Evaporation of Primordial Black Holes with Multimodal Mass and Extended Spin Distributions: Cosmological Imprints on the Effective Number of Relativistic Species
Abstract
Primordial black holes (PBHs) form through several distinct mechanisms, each imprinting a characteristic mass function that a single-mass treatment risks erasing. Building on the FRISBHEE code, we introduce FRISHBEE, implementing four mass functions--log-normal, power-law, critical collapse, metric preheating--in a multimodal framework, with spin modeled via Gaussian and Fishbach profiles. Crucially, each channel's weight is derived from the primordial collapse probability rather than fitted, tying the mass function to the power-spectrum amplitude--a link between inflationary model-building and CMB observables. Solving the Friedmann-Boltzmann equations for MPBHin=107~g in the pre-BBN window, we compute ΔNeff for five distributions, three spin configurations, and three weightings. Extended mass functions enhance ΔNeff over the monochromatic benchmark by factors of ∼ 1.03 (critical collapse) to ∼ 1.84 (log-normal), preserving the hierarchy LN > MM > PL > MP > CC across the mass window {105,107,108}~g. Near-extremal spin (a⋆=0.99) and spin-2 dark radiation invert this trend: superradiant spin loss averages away faster in broad distributions than in a monochromatic population, letting the monochromatic approximation overestimate ΔNeff. Against CMB-S4 and Simons Observatory sensitivities (σ≃ 0.06 and $0.05$), the monochromatic benchmark is undetectable for scalar dark radiation (sDR =0), while log-normal, power-law, and multimodal distributions reach ∼ 1.6--1.7σ; for spin-2 dark radiation the signal drops over an order of magnitude, with none detectable. The formation channel thus governs the magnitude and observational accessibility of the Hawking signal, establishing ΔNeff as a discriminant between single- and multi-channel PBH formation scenarios.
Versions
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BibTeX
@misc{toghrai2026evaporation,
title = {{Evaporation of Primordial Black Holes with Multimodal Mass and Extended Spin Distributions: Cosmological Imprints on the Effective Number of Relativistic Species}},
author = {T. Toghrai and A. Daassou and Y. Ouchhaine and H. Laassiri and R. Benbrik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.10127},
eprint = {2608.10127},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10127},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evaporation of Primordial Black Holes with Multimodal Mass and Extended Spin Distributions: Cosmological Imprints on the Effective Number of Relativistic Species
AU - T. Toghrai
AU - A. Daassou
AU - Y. Ouchhaine
AU - H. Laassiri
AU - R. Benbrik
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2608.10127
UR - https://arxiv.org/abs/2608.10127
AB - Primordial black holes (PBHs) form through several distinct mechanisms, each imprinting a characteristic mass function that a single-mass treatment risks erasing. Building on the FRISBHEE code, we introduce FRISHBEE, implementing four mass functions--log-normal, power-law, critical collapse, metric preheating--in a multimodal framework, with spin modeled via Gaussian and Fishbach profiles. Crucially, each channel's weight is derived from the primordial collapse probability rather than fitted, tying the mass function to the power-spectrum amplitude--a link between inflationary model-building and CMB observables. Solving the Friedmann-Boltzmann equations for M_PBH^in=10^7~g in the pre-BBN window, we compute ΔN_eff for five distributions, three spin configurations, and three weightings. Extended mass functions enhance ΔN_eff over the monochromatic benchmark by factors of ∼ 1.03 (critical collapse) to ∼ 1.84 (log-normal), preserving the hierarchy LN > MM > PL > MP > CC across the mass window {10^5,10^7,10^8}~g. Near-extremal spin (a_⋆=0.99) and spin-2 dark radiation invert this trend: superradiant spin loss averages away faster in broad distributions than in a monochromatic population, letting the monochromatic approximation overestimate ΔN_eff. Against CMB-S4 and Simons Observatory sensitivities (σ≃ 0.06 and $0.05$), the monochromatic benchmark is undetectable for scalar dark radiation (sDR =0), while log-normal, power-law, and multimodal distributions reach ∼ 1.6--1.7σ; for spin-2 dark radiation the signal drops over an order of magnitude, with none detectable. The formation channel thus governs the magnitude and observational accessibility of the Hawking signal, establishing ΔN_eff as a discriminant between single- and multi-channel PBH formation scenarios.
ER -