The redshift distribution of dusty star forming galaxies from the SPT
  survey
  We use the Atacama Large Millimeter/submillimeter Array (ALMA) in Cycle 1 to
determine spectroscopic redshifts of high-redshift dusty star-forming galaxies
(DSFGs) selected by their 1.4mm continuum emission in the South Pole Telescope
(SPT) survey. We present ALMA 3mm spectral scans between 84-114GHz for 15
galaxies and targeted ALMA 1mm observations for an additional eight sources.
Our observations yield 30 new line detections from CO, [CI] , [NII] , H_2O and
NH_3. We further present APEX [CII] and CO mid-J observations for seven sources
for which only a single line was detected in spectral-scan data from ALMA Cycle
0 or Cycle 1. We combine the new observations with previously published and new
mm/submm line and photometric data of the SPT-selected DSFGs to study their
redshift distribution. The combined data yield 39 spectroscopic redshifts from
molecular lines, a success rate of >85%. Our sample represents the largest data
set of its kind today and has the highest spectroscopic completeness among all
redshift surveys of high-z DSFGs. The median of the redshift distribution is
z=3.9+/-0.4, and the highest-redshift source in our sample is at z=5.8. We
discuss how the selection of our sources affects the redshift distribution,
focusing on source brightness, selection wavelength, and strong gravitational
lensing. We correct for the effect of gravitational lensing and find the
redshift distribution for 1.4mm-selected sources with a median redshift of
z=3.1+/-0.3. Comparing to redshift distributions selected at shorter
wavelengths from the literature, we show that selection wavelength affects the
shape of the redshift distribution.
