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Primordial black holes as dark matter candidates: Multi-frequency constraints from cosmic radiation backgrounds

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2505.10706 v1 pith:OC2ZTJ6T submitted 2025-05-15 astro-ph.CO

C. Casanueva-Villarreal , N. Padilla , P. B. Tissera , B. Liu , V. Bromm This is my paper · ORCID
classification astro-ph.CO PACS 95.35.+d97.60.Lf98.70.Vc
keywords primordialblackholesdarkmattercosmicX-raybackgroundLyman-WernerradioBondi-Hoyle-Lyttletonaccretionadvection-dominatedflowearlyuniverse
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

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.

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 (4)
  1. [Section 3.2, Fig. 6, Abstract, Section 4] 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.
  2. [Section 2.2.3 after Eq. (16), Eq. (13), Section 3.1.1] 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.
  3. [Section 3.1.1 and Cappelluti et al. (2017) nsCXB data] 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.
  4. [Section 3.1.1 and Section 3.1.2] 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.
minor comments (4)
  1. [Eqs. (8) and (34)] 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.
  2. [Section 2.3 after Eq. (35)] The phrase 'viral temperature' should be 'virial temperature'.
  3. [Section 3.1.1] 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.
  4. [Section 3.1.3 and Table 1] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: PBH limits are derived from external background measurements and a stated accretion model, not from fitted inputs or self-citation chains.

full rationale

The derivation chain is not circular. The PBH fraction f_PBH is a free parameter; predicted background intensities are computed from an explicit Bondi-Hoyle accretion model (Eqs. 13-28), halo gas profiles (Eqs. 29-36), and radiative-transfer integrals (Eqs. 40-46), then compared with external measured backgrounds (Cappelluti et al. 2017 nsCXB; Fixsen et al. 2011 ARCADE 2; EDGES) and the external J_LW ~ 1 threshold. The headline limits are inversions of this comparison, not quantities fitted and then renamed as predictions. The 'up to 99 per cent' statements restate the upper-limit normalization rather than being independent predictions, which is standard limit-setting. The paper explicitly tests sensitivity by removing ADAF subregimes, changing density profiles, velocities, and the halo mass function, showing factor-of-few to order-of-magnitude shifts; this is model uncertainty, not circularity. Self-citations to CV2024, Liu et al. (2022), and Zhang et al. (2024a) are present, but the underlying equations are restated and traceable to external sources (Takhistov et al. 2022; Mahadevan 1997; Makino et al. 1998; Yuan and Narayan 2014), and the cited ingredients are tested through variations, so they are not load-bearing. The abstract versus Section 3.2 discrepancy in the relaxed 1 Msun limit is a reporting issue, not a circular step. No step in the derivation reduces to its own input by definition.

Assumptions & free parameters 5 free parameters · 10 assumptions · 0 invented entities

The model pulls its accretion physics, halo profiles, and background data from prior literature, mainly Takhistov et al. (2022), Ziparo et al. (2022), Liu et al. (2022), and Zhang et al. (2024a). No new particles or forces are introduced. The central constraints rest on a chain of standard but uncertain assumptions about accretion efficiency, gas density profiles, and the halo mass function.

free parameters (5)
  • ADAF electron heating fraction delta = 0.3
    Adopted from Takhistov et al. (2022) and Yuan & Narayan (2014); chosen by hand and directly affects ADAF spectra and therefore the X-ray, LW, and radio yields.
  • ADAF viscosity parameter alpha = 0.1
    Standard value used in the accretion regime boundaries and in the synchrotron and bremsstrahlung spectra; affects thin-disc versus ADAF transitions and overall luminosity.
  • Plasma beta (gas pressure fraction) = 10/11
    Set following Takhistov et al. (2022); enters the synchrotron peak luminosity and the ADAF spectra.
  • Radiative efficiency epsilon_0 = 0.1
    Used to define the Eddington accretion rate and the thin-disc normalization; a typical value for thin disks adopted from Takhistov et al. (2022).
  • Bremsstrahlung normalization c_1 = 0.5
    Introduced in Eq. 27 following Mahadevan (1997); a fixed constant in the bremsstrahlung luminosity.
assumptions (10)
  • domain assumption Bondi-Hoyle-Lyttleton accretion rate without the Bondi-Eigenvalue lambda factor
    Section 2.2.1; follows Takhistov et al. (2022) and omits the ad hoc lambda correction, setting the accretion rate directly from local gas conditions.
  • domain assumption Monochromatic PBH mass function
    Section 2.1.1; adopted for comparison with prior work; extended mass functions are deferred to future work.
  • domain assumption Halo gas density profiles (simple isothermal, Makino+1998, Liu+2022 rescaled) represent the gas around PBHs
    Section 2.3; the accretion luminosity is directly proportional to gas density, so the constraints depend on this choice.
  • domain assumption Virial velocity of the host halo is the characteristic velocity in the Bondi accretion rate
    Eq. 29; this is varied in Section 3.2 against the Ziparo+2022 sound-speed prescription.
  • domain assumption The Press-Schechter/Sheth-Tormen HMF with the PBH-modified power spectrum from Zhang et al. (2024a) is valid for the relevant halo mass range
    Section 2.1.2; known to underestimate small halos and overpredict massive halos; a correction factor is applied for extreme f_PBH values.
  • domain assumption The ADAF emission model with thermal electrons only and spherical symmetry captures PBH spectra
    Section 2.2.3; non-thermal particles, angular momentum, and anisotropies are neglected, with the limitations acknowledged.
  • domain assumption The IGM gas density follows Ricotti et al. (2008b) and the sound speed follows Luca et al. (2020)
    Section 2.4; the IGM contribution is subdominant in most constrained cases, reducing the impact of this assumption.
  • domain assumption The nsCXB from Cappelluti et al. (2017) is an upper limit on any PBH contribution
    Section 3.1.1; if a portion of nsCXB is later resolved into astrophysical sources, the limits weaken; the paper acknowledges this in the introduction.
  • ad hoc to paper HMF correction factor scaling halos to the total DM density when the modified HMF integrates to overclosure
    Section 2.1.2; applied for f_PBH = 1 and some 100 M_sun cases; the authors test that it does not affect the low-f_PBH constraints.
  • ad hoc to paper Restriction of the Liu+2022 rescaled halo profile to z >= 20
    Section 2.3; a modeling choice made to avoid regimes where the reference halo assumptions break down.

