, the unit efficiency inside the ionized region, or the ρin and vin relations in Eqs. (4.3)-(4.6)) is needed to support the conclusion that PR growth is negligible across the full redshift range.","section":"Sec. 4.1, Eq. (4.8)"}],"minor_comments":[{"comment":"Both captions say 'The left panel shows ... while the left panel depicts ...'; the second occurrence should be 'right panel'. This typo should be corrected.","section":"Figs. 6 and 11 captions"},{"comment":"The exponent labels '10□8', '10□6', etc. appear to be rendering artifacts in the provided manuscript; the published version should ensure the exponents are legible.","section":"Fig. 10"},{"comment":"The paper reports an unexplained discrepancy between its accretion rates and those of ROM07 and Ref. [61], attributing it possibly to the velocity averaging choice. Since the velocity-profile comparison is central to the uncertainty analysis, a sentence identifying the likely origin (or a check against the original code) would substantially increase confidence in the comparison.","section":"Appendix B, footnote 3"},{"comment":"The manuscript does not include a data or code availability statement. Given that the main output is a set of sensitivity scans and integrated mass-growth curves, making the integration code available would aid reproducibility and let readers test the c_in_s sensitivity directly.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is a sincere and useful uncertainty-mapping study, and the radiation-accretion section alone is a clean contribution. However, the headline 'PR growth is negligible' conclusion is currently tied to a single arbitrary closure (c_in_s = 25 c_s) that the authors themselves show changes the accreted mass by orders of magnitude when varied. The appropriate scope of revision is to add the missing sensitivity curves and qualify the abstract accordingly, rather than to reject the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper is worth a serious referee. The genuinely new pieces are the radiation-era accretion cap (~4% for λ=0.1, versus the earlier ~40%) from including γ and using a more careful z(t), and the first systematic comparison of BHL and PR baryonic accretion over cosmic time, with and without DM halos and with two velocity-profile sets. The authors are also honest: they flag an unresolved discrepancy with ROM07 and De Luca et al. accretion rates, and they stress that large growth occurs only under BHL + DM halos + high efficiency.\n\nWhere it does well: Secs. 2–4 are transparent, Eq. (2.12) is a useful closed form, Fig. 12 summarizes the central message clearly, and parameter sensitivity is explored rather than hidden. The main qualitative conclusion—that large PBH mass growth by accretion is by no means guaranteed—survives my reading.\n\nThe soft spots are real but not fatal. The stress-test concern about c_in^s = 25 c_s lands. The PR suppression scales as (c_in^s)^{-5}, and fixing c_in^s = 25 c_s gives c_in^s ~ 150 km/s at z ~ 1000, far above the ~10–20 km/s expected for photoionized gas. The authors report that varying c_in^s from 10 to 50 km/s changes accreted mass by five orders of magnitude, but they never show the constant-c_in^s curves. If a physically motivated c_in^s ~ 10 km/s is used, PR growth for Mi ≳ 100 M_sun could be non-negligible, making the abstract's \"negligible change\" too strong. This should be fixed either with a dedicated figure or a more careful justification.\n\nSecond, the ROM07 λ formula and secondary-infall halo profiles are applied down to z ~ 10, beyond their calibration, and the authors themselves note the λ formula breaks down there. They should either restrict the quantitative claims or provide code/data so the discrepancy with ROM07 can be resolved. No code or data is shipped, which weakens the quantitative comparisons.\n\nWho is this for: PBH phenomenology, CMB constraints, and SMBH seed formation. A serious referee should engage, and the authors should be pushed to clarify the c_in^s dependence and release their integration code.","headline":"A careful uncertainty map of PBH accretion; the radiation-growth correction and BHL-vs-PR comparison are genuinely new, but the 'negligible PR growth' headline leans on a poorly justified sound-speed choice.","tokens_in":27565,"tokens_out":2870,"would_cite":true,"duration_ms":28544,"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":"Primordial black holes are unlikely to grow substantially by accreting radiation or gas once radiative feedback is included; the large growth previously predicted requires a specific stack of optimistic assumptions.","keywords":["primordial black holes","accretion","Bondi-Hoyle-Lyttleton model","Park-Ricotti