Lower edge of the dark-matter window for 5D primordial black holes: an independent check with hard X-ray and soft gamma-ray data
- 1Independent researcher
Abstract
In the dark-dimension scenario, light primordial black holes (PBHs) are five-dimensional (5D): colder and longer-lived than four-dimensional (4D) black holes of the same mass (arXiv:2506.14874). Earlier work estimated that 5D PBHs on the brane can make up all of the dark matter above about 10^14 g (arXiv:2206.07071) or 10^15 g (arXiv:2403.19604); both values follow from rescaling 4D gamma-ray limits at equal Hawking temperature (arXiv:2403.19604, arXiv:2401.09087). Assuming that black holes on the brane emit Standard Model particles with 5D brane greybody factors, I compute the photon limits directly, with corrected BlackHawk v3.0 spectra, Galactic and extragalactic X-ray and gamma-ray data, including calibrated XMM-Newton blank-sky data of the inner Galaxy, and a conservative criterion (prediction below data plus 2 sigma in every bin, no background model). For a micrometre-size extra dimension (M_KK = 0.01-0.1 eV) the lower edge of the window lies at 2.0x10^13-3.5x10^13 g; labelled variants raise the upper value to 5.3x10^13 g (NuSTAR stray-light spectrum), 1.2x10^14 g (RXTE Galactic-ridge data) or 1.3x10^14 g (outer XMM-Newton rings subtracted). For the value of the 5D Planck scale used in the earlier work it lies at 1.0x10^16 g: at equal temperature, 5D black holes are more numerous and each emits more photons, two factors that the rescaling does not include. The edge grows approximately as the square of the reduced 5D Planck mass. Published searches for PBH bursts are insensitive to 5D PBHs.
Version 3 (23 October 2026) adds the Galactic X-ray data below 23 keV that version 2 identified as the most direct test of the micrometre-size edges: calibrated XMM-Newton blank-sky data of the inner Galaxy in the nominal data, and the NuSTAR stray-light spectrum as a labelled variant. The M_KK = 0.01 eV edge moves from 1.3x10^13 to 2.0x10^13 g; no other edge of Table 1 changes.
Changes from version 2:
- Secs. 2.3 and 4.1, Appendix A.7: XMM-Newton blank-sky data (arXiv:2102.02207) in 30 rings of 6 degrees around the Galactic centre (MOS 2.5-8 keV, PN 2.5-7 keV), folded with the response of each ring (doi:10.5281/zenodo.4498564), normalized with exposure times solid angle rather than the geometric solid angle (arXiv:2506.02310), absorbed with HI4PI columns (arXiv:1610.06175), with no background subtracted. They set the M_KK = 0.01 eV edge, at 3.1 keV in the innermost ring.
- Two new labelled variants: the inner XMM-Newton rings minus the outer ones (Appendix A.7) and the NuSTAR stray-light spectrum at |b| >= 3 degrees (arXiv:2405.17861, arXiv:2509.08506; Appendix A.8). Fig. 1 and Tables 1-2 include them; Fig. 1 shows the results without XMM-Newton (version 2) in grey.
- New Sec. 4.6: comparison with black holes on a Randall-Sundrum II brane (arXiv:2509.13409). For an AdS radius of 1 micrometre the lower edge is 2.6x10^14 g here, against about 3.5x10^14 g there; below about 10^14 g these limits are 10-300 times stronger.
- Sec. 4.2 explains why the full calculation gives edges 0.7-0.8 times those of the rescaling with integrated photon rates: in the Wien tail the 5D/4D photon ratio is below its integrated value 9.6 (64/27 in the geometric-optics limit).
- Table 3 adds the LHAASO burst search (arXiv:2505.24586), with ratios of at least 3.3x10^5; Appendix A.6 checks the 1 GeV threshold of the Fermi-LAT proper-motion analysis.
- Sec. 5 adds the systematic checks of the XMM-Newton edge (halo profile, effective area, camera, absorption, channel width), the NuSTAR variant, eROSITA (not used), NuSTAR measurements of the X-ray background for the HEAO-1 normalization (arXiv:2011.11469, arXiv:2304.07962) and an estimate of CMB limits from arXiv:2509.13409. Sec. 2.1 notes that arXiv:2509.13409 disputes the suppressed emission of arXiv:2505.23414, which proposes 5D black holes as the source of the KM3NeT event KM3-230213A.
- Sec. 3 and Appendix A.5: a second, blind re-implementation reproduces the XMM-Newton edge within 0.13%; with 3 sigma, or with two adjacent bins, the edges fall by at most 24%.
- References: 6 new, 65 in total.
The calculations, code and text were prepared with the assistance of an AI system (Claude, Anthropic) under the direction of the author.
