Measuring Supermassive Black Holes in Distant Galaxies with Central Lensed Images

The supermassive black hole at the center of a distant galaxy can be weighed, in rare but realistic cases, when the galaxy acts as a strong gravitational lens. The central image that should be produced by the lens is either destroyed or accompanied by a second central image, depending on the mass of the black hole. We demonstrate that when a central image pair is detected, the mass of the black hole can be determined with an accuracy of ≲0.1 dex, if the form of the smooth mass distribution near the galaxy core is known. Uncertainty in the central mass distribution introduces a systematic error in the black hole mass measurement. However, even with nearly complete ignorance of the inner mass distribution, the black hole mass can still be determined to within a factor of 10. Central image pairs should be readily observable with future radio interferometers, allowing this technique to be used for a census of supermassive black holes in inactive galaxies at significant redshift (0.2 ≲ z ≲ 1.0).