model","radiative feedback","dark matter halos","cosmic history","supermassive black hole seeds"],"falsifier":"A radiation-hydrodynamic simulation of a $10^2$-$10^3\\,M_\\odot$ black hole with a dark-matter mini-halo at $z\\sim10$-$20$, resolving the ionization front and measuring the baryonic accretion rate, would settle the matter: if the rate approaches the Bondi-Hoyle-Lyttleton prediction rather than the Park-Ricotti suppression, the paper's central conclusion fails.","tokens_in":26387,"feed_emoji":"🕳️","tokens_out":9766,"duration_ms":78859,"temperature":0.7,"pith_summary":"This paper asks whether primordial black holes (PBHs) grow substantially by accreting radiation and baryons after formation, and answers that large growth is possible only under a narrow set of assumptions. Radiation accretion before matter-radiation equality adds at most 4% to a PBH's mass for an accretion efficiency of $\\lambda=0.1$; earlier claims of up to 40% missed the formation-time factor $\\gamma$. For baryons, the traditional Bondi-Hoyle-Lyttleton model predicts that PBHs heavier than about $100\\,M_\\odot$ can grow by several orders of magnitude by $z\\lesssim10$, but only when dark-matter halos are present and the accretion efficiency is large. When radiative feedback is included through the Park-Ricotti model, baryonic accretion changes PBH masses by a negligible amount over cosmic time. The outcome matters for gravitational-wave merger rates, dark-matter constraints, and the proposed role of PBHs as seeds of early supermassive black holes.","feed_headline":"Radiation feedback suppresses primordial black hole growth","feed_subtitle":"Baryonic accretion changes PBH masses negligibly once feedback is included; only specific assumptions yield large growth.","key_machinery":"The load-bearing machinery is the Bondi radius together with the Park-Ricotti radiative-feedback prescription. In the standard BHL model the accretion rate is $\\dot M = 4\\pi\\lambda \\rho v_{\\rm eff} r_B^2$ with $r_B = GM/v_{\\rm eff}^2$; in the PR model the accreting black hole ionizes a surrounding bubble, the sound speed inside rises to $c_s^{\\rm in} = 25 c_s$, and the accretion rate is computed from the density and effective velocity inside that ionized region, $\\dot M_{\\rm PR} = 4\\pi \\rho_{\\rm in} v^{\\rm in}_{\\rm eff} (r^{\\rm in}_B)^2$. The ionization front and the heated gas suppress inflow, which is why the PR rates lie far below BHL rates. A second piece of machinery is the ROM07 analytic accretion-efficiency formula $\\lambda(z)$, which encodes gas viscosity, Compton drag, and Hubble expansion, and the two velocity profiles (ROM07 and SPIK20) used to quantify the spread in predictions.","core_discovery":"The paper establishes that the answer to 'do PBHs grow by accretion?' depends on which accretion model is used, and that the more complete model suppresses growth. For radiation accretion, the fractional mass increase is at most 4% for $\\lambda=0.1$ and is independent of the initial PBH mass once the formation redshift is computed self-consistently with the collapse fraction $\\gamma$, correcting earlier estimates of up to 40%. For baryons, the BHL model with the ROM07 efficiency and dark-matter mini-halos yields several orders of magnitude of growth for PBHs with initial masses above roughly $100\\,M_\\odot$ by $z\\lesssim10$, but this requires the accretion efficiency to saturate near unity after recombination. In the Park-Ricotti model, whose radiative feedback was calibrated on simulations of intermediate-mass black holes, the accretion rate is suppressed so strongly that the fractional mass change is negligible for the entire mass range and is insensitive to the cutoff redshift.","pith_inferences":["If the PR feedback description is right, PBHs need to form with nearly their final masses if they are to explain early supermassive black holes; accretion cannot do the heavy lifting after formation.","The five-orders-of-magnitude sensitivity of the accreted mass to the assumed ionized-region sound speed suggests that observations of PBH accretion luminosity, for instance through the cosmic microwave background or the 21-cm signal, could be used in reverse to measure the effective feedback strength rather than treat it as a free parameter.","The ROM07 accretion-efficiency formula is applied down to $z\\sim10$ even though the authors note it breaks down in the structured low-redshift universe, so the 'several orders of magnitude' BHL growth estimate should be read as an upper bound until a local, inhomogeneous treatment of accretion is available.","The large disagreement between the ROM07 and SPIK20 velocity profiles highlights that the relative velocity between baryons