Planck's Dusty GEMS. III. A massive lensing galaxy with a bottom-heavy
  stellar initial mass function at z=1.5
  We study the properties of the foreground galaxy of the Ruby, the brightest
gravitationally lensed high-redshift galaxy on the sub-millimeter sky as probed
by the Planck satellite, and part of our sample of Planck's Dusty GEMS. The
Ruby consists of an Einstein ring of 1.4" diameter at z = 3.005 observed with
ALMA at 0.1" resolution, centered on a faint, red, massive lensing galaxy seen
with HST/WFC3, which itself has an exceptionally high redshift, z = 1.525 $\pm$
0.001, as confirmed with VLT/X-Shooter spectroscopy. Here we focus on the
properties of the lens and the lensing model obtained with LENSTOOL. The
rest-frame optical morphology of this system is strongly dominated by the lens,
while the Ruby itself is highly obscured, and contributes less than 10% to the
photometry out to the K band. The foreground galaxy has a lensing mass of (3.70
$\pm$ 0.35) $\times$ 10$^{11}$ M$_{\odot}$. Magnification factors are between 7
and 38 for individual clumps forming two image families along the Einstein
ring. We present a decomposition of the foreground and background sources in
the WFC3 images, and stellar population synthesis modeling with a range of
star-formation histories for Chabrier and Salpeter initial mass functions
(IMFs). Only the stellar mass range obtained with the latter agrees well with
the lensing mass. This is consistent with the bottom-heavy IMFs of massive
high-redshift galaxies expected from detailed studies of the stellar masses and
mass profiles of their low-redshift descendants, and from models of turbulent
gas fragmentation. This may be the first direct constraint on the IMF in a lens
at z = 1.5, which is not a cluster central galaxy.
