Fitting and Comparing Galactic Foreground Models for Unbiased 21-cm Cosmology

TL;DR

This study evaluates and compares the effectiveness of seven foreground models in accurately fitting simulated galactic foreground spectra for 21-cm cosmology, highlighting the importance of model choice in unbiased signal detection.

Contribution

It systematically tests various foreground models against realistic simulations, providing insights into their fitting performance and biases in 21-cm cosmology experiments.

Findings

Nonlinear models with 4 parameters fit well for single spectra.

Linear models with 6-7 parameters perform comparably or better in multiple LST bins.

Polynomials require more parameters to achieve acceptable fits, with higher p-values at 6-9 parameters.

Abstract

Accurate detection of the cosmological 21-cm global signal requires galactic foreground models which can remove power over ~$10^6$. Although foreground and global signal models unavoidably exhibit overlap in their vector-spaces inducing bias error in the extracted signal, a second source of bias and error arises from inadequate foreground models, i.e. models which cannot fit spectra down to the noise level of the signal. We therefore test the level to which seven commonly employed foreground models -- including nonlinear and linear forward-models, polynomials, and maximally-smooth polynomials -- fit realistic simulated mock foreground spectra, as well as their dependence upon model inputs. The mock spectra are synthesized for an EDGES-like experiment and we compare all models' goodness-of-fit and preference using a Kolomogorov-Smirnov test of the noise-normalized residuals in order to compare models with differing, and sometimes indeterminable, degrees of freedom. For a single LST bin spectrum and p-value threshold of $p=0.05$, the nonlinear-forward model with 4 parameters is preferred ($p=0.99$), while the linear forward-model fits well with 6-7 parameters ($p=0.94,0.97$ respectively). The polynomials and maximally-smooth polynomials, like those employed by the EDGES and SARAS3 experiments, cannot produce good fits with 5 parameters for the experimental simulations in this work ($p<10^{-6}$). However, we find that polynomials with 6 parameters pass the KS-test ($p=0.4$), although a 9 parameter fit produces the highest p-value ($p\sim0.67$). When fitting multiple LST bins simultaneously, we find that the linear forward-model outperforms (a higher p-value) the nonlinear for 2, 5 and 10 LST bins. Importantly, the KS-test consistently identifies best-fit \textit{and} preferred models.