The impact of lunar topography on the 21-cm power spectrum for grid-based arrays: Insights for the Dark-ages EXplorer (DEX)

The Dark Ages (DA) provides a crucial window into the physics of the infant Universe, with the 21-cm signal offering the only direct probe for mapping out the three-dimensional distribution of matter at this epoch. To measure this cosmological signal, the Dark-ages EXplorer (DEX) has been proposed as a compact, grid-based radio array on the lunar farside. The minimal design consists of a 32 × 32 array of 3-m dipole antennas, operating in the 7–50 MHz band. A practical challenge on the lunar surface is that the antennas may get displaced from their intended positions due to deployment imprecisions and non-coplanarity arising from local surface undulations. We present, for the first time, an end-to - end simulation pipeline, called SPADE-21 cm, that int egrat es a sky model with a DA 21-cm signal model simulated in the lunar frame and incorporating lunar topography data. We study the effects of both lateral ( xy ) and vertical ( z ) offsets on the two- dimensional power spectra across the 7–12 and 30–35 MHz spectral windows, with tolerance thresholds derived only for the latter. Our results show that positional offsets bias the power spectrum by 10–30 per cent relative to the expected 21-cm power spectrum during DA. Lateral offsets within σxy /λ ≲ 0 . 027 (at 32.5 MHz) keep the fraction of Fourier modes with strong contamination ( > 50 per cent of the signal) to less than 1 per cent, whereas vertical height offsets affect a larger fraction. This conclusion holds for the 21-cm window with k > 0 . 5 h cMpc −1 over the range of k ⊥ = 0 . 003 - 0 . 009 h cMpc −1 .