Point spread function requirements for dark matter subhalo detection with the Habitable Worlds Observatory

Different theories of dark matter predict different populations and morphologies of galactic subhaloes below about 10^8M_{odot}. The planned angular resolution and optical stability of the Habitable Worlds Observatory (HWO) should enable it to detect subtle subhalo perturbations in strongly lensed galaxy images. We simulate 2000-second exposures with its High Resolution Imager (HRI) under the fiducial Exploratory Analytic Case 1 (EAC1) design, assuming known source structure and omitting lens-galaxy light. Pre-selecting the top 50 of 965 lenses (5.2%) using only arc signal-to-noise and relative gradient power lowers the median mass threshold for 10% aperture coverage roughly tenfold relative to the full ensemble. The top 12 (1.2%) reach a median of 6.6times10^7M_{odot} for the same coverage. At their most sensitive positions, the top 50 and top 12 reach median thresholds of 3times10^7M_{odot} and 1.5times10^7M_{odot}, respectively. Non-linear fits support the Fisher forecasts at the tested masses and positions. For these 12 lenses, increasing the physical wavefront error from 35 to 65 nm RMS raises the median thresholds by only 0.1 dex when the point spread function (PSF) is modelled correctly. Deliberately mismodelling the 35-nm reference PSF removes detectable positions, although false detections remain rare. Under our illustrative retention criteria, loss of sensitive area sets a median tolerated wavefront mismatch of 5 nm RMS (range 2--10 nm). Selective HWO follow-up of lenses discovered by Euclid or Roman could therefore transform our understanding of the nature of dark matter, provided that the PSF is characterized accurately enough to preserve this sensitivity.