[Paper Review] Learning Reionization History from Quasars with Simulation-Based Inference

Huanqing Chen, Joshua S. Speagle+1 more|arXiv (Cornell University)|Nov 27, 2023

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper proposes using simulation-based inference (SBI) with conditional normalizing flows to extract the neutral fraction of the universe from high-redshift quasar spectra, leveraging damping wing features to break degeneracies between parameters. SBI outperforms traditional pseudo-likelihood methods by enabling unbiased, precise inference with realistic uncertainties, achieving an RMS bias of 0.06 in neutral fraction estimation.

ABSTRACT

Understanding the entire history of the ionization state of the intergalactic medium (IGM) is at the frontier of astrophysics and cosmology. A promising method to achieve this is by extracting the damping wing signal from the neutral IGM. As hundreds of redshift $z>6$ quasars are observed, we anticipate determining the detailed time evolution of the ionization fraction with unprecedented fidelity. However, traditional approaches to parameter inference are not sufficiently accurate. We assess the performance of a simulation-based inference (SBI) method to infer the neutral fraction of the universe from quasar spectra. The SBI method adeptly exploits the shape information of the damping wing, enabling precise estimations of the neutral fraction $\left_{ m v}$ and the wing position $w_p$. Importantly, the SBI framework successfully breaks the degeneracy between these two parameters, offering unbiased estimates of both. This makes the SBI superior to the traditional method using a pseudo-likelihood function. We anticipate that SBI will be essential to determine robustly the ionization history of the Universe through joint inference from the hundreds of high-$z$ spectra we will observe.

Motivation & Objective

• To develop a robust method for inferring the global neutral fraction ⟨x_HI⟩_v from high-redshift quasar spectra, overcoming limitations of traditional likelihood-based approaches.
• To address the degeneracy between the damping wing position wp and the neutral fraction ⟨x_HI⟩_v, which plagues conventional pseudo-likelihood methods.
• To enable accurate, joint inference of reionization history from hundreds of upcoming high-z quasar spectra using simulation-based inference.
• To calibrate uncertainties in parameter estimates and validate the reliability of the inference framework through probability calibration checks.

Proposed method

• The method employs simulation-based inference (SBI) using conditional normalizing flows to model the likelihood of observed quasar spectra given latent parameters, bypassing intractable analytical likelihoods.
• It combines pre-computed hydrodynamical simulations (CROC) for the Lyα forest and a separate database of damping wings from [5] to generate composite quasar spectra.
• The SBI framework learns a conditional density estimator that maps observed spectra to posterior distributions over ⟨x_HI⟩_v and wp, capturing complex pixel-wise correlations.
• The approach uses a likelihood-free inference strategy that conditions on the full spectral shape, enabling extraction of subtle damping wing features.
• Uncertainty calibration is performed via a Kolmogorov–Smirnov test on rank distributions of estimated quantiles, validating the reliability of posterior PDFs.
• The method is scalable to multiple spectra by concatenating individual spectra as input, enabling joint inference across hundreds of quasars.

Experimental results

Research questions

• RQ1 Can simulation-based inference with normalizing flows outperform traditional pseudo-likelihood methods in estimating the neutral fraction from quasar damping wings?
• RQ2 To what extent does SBI break the degeneracy between the damping wing position wp and the neutral fraction ⟨x_HI⟩_v?
• RQ3 Are the posterior uncertainties from SBI well-calibrated and unbiased across different true parameter values?
• RQ4 How does SBI perform in terms of bias and scatter compared to the pseudo-likelihood method on individual quasar spectra?

Key findings

• The SBI method achieves an RMS bias of 0.06 in ⟨x_HI⟩_v estimation, which is significantly lower than the 0.11 RMS bias of the traditional pseudo-likelihood method.
• The SBI posterior distributions are well-calibrated, with a p-value of 0.16 from the K-S test on rank distributions, indicating no strong evidence of miscalibration.
• The typical scatter in SBI constraints (RMS 0.12) is approximately equal to the cosmic variance of the damping wing, suggesting near-optimal inference performance.
• The SBI framework successfully breaks the degeneracy between ⟨x_HI⟩_v and wp by exploiting correlated pixel information in the damping wing shape.
• The traditional pseudo-likelihood method exhibits a U-shaped rank distribution, indicating under-predicted uncertainties and systematic bias in parameter estimation.
• The SBI method is scalable to multiple spectra by concatenating inputs, making it suitable for joint inference across the hundreds of high-redshift quasars expected in upcoming surveys.