The evolution of the Lyman-alpha forest effective optical depth following HeII reionisation

Three independent observational studies have now detected a narrow (\Delta z ~ 0.5) dip centred at z=3.2 in the otherwise smooth redshift evolution of the Lya forest effective optical depth. This feature has previously been interpreted as an indirect signature of rapid photo-heating in the IGM during the epoch of HeII reionisation. We examine this interpretation using a semi-analytic model of inhomogeneous HeII reionisation and high resolution hydrodynamical simulations of the Lya forest. We instead find that a rapid (\Delta z ~ 0.2) boost to the IGM temperature (\Delta T ~ 10^4 K) beginning at z=3.4 produces a well understood and generic evolution in the Lya effective optical depth, where a sudden reduction in the opacity is followed by a gradual, monotonic recovery driven largely by adiabatic cooling in the low density IGM. This behaviour is inconsistent with the narrow feature in the observational data. If photo-heating during HeII reionisation is instead extended over several redshift units, as recent theoretical studies suggest, then the Lya opacity will evolve smoothly with redshift. We conclude that the sharp dip observed in the Lya forest effective optical depth is instead most likely due to a narrow peak in the hydrogen photo-ionisation rate around z=3.2, and suggest that it may arise from the modulation of either reprocessed radiation during HeII reionisation, or the opacity of Lyman limit systems.

💡 Research Summary

The paper addresses a narrow dip (Δz ≈ 0.5) in the redshift evolution of the Lyman‑α forest effective optical depth (τ_eff) centered at z ≈ 3.2, first reported by three independent observational studies. Earlier works interpreted this feature as an indirect signature of rapid photo‑heating of the intergalactic medium (IGM) during He II reionisation. The authors re‑examine this interpretation using a semi‑analytic model of inhomogeneous He II reionisation and a suite of high‑resolution hydrodynamical simulations.

The semi‑analytic framework builds on the fluctuating Gunn‑Peterson approximation (FGPA) and the methodology of Furlanetto & Oh (2008). It tracks the reionisation history of gas elements of given overdensity Δ, assuming either density‑independent ionisation probabilities (tracing the global ionised fraction (\bar{x}_i(z))) or a density‑driven ordering where high‑density regions ionise first. The model adopts a rapid He II reionisation ending at z = 3.2, with a temperature boost ΔT ≈ 10⁴ K occurring over Δz ≈ 0.2 beginning at z = 3.4. The initial post‑reionisation temperature T_i is set to 4 × 10⁴ K to exaggerate heating effects. Using the Miralda‑Escudé et al. (2000) volume‑weighted density PDF, the authors compute τ_eff by integrating over the joint distribution of density and temperature.

The semi‑analytic results show that a sudden temperature increase produces a characteristic τ_eff evolution: an immediate dip followed by a gradual, monotonic recovery driven primarily by adiabatic cooling of the low‑density IGM. This recovery occurs on a Hubble timescale, far longer than the rapid return to the pre‑dip power‑law trend observed in the data (recovery by z ≈ 2.9). Moreover, variations in the temperature‑density slope γ have limited impact; lowering γ (making under‑dense regions hotter) reduces τ_eff at z ≥ 3 but widens the dip, contrary to observations.

To test these conclusions with more realism, the authors run high‑resolution cosmological hydrodynamical simulations (box size ≈ 20 h⁻¹ Mpc, 2 × 1024³ particles, spatial resolution ≈ 10 kpc). They implement He II reionisation as a spatially uniform heating event with the same ΔT and Δz as in the analytic model, and they follow the subsequent thermal evolution including photo‑heating, recombination cooling, and adiabatic expansion. The simulated τ_eff reproduces the analytic pattern: a sharp decline at the heating epoch and a slow recovery. Even when the extra free‑electron contribution from He II reionisation (χ_He = 1.08 → 1.16) is included, the recovery remains too gradual.

The key discrepancy is the timescale of the recovery. Observations show that τ_eff returns to its original power‑law trend within Δz ≈ 0.3, whereas both the analytic and numerical models predict a recovery spanning Δz ≈ 0.5–1.0. The authors therefore explore alternative explanations. They note that τ_eff depends not only on temperature but also on the hydrogen photo‑ionisation rate Γ_HI (τ_eff ∝ Γ_HI⁻¹). A modest, transient increase in Γ_HI of order 8 % can produce a ∼10 % dip in τ_eff, matching the observed amplitude. Such a Γ_HI peak could arise from (i) re‑processed hard photons emitted during He II reionisation that temporarily boost the metagalactic UV background, or (ii) a temporary reduction in the opacity of Lyman‑limit systems (LLSs), which would increase the mean free path of ionising photons and raise Γ_HI.

The authors argue that He II reionisation is likely an extended process, as indicated by recent radiative‑transfer simulations (e.g., McQuinn et al. 2009), which show a gradual rise in the volume‑averaged IGM temperature over several redshift units. In such a scenario, temperature‑driven τ_eff variations would be smooth, lacking the narrow dip seen in the data. Consequently, the observed feature is more plausibly attributed to a narrow peak in the hydrogen photo‑ionisation rate rather than to rapid heating.

In conclusion, the paper demonstrates that a rapid, large‑scale temperature boost associated with He II reionisation cannot by itself generate the observed narrow τ_eff dip and its swift recovery. Instead, a transient enhancement of the hydrogen ionising background—potentially linked to re‑processed radiation during He II reionisation or to changes in LLS opacity—offers a more consistent explanation. The study highlights the importance of jointly modelling thermal history and ionising background fluctuations to interpret subtle features in Lyman‑α forest statistics, and it suggests future observational strategies (e.g., direct measurements of Γ_HI evolution or LLS opacity studies) to test the proposed scenario.