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Cite this review

Pith. "Pith review of Primordial black holes as dark matter candidates: Multi-frequency constraints from cosmic radiation backgrounds." pith.science (2026). https://pith.science/paper/OC2ZTJ6T

@misc{pith2026250510706,
  author       = {Pith},
  title        = {Pith review of: Primordial black holes as dark matter candidates: Multi-frequency constraints from cosmic radiation backgrounds},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OC2ZTJ6T}},
  note         = {Machine review of arXiv:2505.10706}
}
read the original abstract

Aims. This study investigates the role of primordial black holes (PBHs) in shaping cosmic radiation backgrounds--the cosmic X-ray background (CXB), the Lyman-Werner background (LWB), and the cosmic radio background (CRB)--and evaluates their viability as dark matter (DM) candidates based on observational constraints and theoretical limits. Methods. PBH accretion is modelled using analytical frameworks that include electron advection-dominated accretion flows (eADAF), standard advection-dominated accretion flows (ADAF), luminous hot accretion flows (LHAF), and thin disks. Emission from PBHs in both dark matter halos and the intergalactic medium (IGM) is computed. We assess the impact of variations in model assumptions, such as halo gas density profiles, gas velocities, and emission models. The results are compared with observational limits and theoretical thresholds to constrain the PBH fraction as DM for masses between 1 and 100 solar masses Results. PBHs may contribute up to 99, 93, 80, and 91 per cent of the unresolved soft X-ray background for masses of 1, 10, 33, and 100 solar masses, respectively, and about 33-39 per cent of the hard X-ray background. These contributions limit the PBH DM fraction to 7e-3, 6e-4, 6e-4, and 7e-4, respectively, in our baseline model. These constraints are consistent with those from the LWB, ensuring molecular cooling and early star formation are preserved. However, explaining the radio background excess and the EDGES signal would require PBH fractions well above these limits. For 1 solar mass, excluding ADAF subregimes relaxes the constraint to 3e-2, highlighting the sensitivity to accretion physics. Variations in model assumptions introduce only minor differences in the predicted backgrounds.

Figures

Figures reproduced from arXiv: 2505.10706 by the authors.

Figure 1
Figure 1. Impact of PBHs on the power spectrum and HMF (assuming MPBH = 100 M⊙). Top panel: The total power spectrum Ptot(k) as a function of wavenumber k for various fractions of DM in PBHs (fPBH = 0.0001, 0.001, 0.01, 0.1, and 1), compared to the standard ΛCDM case (fPBH = 0). Bottom panel: The HMF at z = 10, showing the number density of halos as a function of halo mass M, also assuming MPBH = 100 M⊙. The total power spect… view at source ↗
Figure 2
Figure 2. Comparison of hydrogen number density profiles nH(r) within DM halos of different masses (Mh = 104 M⊙, 106 M⊙, and 108 M⊙) at redshifts z = 6 (solid lines), z = 10 (dashed-dotted lines), and z = 40 (dotted lines). The three density profiles examined include a simple isothermal profile (magenta), the profile derived by Makino et al. (1998) (blue), and the rescaled profile from Liu et al. (2022) (green). The vertical … view at source ↗
Figure 3
Figure 3. Contribution of accreting high-z BH sources to the present-day (z = 0) soft X-ray background (0.5–2 keV). The top row shows the cumulative evolution of the integrated background intensity, JX, as a function of redshift z, for PBH masses of MPBH = 1 M⊙, 10 M⊙, 33 M⊙, and 100 M⊙ in each column. Different values of fPBH are represented by distinct colours, as indicated in the legend, ranging from 10−4 to 1. The grey sh… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Background intensity of LW radiation (JLW) produced by accreting high-z PBH sources. The format of panels, colours, and line styles is identical to [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Brightness temperature of the radio background (Tb) as a function of frequency for PBHs accreting in halos, evaluated at z = 0 (top row) and z = 18 (bottom row). Columns correspond to different PBH masses (MPBH = 1, 10, 33, 100 M⊙), while the line styles (solid and das…
Figure 6
Figure 6. Figure 6: Cumulative soft X-ray and Lyman-Werner background intensities from PBHs accreting within halos under different model assumptions. Each column corresponds to a specific PBH mass (MPBH = 1 M⊙, 10 M⊙, 33 M⊙, and 100 M⊙) and the fPBH value derived from the baseline model w…
Figure 7
Figure 7. Figure 7: Constraints on the maximum allowed PBH DM fraction for different monochromatic PBH masses, including results derived in this work under various modelling assumptions, as well as observational limits and previous theoretical results. We consider two gas density profiles…

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Cited by 2 Pith papers

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