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We estimate the mass of the intermediate-mass black hole at the heart of thedwarf elliptical galaxy NGC 404 using Atacama Large Millimeter/submillimeterArray (ALMA) observations of the molecular interstellar medium at anunprecedented linear resolution of ~0.5 pc, in combination with existingstellar kinematic information. These ALMA observations reveal a centraldisc/torus of molecular gas clearly rotating around the black hole. This discis surrounded by a morphologically and kinematically complex flocculentdistribution of molecular clouds, that we resolve in detail. Continuum emissionis detected from the central parts of NGC 404, likely arising from theRayleigh-Jeans tail of emission from dust around the nucleus, and potentiallyfrom dusty massive star-forming clumps at discrete locations in the disc.Several dynamical measurements of the black hole mass in this system have beenmade in the past, but they do not agree. We show here that both the observedmolecular gas and stellar kinematics independently require a ~5x10$^5$ Msunblack hole once we include the contribution of the molecular gas to thepotential. Our best estimate comes from the high-resolution molecular gaskinematics, suggesting the black hole mass of this system is5.5$^{+4.1}_{-3.8}\times$10$^5$ Msun (at the 99% confidence level), in goodagreement with our revised stellar kinematic measurement and broadly consistentwith extrapolations from the black hole mass - velocity dispersion and blackhole mass - bulge mass relations. This highlights the need to accuratelydetermine the mass and distribution of each dynamically important componentaround intermediate-mass black holes when attempting to estimate their masses.

Revealing the intermediate-mass black hole at the heart of the dwarf galaxy NGC 404 with sub-parsec resolution ALMA observations