Breaking the Mass Sheet with Stellar Kinematics: The Velocity-Dispersion Precision the Degeneracy Demands

The mass-sheet degeneracy is broken, in practice, by the stellar velocity dispersion of the lens galaxy, because the dispersion scales with the square root of the sheet parameter. This paper inverts that scaling into a requirements table. A velocity dispersion measured to five per cent constrains the sheet parameter, and hence the Hubble constant from that lens, to 10 per cent. Seven such lenses combine to 3.78 per cent, and forty lenses with seven per cent dispersions reach 2.21 per cent, closely matching the precision the TDCOSMO programme obtained when it replaced assumed profiles with kinematic information. Reaching two per cent on the Hubble constant through this route alone requires of order twenty-five lenses at five per cent dispersion precision. Computed from the scaling relation; not a measurement.