Methods

Overview

The REACH collaboration’s approach to detecting the global 21-cm signal is built around a physically informed forward‐modeling framework that tightly integrates the instrument design, the astrophysical signal, and complex foregrounds into a single Bayesian inference pipeline.  In its foundational radiometer paper, de Lera Acedo et al. describe how REACH uses two complementary ultra-smooth, wide-band antennas alongside an in-field receiver calibrator to capture both the sky signal and instrument systematics.  Full electromagnetic simulations of the antenna beam patterns feed directly into the data model, ensuring that chromatic distortions are explicitly parametrized rather than treated as post-hoc contaminations. 

Bayesian data analysis

At the heart of REACH’s data analysis lies a Bayesian hierarchical model that jointly fits for the cosmological 21-cm brightness temperature, spatially varying foregrounds, and instrument effects.  Foregrounds are decomposed by partitioning the sky into multiple regions—each with its own spectral index—and fitting for both amplitude and spectral‐index errors using nested‐sampling algorithms (e.g. PolyChord) as shown in Anstey et al.  We have demonstrated how extending the foreground model to include region‐dependent scale factors and monopole offsets can absorb map‐level inaccuracies, recovering an unbiased 21-cm signal even when low-frequency sky maps are in error.

Machine learning

On the computational side, the sheer cost of evaluating complex astrophysical models in an MCMC or nested‐sampling loop is mitigated by machine‐learning emulators.  Bevins et al. introduced globalemu, a neural‐network surrogate trained on high-fidelity simulations of the 21-cm global signal (parameterized by star‐formation efficiency, X-ray efficiency, virial velocity threshold, etc.).  By reducing evaluation time from ∼133 ms to ∼1.3 ms per sample—while maintaining ∼10 mK accuracy—globalemu enables rapid exploration of astrophysical parameter space within the REACH pipeline.

End-2-End design studies

Beyond emulating the cosmic signal itself, REACH has also leveraged Bayesian‐driven antenna design studies.  Anstey et al. generated synthetic datasets for several candidate antennas (conical log-spiral, sinuous, polygonal dipole, etc.) and then used the full REACH analysis pipeline to assess detection confidence and bias.  This “simulation‐in‐the-loop” approach provides a robust decision metric without a-priori biases. 

Physical models

REACH’s end‐to‐end forward model goes well beyond generic chromaticity corrections by embedding physically motivated models of every component that can imprint spectral structure onto the measured antenna temperature.  For the celestial sky, REACH combines low-frequency all-sky maps (e.g. the Haslam 408 MHz map scaled via GMOSS or LFmap/PCA‐based interpolators) with catalogued point sources and diffuse synchrotron/emission models to generate a frequency- and direction-dependent brightness‐temperature field .  On the ground, it employs soil dielectric‐constant and conductivity profiles—drawn from in-situ site surveys or geotechnical data—and folds them into full‐wave electromagnetic simulations (e.g. FEKO/FAST) to predict how the Earth beneath the antenna both reflects and emits thermal noise, capturing the so-called “hot horizon” effect that can mimic a global absorption feature.  The horizon model itself treats the grass, rocks, or dusty pan alike as a thermal emitter with frequency-dependent emissivity and reflectivity, parametrised in the Bayesian pipeline so that any residual bias is marginalized over.  By folding sky, soil, horizon, ionosphere and polarisation physics into a single hierarchical model, REACH turns every potential systematic into a parameter to be constrained—rather than a post-hoc nuisance to be patched over.