Detectability Thresholds for Shadow Imaging: Mass, Distance and the Earth-Diameter Wall

An Earth-diameter array at 230 gigahertz has a fringe spacing of 21.1 microarcseconds, and a shadow is marginally detectable only if its diameter exceeds that spacing. On that criterion an M87*-mass black hole is marginally detectable out to 32 megaparsecs and securely detectable, at twice the fringe spacing, out to 16 megaparsecs; a Sagittarius A*-mass hole is marginally detectable only within 0.021 million parsecs, essentially the Local Group. At the distance of the Virgo cluster the marginal mass threshold is 3.46 billion solar masses, falling to 1.64 billion at a stated future resolution of ten microarcseconds. The catalogue of imageable black holes is therefore short and its membership is computable in advance: it consists of the most massive holes in the nearest clusters plus the Galactic Centre, and no improvement in sensitivity alone can lengthen it, because the wall is angular size, not flux. Computed from stated thresholds; simulated, not measured.