Exploring the role of the halo mass function for inferring astrophysical parameters during reionisation

TL;DR

This paper investigates how incorrect assumptions about the halo mass function can bias astrophysical parameter inference during reionisation and proposes a flexible model to mitigate this bias, improving the robustness of 21-cm signal analysis.

Contribution

It introduces a generalized five-parameter halo mass function model and demonstrates its effectiveness in unbiasedly recovering astrophysical parameters from 21-cm data.

Findings

Incorrect HMF assumptions can bias parameters by up to 3-4 sigma.

Using the generalized HMF increases uncertainties but removes bias.

The approach is validated with mock SKA observations.

Abstract

The detection of the 21-cm signal at $z\gtrsim6$ will reveal insights into the properties of the first galaxies responsible for driving reionisation. To extract this information, we perform parameter inference which requires embedding 3D simulations of the 21-cm signal within a Bayesian inference pipeline. Presently, when performing inference we must choose which sources of uncertainty to sample and which to hold fixed. Since the astrophysics of galaxies are much more uncertain than those of the underlying halo-mass function (HMF), we usually parameterise and model the former while fixing the latter. However, in doing so we may bias our inference of the properties of these first galaxies. In this work, we explore the consequences of assuming an incorrect choice of HMF and quantify the relative biases in our inferred astrophysical model parameters when considering the wrong HMF. We then relax this assumption by constructing a generalised five parameter model for the HMF and simultaneously recover these parameters along with our underlying astrophysical model. For this analysis, we use 21cmFAST and perform Simulation-Based Inference by applying marginal neural ratio estimation to learn the likelihood-to-evidence ratio using Swyft. Using a mock 1000 hour observation of the 21-cm power spectrum from the forthcoming Square Kilometre Array, conservatively assuming foreground wedge avoidance, we find assuming the incorrect HMF can bias the recovered astrophysical parameters by up to $\sim3-4\sigma$ even when including independent information from observed luminosity functions. When considering our generalised HMF model, we recover constraints on our astrophysical parameters with a factor of $\sim2-4$ larger marginalised uncertainties. Importantly, these constraints are unbiased, agnostic to the underlying HMF and therefore more conservative.