Forecasting a Cosmological 21 cm Stacking Detection with Early HIRAX Data

Post-reionization 21 cm intensity mapping provides a powerful technique for efficiently mapping the Universe on large scales. The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a compact and highly redundant radio interferometer designed to exploit this technique. We present a forward modelling pipeline for forecasting a statistical detection of the cosmological 21 cm signal with HIRAX through cross-correlation with an external source catalogue. We simulate the cosmological signal using the halo model and propagate it, together with Galactic and extragalactic foreground emission and instrumental noise, through a model of an early-stage 36-dish HIRAX array configuration. We generate simulated visibilities, apply delay-domain foreground filtering, and construct cross-correlation-ready ringmaps for an observing time of 120 days with a single zenith pointing over the frequency range from 700 to 800 MHz, covering approximately 3547 deg squared of the sky. We investigate the prospects for an early statistical signal detection by stacking these ringmaps at the known three-dimensional positions of sources from an overlapping external survey. Specifically, we quantify how delay-domain foreground filtering, the number of stacking sources, catalogue completeness, and source redshift uncertainties affect the detection significance. We find that redshift precision is the most critical requirement: while spectroscopic redshifts with σ z / (1+z) about 0.001 preserve a significant stacking signal even under realistic foreground filtering and substantial catalogue incompleteness, photometric redshift uncertainties of σ z / (1+z) about 0.01 strongly suppress the signal for realistic delay cutoffs. Applying the framework to a Euclid-like spectroscopic galaxy sample, we recover a minimum signal-to-noise ratio of 11 for our most conservative delay cutoff of 100 ns.