A New Method to Measure the Post-reionization Ionizing Background from the Joint Distribution of Lyα and Lyβ Forest Transmission ∗

Abstract

The amplitude of the ionizing background that pervades the intergalactic medium (IGM) at the end of the epoch of reionization provides a valuable constraint on the emissivity of the sources that reionized the universe. While measurements of the ionizing background at lower redshifts rely on a simulation-calibrated mapping between the photoionization rate and the mean transmission of the Ly α forest, at z  ≳ 6 the IGM becomes increasingly opaque and transmission arises solely in narrow spikes separated by saturated Gunn–Peterson troughs. In this regime, the traditional approach of measuring the average transmission over large ∼50 Mpc/ h regions is less sensitive and suboptimal. In addition, the five times smaller oscillator strength of the Ly β transition implies that the Ly β forest is considerably more transparent at z  ≳ 6, even in the presence of contamination by foreground z  ∼ 5 Ly α forest absorption. In this work we present a novel statistical approach to analyze the joint distribution of transmission spikes in the cospatial z  ∼ 6 Ly α and Ly β forests. Our method relies on approximate Bayesian computation (ABC), which circumvents the necessity of computing the intractable likelihood function describing the highly correlated Ly α and Ly β transmission. We apply ABC to mock data generated from a large-volume hydrodynamical simulation combined with a state-of-the-art model of ionizing background fluctuations in the post-reionization IGM and show that it is sensitive to higher IGM neutral hydrogen fractions than previous techniques. As a proof of concept, we apply this methodology to a real spectrum of a z  = 6.54 quasar and measure the ionizing background from 5.4 ≤  z  ≤ 6.4 along this sightline with ∼0.2 dex statistical uncertainties.