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.
