When the Shadow Meets Its Measure: Assessing the Feasibility of Submillimeter Black Hole Shadow Imaging in Megamaser Disk AGN

Abstract: AGN hosting water megamaser disks enable exceptionally precise geometric determinations of Black Hole (BH) mass, distance, inclination, and dynamical center. In anticipation of upcoming space-based very long baseline Interferometry (SVLBI) missions, megamaser disk AGN offer a uniquely valuable probe of strong-gravity regimes through black hole shadow (BHS) imaging beyond Sgr~A* and M87*. In this work, we (1) map the predicted BHS diameters of twenty-one of the most precisely characterized megamaser disk AGN to submillimeter-millimeter (submm-mm) interferometric baseline requirements, (2) estimate their respective AGN-core flux densities at submm-mm wavelengths, accounting for thermal-dust contamination, extended-jet emission, and intrinsic variability, and (3) determine the astrometric precision required to detect spin-dependent positional offsets between the BHS and the megamaser disk dynamical center. NGC~4258 stands out as the only megamaser disk AGN detectable on Earth-L2 baselines in the submm-mm regime, while other megamaser disk AGN in the sample would require baselines approaching Earth-L4/L5 distances; moreover, only a handful exhibit flux densities above $\sim$10~mJy. Our results further indicate a submillimeter excess in NGC~4258, suggesting that the accretion disk remains thin down to a transitional radius of $\lesssim 100$~Schwarzschild radii, within which the flow becomes advection dominated. For a maximally spinning supermassive black hole in NGC~4258, we show that the astrometric precision of the BHS centroid necessary to detect the BHS-dynamical center offset could, in principle, be achieved with Earth-Moon baselines; however, it would also demand astrometric precision of the water maser dynamical center roughly fifty times better than what is currently attainable.