and dark matter, rather than the accretion model itself, may dominate the uncertainty in PBH growth predictions."],"forward_implications":["Under the PR model, baryonic accretion changes PBH masses by a negligible amount for the whole mass range considered, so claims that accretion-driven growth weakens PBH abundance constraints would not hold if feedback operates as in the simulations.","Under the BHL model with dark-matter halos and high late-time accretion efficiency, PBHs above roughly 100 solar masses can grow by several orders of magnitude by $z\\sim10$, which would affect their mass function, merger rates, and possible role as seeds for early supermassive black holes.","Radiation accretion alone saturates at about a 4% mass increase for $\\lambda=0.1$, independent of initial mass, so pre-recombination growth cannot substantially alter the PBH mass function unless the accretion efficiency is near unity, where it reaches about 60%.","The accretion rate and final mass depend so strongly on the assumed sound speed and PBH velocity profiles that order-of-magnitude growth should be treated as model-dependent rather than a generic PBH property."],"supporting_citations":[{"why":"Supplies the ROM07 Bondi accretion-rate formalism, the redshift-dependent efficiency $\\lambda(z)$, and one of the two velocity profiles used for comparison.","marker":"[30]"},{"why":"Supplies the SPIK20 sound-speed and PBH-velocity profiles that the paper uses as its default for linear and non-linear regimes.","marker":"[35]"},{"why":"Establishes the earlier BHL-with-DM-halos prediction of order-of-magnitude PBH growth that this paper tests against the PR model.","marker":"[61]"},{"why":"Introduces the Park-Ricotti radiative-feedback accretion prescription calibrated on intermediate-mass black hole simulations.","marker":"[63]"},{"why":"Extends the PR model to supersonic black hole velocities and underpins the $c_s^{\\rm in}=25 c_s$ and density relations used here.","marker":"[65]"},{"why":"Applies the PR model to isolated black holes in the Milky Way and provides the ionized-region accretion-rate formula adopted by this paper.","marker":"[67]"},{"why":"Made the earlier 40% radiation-accretion growth claim that the paper corrects by including the formation-time factor $\\gamma$.","marker":"[50]"},{"why":"Provides a prior application of PR accretion to PBH CMB bounds, setting the context for the CMB implications of suppressed growth.","marker":"[68]"}],"fun_headline_variants":["Radiative feedback blocks primordial black hole growth","Accretion uncertain: PBH growth ranges from negligible to huge","Model choice decides if primordial black holes grow","Feedback kills PBH growth, but model assumptions matter","Primordial black hole accretion: growth not guaranteed"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the radiative-feedback prescription calibrated for intermediate-mass black holes in low-redshift simulations, with the ionized bubble's sound speed set to 25 times the ambient speed of sound and accretion efficiency unity inside the bubble, also holds for primordial black holes accreting the cosmological baryon fluid at all redshifts, including the nonlinear regime of structure formation.","fun_headline_variants_meta":{"raw":{"variants":["Radiative feedback blocks primordial black hole growth","Accretion uncertain: PBH growth ranges from negligible to huge","Model choice decides if primordial black holes grow","Feedback kills PBH growth, but model assumptions matter","Primordial black hole accretion: growth not guaranteed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000216,"raw_usage":{"total_tokens":1482,"prompt_tokens":1043,"completion_tokens":439,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":659,"completion_tokens_details":{"reasoning_tokens":364}},"tokens_in":659,"tokens_out":439,"duration_ms":5134,"temperature":1.0,"reasoning_tokens":364,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T14:27:07.750537+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A radiation-hydrodynamic simulation of a $10^2$-$10^3\\,M_\\odot$ black hole with a dark-matter mini-halo at $z\\sim10$-$20$, resolving the ionization front and measuring the baryonic accretion rate, would settle the matter: if the rate approaches the Bondi-Hoyle-Lyttleton prediction rather than the Park-Ricotti suppression, the paper's central conclusion fails.","supporting_citations":[{"cited_title":"Effect of Vacuum Energy on Evolution of Primordial Black Holes in Einstein Gravity","cited_arxiv_id":"1107.2025","evidence_quote":"Made the earlier 40% radiation-accretion growth claim that the paper corrects by including the formation-time factor $\\gamma$."}],"review_version":1}