High-resolution ALMA observations of SDP.81. I. The innermost mass profile of the lensing elliptical galaxy probed by 30 milli-arcsecond images

We report a detailed modeling of a mass profile of a $z = 0.2999$ massive elliptical galaxy using 30 milli-arcsecond resolution 1-mm Atacama Large Millimeter/submillimeter Array (ALMA) images of the galaxy-galaxy lensing system SDP.81. The detailed morphology of the lensed multiple images of the $z = 3.042$ infrared-luminous galaxy, which is found to consist of tens of $\lesssim 100$-pc-sized star-forming clumps embedded in a $\sim 2$ kpc disk, are well reproduced by a lensing galaxy modeled by an isothermal ellipsoid with a 400 pc core. The core radius is consistent with that of the visible stellar light, and the mass-to-light ratio of $\sim 2\,M_{\odot}\,L_{\odot}^{-1}$ is comparable to the locally measured value, suggesting that the inner 1 kpc region is dominated by luminous matter. The position of the predicted mass centroid is consistent to within $\simeq 30$ mas with that of a non-thermal source detected with ALMA, which likely traces an active galactic nucleus of the foreground elliptical galaxy. A point source mass of $> 3 \times 10^8\,M_{\odot}$ mimicking a supermassive black hole is required to explain the non-detection of a central image of the background galaxy, although the black hole mass degenerates with the core radius of the elliptical galaxy. The required mass is consistent with that predicted from the well-known correlation between black hole mass and host velocity dispersion. Our analysis demonstrates the power of ALMA imaging of strong gravitational lensing for studying the innermost mass profiles and the central supermassive black hole of distant elliptical galaxies.