A structural degeneracy explains reionization tensions and limits dark matter constraints

TL;DR

The paper reveals a fundamental structural degeneracy in reionization studies where key parameters are only constrained by their product, limiting the ability to distinguish different models or dark matter scenarios.

Contribution

It identifies an exact degeneracy in reionization parameters, showing that all probes depend only on their product, and suggests spatial topology observables are needed to break this degeneracy.

Findings

Reionization probes are sensitive only to the product of escape fraction and star formation efficiency.

Galaxy-scale structure changes do not affect observables once ionizing emissivity is matched.

Spatial topology of ionized regions can break the degeneracy.

Abstract

Over the past decade, reionization studies have yielded persistent factor-of-two-to-five disagreements in the inferred ionizing escape fraction $f_{\mathrm{esc}}$ and peak star formation efficiency $f_{*,0}$, compounded by JWST's discovery of unexpectedly bright $z>10$ galaxies. We show that this discrepancy arises from an algebraically exact structural degeneracy: the ionizing photon rate $\dot{n}_{\mathrm{ion}} \propto f_{\mathrm{esc}} \times f_{*,0}$ renders all reionization-history probes, including Thomson optical depth, neutral hydrogen fraction, UV luminosity function, and quasar proximity zones, sensitive only to their product, leading to an intrinsically non-invertible mapping between model parameters and observations. We demonstrate the robustness of this degeneracy using a large suite of N-body simulations of self-interacting dark matter haloes spanning $10^9$-$10^{11} M_\odot$. Despite substantial changes to galaxy-scale structure, observables remain indistinguishable once the effective ionizing emissivity is matched, severely limiting reionization-based dark matter probes. We identify that only observables sensitive to the spatial topology of ionized regions can break this degeneracy. Our results provide a unified explanation for the scatter among published constraints and establish a framework for interpreting reionization observations and their implications for early galaxy formation and dark matter.