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

Detecting the 21-cm signal at z greater than or similar to 6 will reveal insights into the properties of the first galaxies responsible for driving reionization. To extract this information, we perform parameter inference with three-dimensional simulations of the 21-cm signal embedded 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 is much more uncertain than that of the underlying halo-mass function (HMF), we typically parametrize and model the former while fixing the latter. However, doing so may bias our inference of the galaxy properties. In this work, we explore the consequences of assuming an incorrect HMF and quantify the relative biases on our inferred astrophysical model parameters when considering the wrong HMF. We then relax this assumption by constructing a generalized five parameter HMF model and simultaneously recover it with our underlying astrophysical model. For this, we use 21cmfast and perform simulation-based inference using marginal neural ratio estimation to learn the likelihood-to-evidence ratio with Swyft. Using a mock 1000-h observation of the 21-cm power spectrum from the forthcoming Square Kilometre Array, conservatively assuming foreground wedge avoidance, we find that assuming the incorrect HMF can bias the recovered astrophysical parameters by up to similar to 3-4 sigma even when including independent information from observed luminosity functions. Using our generalized HMF model, although we recover our astrophysical parameters with a factor of similar to 2-4 larger marginalized uncertainties, the constraints are unbiased, agnostic to the underlying HMF and therefore more conservative.