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Stronger Constraints on Primordial Black Holes as Dark Matter Derived from the Thermal Evolution of the Intergalactic Medium over the Last Twelve Billion Years

Nabendu Kumar Khan, Anupam Ray, Girish Kulkarni, Basudeb Dasgupta

TL;DR

This paper uses the thermal history of the intergalactic medium, as inferred from the Lyman-$\alpha$ forest, to place stringent constraints on light primordial black holes (PBHs) as dark matter candidates. It advances the method by self-consistently coupling Hawking-emitted energy deposition from PBHs to the evolving IGM with a realistic ultraviolet background and explicit He$\text{III}$ chemistry, extending the analysis down to $z=0$ and incorporating low-redshift temperature data. The authors find that for $M_{\rm PBH}=7\times10^{16}$ g, $f_{\rm PBH}\leq 8.6\times10^{-3}$ (95% CL), with constraints scaling roughly as $f_{\rm PBH}\propto M_{\rm PBH}^{4}$ across the mass range $7\times10^{15}$ g to $2\times10^{17}$ g. Compared to other bounds, these IGM-based limits are among the strongest and are notably robust to clustering and local astrophysical uncertainties, underscoring the IGM thermal history as a powerful probe of new physics.

Abstract

Primordial black holes (PBHs) have been explored as potential dark matter candidates, with various astrophysical observations placing upper limits on the fraction $f_\mathrm{PBH}$ of dark matter in the form of PBHs. However, a largely underutilized probe of PBH abundance is the temperature of the intergalactic medium (IGM), inferred from the thermal broadening of absorption lines in the Lyman-$α$ forest of quasar spectra. PBHs inject energy into the IGM via Hawking radiation, altering its thermal evolution. In this work, we constrain this energy injection by self-consistently modeling its interplay with the cosmological ultraviolet background from galaxies and supermassive black holes. Leveraging IGM temperature measurements spanning the past twelve billion years ($z \sim 0$ to $6$), we derive one of the most stringent constraints on PBH-induced heating from light PBHs within the mass range $10^{15}$-$10^{17}$ g. Specifically, for $M_\mathrm{PBH} = 10^{16}$ g, we find $f_\mathrm{PBH} < 5 \times 10^{-5}$ at 95\% confidence, with the bound scaling approximately as $M_\mathrm{PBH}^{4}$ at other masses. Our inclusion of helium reionization and low-redshift temperature measurements strengthens previous IGM-based PBH constraints by an order of magnitude or more. Compared to other existing limits, our result is among the strongest, second only to the constraints from the 511 keV line from the Galactic Center, but with distinct systematics. More broadly, this study highlights the IGM thermal history as a powerful and independent probe of beyond-standard model physics.

Stronger Constraints on Primordial Black Holes as Dark Matter Derived from the Thermal Evolution of the Intergalactic Medium over the Last Twelve Billion Years

TL;DR

This paper uses the thermal history of the intergalactic medium, as inferred from the Lyman- forest, to place stringent constraints on light primordial black holes (PBHs) as dark matter candidates. It advances the method by self-consistently coupling Hawking-emitted energy deposition from PBHs to the evolving IGM with a realistic ultraviolet background and explicit He chemistry, extending the analysis down to and incorporating low-redshift temperature data. The authors find that for g, (95% CL), with constraints scaling roughly as across the mass range g to g. Compared to other bounds, these IGM-based limits are among the strongest and are notably robust to clustering and local astrophysical uncertainties, underscoring the IGM thermal history as a powerful probe of new physics.

Abstract

Primordial black holes (PBHs) have been explored as potential dark matter candidates, with various astrophysical observations placing upper limits on the fraction of dark matter in the form of PBHs. However, a largely underutilized probe of PBH abundance is the temperature of the intergalactic medium (IGM), inferred from the thermal broadening of absorption lines in the Lyman- forest of quasar spectra. PBHs inject energy into the IGM via Hawking radiation, altering its thermal evolution. In this work, we constrain this energy injection by self-consistently modeling its interplay with the cosmological ultraviolet background from galaxies and supermassive black holes. Leveraging IGM temperature measurements spanning the past twelve billion years ( to ), we derive one of the most stringent constraints on PBH-induced heating from light PBHs within the mass range - g. Specifically, for g, we find at 95\% confidence, with the bound scaling approximately as at other masses. Our inclusion of helium reionization and low-redshift temperature measurements strengthens previous IGM-based PBH constraints by an order of magnitude or more. Compared to other existing limits, our result is among the strongest, second only to the constraints from the 511 keV line from the Galactic Center, but with distinct systematics. More broadly, this study highlights the IGM thermal history as a powerful and independent probe of beyond-standard model physics.

