Updated dark pixel fraction constraints on reionization's end from the Lyman-series forests of XQR-30

TL;DR

This work uses deep XQR-30 Ly-series forest spectra to tighten constraints on the end of hydrogen reionization via the dark pixel fraction. It employs both model-independent (threshold and negative-pixel) methods on Lyα, Lyβ, and Lyγ forests, and a model-dependent lognormal mixture approach, to bound the mean IGM neutral fraction ⟨x_HI⟩ across z ≈ 5.5–6.0. The fiducial model-independent result from the Lyβ+Lyγ combination gives ⟨x_HI⟩ ≤ {0.030, 0.095, 0.191, 0.199} at z̄ ≈ {5.481, 5.654, 5.831, 6.043}, with a tentative high-z point near z̄ ≈ 6.225. Model-dependent gains from a lognormal flux mixture yield ⟨x_HI⟩ ≤ {0.151, 0.222, 0.295} at z̄ ≈ {5.654, 5.832, 6.041}. Overall, the bulk of reionization appears finished by z > 6, though a soft landing down to z ≈ 5.4 remains plausible; the results demonstrate how extending to higher-order Lyman-series lines enhances constraints and solidify a late-reionization picture.

Abstract

The fraction of "dark pixels" in the Ly$α$ and other Lyman-series forests at $z\sim 5-6$ provides a powerful constraint on the end of the reionization process. Any spectral region showing transmission must be highly ionized, while dark regions could be ionized or neutral, thus the dark pixel fraction provides a (nearly) model independent upper limit to the volume-filling fraction of the neutral intergalactic medium, modulo choices in binning scale and dark pixel definition. Here we provide updated measurements of the 3.3 comoving Mpc dark pixel fraction at $z=4.85-6.25$ in the Ly$α$, Ly$β$, and Ly$γ$ forests of 34 deep $5.8\lesssim z\lesssim 6.6$ quasar spectra from the (enlarged) XQR-30 sample. Using the negative pixel method to measure the dark pixel fraction, we derive fiducial $1σ$ upper limits on the volume-average neutral hydrogen fraction of $\langle x_{\rm{HI}}\rangle \leq \{0.030 + 0.048, 0.095 + 0.037, 0.191 + 0.056, 0.199 + 0.087\}$ at $\bar{z} = \{5.481, 5.654, 5.831, 6.043\}$ from the optimally sensitive combination of the Ly$β$ and Ly$γ$ forests. We further demonstrate an alternative method that treats the forest flux as a mixture of dark and transparent regions, where the latter are modeled using a physically-motivated parametric form for the intrinsic opacity distribution. The resulting model-dependent upper limits on $\langle x_{\rm{HI}}\rangle$ are similar to those derived from our fiducial model-independent analysis. We confirm that the bulk of reionization must be finished at $z>6$, while leaving room for an extended "soft landing" to the reionization history down to $z\sim 5.4$ suggested by Ly$α$ forest opacity fluctuations.

Figures (20)

• Figure 1: Top: Number of quasar sightlines covering the Ly$\alpha$ (black), Ly$\beta$ (blue), and Ly$\gamma$ (red) forests within the eight $\Delta z=0.2$ redshift bins we consider in this work. Bottom: Corresponding number of binned pixels in each forest/redshift bin combination. The green dashed lines in both panels show the corresponding numbers for the Ly$\delta$ forest, discussed in Appendix \ref{['app:delta']}.
• Figure 2: Example of a masked and binned quasar spectrum from our data set (PSO J007$+$04, $z_{\rm q}=6.0015$). Brown and green points below the spectrum indicated undetected (${\rm S/N}<2$) and negative binned pixels, respectively. The forests Ly$\alpha$/Ly$\gamma$ forest transmissions are shown offset by $\pm0.65$ for clarity.
• Figure 3: Limiting effective optical depths $\tau_{\rm eff,lim}=-\ln{\sigma_{\rm bin}/F_{\rm cont}}$ along each quasar sightline for binned pixels in the Ly$\alpha$ (top), Ly$\beta$ (middle), and Ly$\gamma$ (bottom) forests. The vertical stripe of low $\tau_{\rm eff,lim}$ at $z\simeq5.25$ in the Ly$\alpha$ forest is due to strong telluric absorption from the O$_2$ A-band at $\sim7600$ Å. Note also the spectrum of SDSS J0100$+$2802 which has extraordinarily high signal-to-noise, resulting in the horizontal stripes of particularly high $\tau_{\rm eff,lim}$.
• Figure 4: Distribution of detected (${\rm S/N}>2$, blue) and undetected (${\rm S/N}<2$, red) binned pixels in the $35$ E-XQR-30 quasar sightlines used in this work. White binned pixels within the low and high redshift boundaries of each quasar sightline have more than 50% of their spectral pixels masked. The regions with faded color at the high redshift end of each sightline show pixels within the quasar proximity zone exclusion. Left: Binned pixels in the Ly$\alpha$ (top), Ly$\beta$ (middle), and Ly$\gamma$ forests. Right: Forest combinations Ly$\alpha$$+$Ly$\beta$ (top), Ly$\beta$$+$Ly$\gamma$ (middle), and Ly$\alpha$$+$Ly$\beta$$+$Ly$\gamma$ (bottom), where blue pixels are detected in any or all forests while red pixels are undetected in all forests.
• Figure 5: Measurements of the dark pixel fraction in each Lyman-series forest and forest combination inferred from the threshold method applied to the E-XQR-30 data set. Uncertainties (thick: 1$\sigma$, thin: 2$\sigma$) are derived from bootstrap resampling of the quasar sightlines contributing to each bin, or from the confidence interval of the binomial fraction, whichever is larger. For the forest combinations (lower panels), we show the dark pixel fractions of the individual contributing forests in a light color with slight redshift offsets for clarity.