Measuring photo-ionization rate and mean free path of HeII ionizing photons at $2.5 \leq z \leq 3.6$: Evidence for late and rapid HeII reionization Part-II
We present measurements of the spatially averaged HeII photo-ionization rate ($\langle Γ_{\rm HeII} \rangle$), mean free path of HeII ionizing photons ($λ_{\rm mfp, HeII}$), and HeII fraction ($f_{\rm HeII}$) across seven redshift bins within the redshift range $2<z<4$. The measurements are obtained by comparing the observed effective optical depth distribution of HeII ($τ_{\rm eff, HeII}$) with models generated by post-processing of the Sherwood simulation suite using our code EXCITE. With EXCITE, we efficiently explore a large parameter space ($\sim 15000$ models) by varying $λ_{\rm mfp, HeII}$ and $\langle Γ_{\rm HeII} \rangle$. We employ Anderson-Darling test for the cumulative distribution of $τ_{\rm eff, HeII}$ to simultaneously measure $λ_{\rm mfp, HeII}$ and $\langle Γ_{\rm HeII} \rangle$. Our measurements account for possible observational and modeling uncertainties stemming mainly from the finite signal-to-noise ratio of the observed data and thermal parameter uncertainties. We find significant evolution, with the best-fit $\langle Γ_{\rm HeII} \rangle$ and $λ_{\rm mfp, HeII}$ decreasing by factors of $\sim 4.32$ and $ \sim 3.27$, respectively, from $z = 2.88$ to $z = 3.16$. Based on these measurements, we constrain the emissivity at the HeII ionization frequency ($ε_{228}$) and HeII ionizing photon emission rate ($\dot{n}$), finding consistency with results from galaxy and QSO surveys. Comparison of our measured parameters with widely used uniform UVB models supports a scenario where HeII reionization is not completed before $z\sim2.74$. Our measured evolution is complementary and in good agreement with recent measurements of thermal parameters of the IGM, suggesting a coherent picture of rather late and rapid HeII reionization.