Paper Structure

This paper contains 16 sections, 35 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Hawking Radiation from Evaporating Primordial Black Holes
  3. IGM Thermal and Ionization History in Presence of PBH Energy Injection
  4. Modifications to DarkHistory
  5. Results from Modified DarkHistory
  6. The Temperature Measurements of the Intergalactic Medium from the Lyman-$\alpha$ Forest
  7. Constraints on PBHs from IGM temperature
  8. Conclusions
  9. Standard Heating and Cooling Processes in the IGM
  10. Temperature Evolution
  11. Ionization Evolution
  12. Coulomb Heating and Energy Deposition
  13. Coulomb Heating in the IGM
  14. Recursive Energy Deposition Framework
  15. Table of Constraints on $f_{\mathrm{PBH}}$
  16. ...and 1 more sections

Figures (5)

  • Figure 1: The energy spectrum of photons, electrons and positrons emitted by a PBH with mass $M_\mathrm{PBH} = 7 \times 10^{16} \, \mathrm{g}$. The spectra peak at $E \sim 1 \, \mathrm{MeV}$ and display a blackbody-like profile: an exponential decline at higher energies and a power-law trend at lower energies. The electron spectrum features a kinematic cutoff at the electron rest mass.
  • Figure 2: Values of the quantity $f_\mathrm{Cnl}$, which describe the fraction of the energy injected by PBHs that is deposited into the IGM through channel 'Cnl', as a function of redshift. These fractions are found self-consistently via a computation of the thermochemical evolution of the IGM in the presence of a UV background produced by galaxies and supermassive black holes. For this figure, we fix $M_{\text{PBH}} = 7 \times 10^{16}$ and $f_{\text{PBH}} = 5 \times 10^{-3}$. The channels shown are hydrogen ionization, helium ionization, Lyman-$\alpha$ excitation, and Coulomb heating. We see a strong contribution of PBHs to the IGM heating, and negligible contribution to IGM ionization.
  • Figure 3: Left panel shows the evolution of temperature of the IGM at mean density with redshift for $M_\mathrm{PBH} = 7 \times 10^{16}$ g, with three $f_\mathrm{PBH}$ values, 0 (no PBHs; blue curve), $5 \times 10^{-3}$ (orange curve), and $5 \times 10^{-2}$ (green curve), in comparison with various measurements from $z\sim 0$--$6$. The right panel shows the evolution of the ionization fractions of hydrogen (solid curve), singly-ionized helium (dashed curve), and doubly-ionized helium (dot-dashed curve). These ionization fractions remain largely unaffected by the inclusion of PBHs; it is the IGM temperature that shows the more significant effect. The gray curves in both panels represent a model without He$\,$iii evolution for $f_\mathrm{PBH} = 5 \times 10^{-3}$, which leads to an unphysical temperature increase.
  • Figure 4: Our limits on $f_\mathrm{PBH}$ for PBH masses between $10^{15} \,\mathrm{g}$ and $2\times 10^{17} \,\mathrm{g}$, inferred at the 95% confidence level from measurements of the IGM temperature between redshifts 0 and 6, are shown in the figure. The shaded region represents the excluded parameter space based on observational data. For comparison, we also show similar constraints from Ref. 2024arXiv240910617S, depicted in gray, where we have adopted their strongest reported constraint from the "photoheating" model variations. Our constraints are stronger than those from Ref. 2024arXiv240910617S by an order of magnitude or more.
  • Figure 5: Constraints on the PBH fraction $f_\mathrm{PBH}$ as a function of PBH mass $M_\mathrm{PBH}$. Our new constraint (red solid line) is shown alongside existing bounds from: extragalactic gamma rays Carr:2009jm in blue, the 511 keV gamma-ray line 2024PhRvD.110l3022L in orange, modifications of the CMB spectrum Clark:2016nst in green, electron/positron measurements from Voyager 1 Boudaud:2018hqb in cyan, the MeV background Laha:2020ivk in dodger blue, heating effects in the dwarf galaxy Leo T Laha:2020vhg in brown, neutrino evaporation limits from Super-Kamiokande Dasgupta:2019cae in maroon, COMPTEL GC observations Coogan:2020tuf in red, and the X-ray background 2024PhRvD.110l3022L in purple. Some of these constraints, including the 511 keV one (orange), depends on assumed dark matter density profile and can therefore be relaxed under different profile choices, whereas our constraint is based on the cosmological dark matter density and is independent of such uncertainties.