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We report a detailed modeling of a mass profile of a $z = 0.2999$ massiveelliptical galaxy using 30 milli-arcsecond resolution 1-mm Atacama LargeMillimeter/submillimeter Array (ALMA) images of the galaxy-galaxy lensingsystem 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 witha 400 pc core. The core radius is consistent with that of the visible stellarlight, and the mass-to-light ratio of $\sim 2\,M_{\odot}\,L_{\odot}^{-1}$ iscomparable to the locally measured value, suggesting that the inner 1 kpcregion is dominated by luminous matter. The position of the predicted masscentroid is consistent to within $\simeq 30$ mas with that of a non-thermalsource detected with ALMA, which likely traces an active galactic nucleus ofthe foreground elliptical galaxy. A point source mass of $> 3 \times10^8\,M_{\odot}$ mimicking a supermassive black hole is required to explain thenon-detection of a central image of the background galaxy, although the blackhole mass degenerates with the core radius of the elliptical galaxy. Therequired mass is consistent with that predicted from the well-known correlationbetween black hole mass and host velocity dispersion. Our analysis demonstratesthe power of ALMA imaging of strong gravitational lensing for studying theinnermost mass profiles and the central supermassive black hole of distantelliptical galaxies.

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