The Complete Redshift Distribution of Dusty Star-forming Galaxies from
  the SPT-SZ Survey
  The South Pole Telescope (SPT) has systematically identified 81
high-redshift, strongly gravitationally lensed, dusty star-forming galaxies
(DSFGs) in a 2500 square degree cosmological mm-wave survey. We present the
final spectroscopic redshift survey of this flux-limited ($S_{870\, \mathrm{\mu
m}} > 25\, \mathrm{mJy}$) sample, initially selected at $1.4$ mm. The redshift
survey was conducted with the Atacama Large Millimeter/submillimeter Array
across the $3$ mm spectral window, targeting carbon monoxide line emission. By
combining these measurements with ancillary data, the SPT sample is now
spectroscopically complete, with redshifts spanning $1.9$$<$$z$$<$$6.9$ and a
median of $z=3.9 \pm 0.2$. We present the mm through far-infrared photometry
and spectral energy density fits for all sources, along with their inferred
intrinsic properties.
  Comparing the properties of the SPT sources to the unlensed DSFG population,
we demonstrate that the SPT-selected DSFGs represent the most extreme
infrared-luminous galaxies, even after accounting for strong gravitational
lensing. The SPT sources have a median star formation rate of $2.3(2)\times
10^3\, \mathrm{M_\odot yr^{-1}}$ and a median dust mass of $1.4(1)\times10^9\,
\mathrm{M_\odot}$. However, the inferred gas depletion timescales of the SPT
sources are comparable to those of unlensed DSFGs, once redshift is taken into
account. This SPT sample contains roughly half of the known spectroscopically
confirmed DSFGs at $z$$>$$5$, making this the largest sample of high-redshift
DSFGs to-date, and enabling the "high-redshift tail" of extremely luminous
DSFGs to be measured. Though galaxy formation models struggle to account for
the SPT redshift distribution, the larger sample statistics from this complete
and well-defined survey will help inform future theoretical efforts.
