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Peer-reviewedCC BYThe Astrophysical Journal

The Predicament of Absorption-dominated Reionization. II. Observational Estimate of the Clumping Factor at the End of Reionization

  • Frederick B. Davies1
  • Sarah E. I. Bosman2,1
  • Steven R. Furlanetto3
  1. 1Max-Planck-Institut für Astronomie
  2. 2Heidelberg University
  3. 3University of California
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Abstract

The history of reionization reflects the cumulative injection of ionizing photons by sources and the absorption of ionizing photons by sinks. The latter process is traditionally described in terms of a “clumping factor,” which encodes the average quadratic increase in the recombination rate of dense gas within the cosmic web. The recent measurement of a short mean free path of ionizing photons from stacked quasar spectra at z ≃ 6 has placed the importance of sinks under increased scrutiny, but its connection to the recombination rate is not immediately obvious. Here, we present analytic arguments to connect the clumping factor to the mean free path by invoking ionization equilibrium within the ionized phase of the intergalactic medium at the end of (and after) reionization. We find that the latest mean free path and hydrogen photoionization rate measurements at z = 5–6 imply a global clumping factor C ≈ 12, much higher than previous determinations from radiation-hydrodynamic simulations of the reionization process. Similar values of C are also derived when applying the same procedure to observations at 2 < z < 5. Compared to the traditional assumption of C = 3, high-redshift galaxies must produce roughly twice as many ionizing photons (≈3 photons per baryon) to reionize the Universe by z ∼ 6. This additional requirement on the ionizing photon budget may help to reconcile the reionization history with JWST observations that suggest a far greater output of ionizing photons by the most distant galaxy populations.

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Cite

BibTeXRIS
BibTeX
@article{davies2026predicament,
  title = {{The Predicament of Absorption-dominated Reionization. II. Observational Estimate of the Clumping Factor at the End of Reionization}},
  author = {Frederick B. Davies and Sarah E. I. Bosman and Steven R. Furlanetto},
  journal = {The Astrophysical Journal},
  year = {2026},
  month = jun,
  doi = {10.3847/1538-4357/ae75b3},
  url = {https://doi.org/10.3847/1538-4357/ae75b3},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - The Predicament of Absorption-dominated Reionization. II. Observational Estimate of the Clumping Factor at the End of Reionization
AU  - Frederick B. Davies
AU  - Sarah E. I. Bosman
AU  - Steven R. Furlanetto
PY  - 2026
DA  - 2026/06/23
JO  - The Astrophysical Journal
DO  - 10.3847/1538-4357/ae75b3
UR  - https://doi.org/10.3847/1538-4357/ae75b3
AB  - The history of reionization reflects the cumulative injection of ionizing photons by sources and the absorption of ionizing photons by sinks. The latter process is traditionally described in terms of a “clumping factor,” which encodes the average quadratic increase in the recombination rate of dense gas within the cosmic web. The recent measurement of a short mean free path of ionizing photons from stacked quasar spectra at z ≃ 6 has placed the importance of sinks under increased scrutiny, but its connection to the recombination rate is not immediately obvious. Here, we present analytic arguments to connect the clumping factor to the mean free path by invoking ionization equilibrium within the ionized phase of the intergalactic medium at the end of (and after) reionization. We find that the latest mean free path and hydrogen photoionization rate measurements at z = 5–6 imply a global clumping factor C ≈ 12, much higher than previous determinations from radiation-hydrodynamic simulations of the reionization process. Similar values of C are also derived when applying the same procedure to observations at 2 < z < 5. Compared to the traditional assumption of C = 3, high-redshift galaxies must produce roughly twice as many ionizing photons (≈3 photons per baryon) to reionize the Universe by z ∼ 6. This additional requirement on the ionizing photon budget may help to reconcile the reionization history with JWST observations that suggest a far greater output of ionizing photons by the most distant galaxy populations.
SN  - 0004-637X
SN  - 1538-4357
ER  -