Recombination Clumping Factor of Physically Defined Intergalactic Medium at the Epoch of Reionization

TL;DR

Oku and Cen introduce a physically motivated definition of the IGM for recombination during cosmic reionization based on the effective transmission factor $\mathcal{F}$ and quantify the resulting clumping factor using high-resolution GAMER-2 AMR simulations with a uniform UV background. They find that the normalized clumping factor $C_{\rm norm,\mathcal{F}}$ is substantially lower than conventional overdensity-based estimates, especially when the IGM is only partially ionized, and provide fitting formulas linking $C_{\rm norm,\mathcal{F}}$ to the volume-weighted neutral fraction. An analytic model comparing mass-weighted and volume-weighted neutral fractions reveals topology-driven shifts in reionization timing, with outside-in reionization producing $\Delta z \sim 2$ differences at mid-reionization relative to SCORCH-like results. Zoom-in simulations show SN feedback boosts clumping locally within $\sim100$ kpc but leaves the global clumping factor largely intact on larger scales, while also increasing the transmission and potentially aiding photon escape. Collectively, the results imply a lower ionizing photon budget is sufficient in bright-source–driven reionization scenarios, motivating further radiation-hydrodynamic studies across varied source populations and topologies.

Abstract

The recombination clumping factor, $C$, is a key parameter in modeling cosmic reionization, but its value is sensitive to the definition of the Intergalactic Medium (IGM). We investigate the clumping factor using the GAMER adaptive mesh refinement cosmological hydrodynamical simulation code. We introduce a new, physically-motivated definition of the IGM based on the effective transmission factor of ionizing photons. We perform large-scale, full-box simulations with varying intensities of the uniform ultraviolet background, and we find that our physically-defined clumping factor is significantly lower than the values derived from traditional overdensity thresholds. We also introduce an analytic model that distinguishes between the volume-weighted and mass-weighted averages of the neutral fraction, and we find the difference in reionization timing of $Δz \sim 2$ depending on the assumed clumping factor and the relation between the volume-weighted and mass-weighted neutral fractions. Our zoom-in simulations further show that, while SN feedback increases the clumping factor locally, the effect is limited to $\sim 100$ kpc scales and does not significantly alter the global clumping factor. The substantially lower clumping factor reduces the required ionizing photon budget, potentially alleviating tension for reionization scenarios driven by rare, bright sources like active galactic nuclei.

Figures (10)

• Figure 1: shows slices of the WeakUVB run (left), HM12UVB run (middle), and StrongUVB run (right) at $z=10$. From top to bottom: gas density, H1 number density, H2 number density, temperature, and effective transmission factor of ionizing photon.
• Figure 2: shows redshift evolution of the (a) recombination clumping factor, (b) normalized clumping factor, (c) volume-averaged temperature, (d) mean recombination time, (e) mass-weighted average of the neutral fraction of hydrogen, and (f) volume-weighted average of the neutral fraction of hydrogen. The yellow, magenta, and blue lines are from StrongUVB, HM12UVB, and WeakUVB runs, respectively. The dashed line in the panel (d) indicates the Hubble time.
• Figure 3: shows redshift evolution of the normalized clumping factor from HM12UVB. The solid line shows the $C_{{\rm norm}, \mathcal{F}}$, and dashed, dot-dashed, and dotted lines are $C_{{\rm norm}, \Delta_{\rm th}}$ with $\Delta_{\rm {th}}=50$, 100, and 200, respectively. The gray solid and dashed lines display fitting functions from 2012ApJ...747..100S and 2012MNRAS.427.2464F, respectively.
• Figure 4: illustrates volume-weighted vs. mass-weighted neutral fraction of hydrogen. The solid lines show the results from our simulations. The gray dot dashed line is the relation taken from the SCORCH II radiation hydrodynamical simulation 2019ApJ...870...18D. The dotted lines are our fits to our simulations and the SCORCH II results (Eq. (\ref{['eq:xHI_fit']}) and (\ref{['eq:xHI_fit_scorch']})).
• Figure 5: shows the recombination clumping factor as a function of volume-weighted neutral fraction. The solid lines show $C_{{\rm norm}, \mathcal{F}}$, and the dashed lines show the $C_{\rm norm, \Delta_{\rm th}}$ with threshold density $\Delta_{\rm th} = 100$, respectively. The dotted line is the fitting function to $C_{{\rm norm}, \mathcal{F}}$ (Eq. (\ref{['eq:crec_xHI']})).