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BibTeX
@misc{zorzi2026lower,
title = {{Lower edge of the dark-matter window for 5D primordial black holes: an independent check with hard X-ray and soft gamma-ray data}},
author = {Marco Zorzi},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23593872},
url = {https://zenodo.org/records/23593872},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lower edge of the dark-matter window for 5D primordial black holes: an independent check with hard X-ray and soft gamma-ray data
AU - Marco Zorzi
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23593872
UR - https://zenodo.org/records/23593872
AB - In the dark-dimension scenario, light primordial black holes (PBHs) are five-dimensional (5D): colder and longer-lived than four-dimensional (4D) black holes of the same mass (arXiv:2506.14874). Earlier work estimated that 5D PBHs on the brane can make up all of the dark matter above about 10^14 g (arXiv:2206.07071) or 10^15 g (arXiv:2403.19604); both values follow from rescaling 4D gamma-ray limits at equal Hawking temperature (arXiv:2403.19604, arXiv:2401.09087). Assuming that black holes on the brane emit Standard Model particles with 5D brane greybody factors, I compute the photon limits directly, with corrected BlackHawk v3.0 spectra, Galactic and extragalactic X-ray and gamma-ray data, including calibrated XMM-Newton blank-sky data of the inner Galaxy, and a conservative criterion (prediction below data plus 2 sigma in every bin, no background model). For a micrometre-size extra dimension (M_KK = 0.01-0.1 eV) the lower edge of the window lies at 2.0x10^13-3.5x10^13 g; labelled variants raise the upper value to 5.3x10^13 g (NuSTAR stray-light spectrum), 1.2x10^14 g (RXTE Galactic-ridge data) or 1.3x10^14 g (outer XMM-Newton rings subtracted). For the value of the 5D Planck scale used in the earlier work it lies at 1.0x10^16 g: at equal temperature, 5D black holes are more numerous and each emits more photons, two factors that the rescaling does not include. The edge grows approximately as the square of the reduced 5D Planck mass. Published searches for PBH bursts are insensitive to 5D PBHs. Version 3 (23 October 2026) adds the Galactic X-ray data below 23 keV that version 2 identified as the most direct test of the micrometre-size edges: calibrated XMM-Newton blank-sky data of the inner Galaxy in the nominal data, and the NuSTAR stray-light spectrum as a labelled variant. The M_KK = 0.01 eV edge moves from 1.3x10^13 to 2.0x10^13 g; no other edge of Table 1 changes. Changes from version 2: - Secs. 2.3 and 4.1, Appendix A.7: XMM-Newton blank-sky data (arXiv:2102.02207) in 30 rings of 6 degrees around the Galactic centre (MOS 2.5-8 keV, PN 2.5-7 keV), folded with the response of each ring (doi:10.5281/zenodo.4498564), normalized with exposure times solid angle rather than the geometric solid angle (arXiv:2506.02310), absorbed with HI4PI columns (arXiv:1610.06175), with no background subtracted. They set the M_KK = 0.01 eV edge, at 3.1 keV in the innermost ring. - Two new labelled variants: the inner XMM-Newton rings minus the outer ones (Appendix A.7) and the NuSTAR stray-light spectrum at |b| >= 3 degrees (arXiv:2405.17861, arXiv:2509.08506; Appendix A.8). Fig. 1 and Tables 1-2 include them; Fig. 1 shows the results without XMM-Newton (version 2) in grey. - New Sec. 4.6: comparison with black holes on a Randall-Sundrum II brane (arXiv:2509.13409). For an AdS radius of 1 micrometre the lower edge is 2.6x10^14 g here, against about 3.5x10^14 g there; below about 10^14 g these limits are 10-300 times stronger. - Sec. 4.2 explains why the full calculation gives edges 0.7-0.8 times those of the rescaling with integrated photon rates: in the Wien tail the 5D/4D photon ratio is below its integrated value 9.6 (64/27 in the geometric-optics limit). - Table 3 adds the LHAASO burst search (arXiv:2505.24586), with ratios of at least 3.3x10^5; Appendix A.6 checks the 1 GeV threshold of the Fermi-LAT proper-motion analysis. - Sec. 5 adds the systematic checks of the XMM-Newton edge (halo profile, effective area, camera, absorption, channel width), the NuSTAR variant, eROSITA (not used), NuSTAR measurements of the X-ray background for the HEAO-1 normalization (arXiv:2011.11469, arXiv:2304.07962) and an estimate of CMB limits from arXiv:2509.13409. Sec. 2.1 notes that arXiv:2509.13409 disputes the suppressed emission of arXiv:2505.23414, which proposes 5D black holes as the source of the KM3NeT event KM3-230213A. - Sec. 3 and Appendix A.5: a second, blind re-implementation reproduces the XMM-Newton edge within 0.13%; with 3 sigma, or with two adjacent bins, the edges fall by at most 24%. - References: 6 new, 65 in total. The calculations, code and text were prepared with the assistance of an AI system (Claude, Anthropic) under the direction of the author.
ER -