The central image of a strongly lensed background source places constraints on the foreground lens galaxy ’ s inner mass profile slope , core radius and mass of its nuclear supermassive black hole .
Using high-resolution long-baseline Atacama Large Millimeter/submillimeter Array ( ALMA ) observations and archival Hubble Space Telescope ( HST ) imaging , we model the gravitational lens H-ATLAS J090311.6+003906 ( also known as SDP.81 ) and search for the demagnified central image .
There is central continuum emission from the lens galaxy ’ s active galactic nucleus ( AGN ) but no evidence of the central lensed image in any molecular line .
We use the CO maps to determine the flux limit of the central image excluding the AGN continuum .
We predict the flux density of the central image and use the limits from the ALMA data to constrain the innermost mass distribution of the lens .
For a power-law profile with a core radius of 0.15 \arcsec measured from HST photometry of the lens galaxy assuming that the central flux is attributed to the AGN , we find that a black hole mass of \mathrm { \log ( M _ { BH } / M _ { \odot } ) } \gtrsim 8.5 is preferred .
Deeper observations with a detection of the central image will significantly improve the constraints of the innermost mass distribution of the lens galaxy .