ALMA redshifts of millimeter-selected galaxies from the SPT survey: The
  redshift distribution of dusty star-forming galaxies
  Using the Atacama Large Millimeter/submillimeter Array (ALMA), we have
conducted a blind redshift survey in the 3 mm atmospheric transmission window
for 26 strongly lensd dusty star-forming galaxies (DSFGs) selected with the
South Pole Telescope (SPT). The sources were selected to have S_1.4mm>20 mJy
and a dust-like spectrum and, to remove low-z sources, not have bright radio
(S_843MHz<6mJy) or far-infrared counterparts (S_100um<1 Jy, S_60um<200mJy). We
robustly detect 44 line features in our survey, which we identify as redshifted
emission lines of 12CO, 13CO, [CI], H2O, and H2O+. We find one or more spectral
features in 23 sources yielding a ~90% detection rate for this survey; in 12 of
these sources we detect multiple lines, while in 11 sources we detect only a
single line. For the sources with only one detected line, we break the redshift
degeneracy with additional spectroscopic observations if available, or infer
the most likely line identification based on photometric data. This yields
secure redshifts for ~70% of the sample. The three sources with no lines
detected are tentatively placed in the redshift desert between 1.7<z<2.0. The
resulting mean redshift of our sample is <z>=3.5. This finding is in contrast
to the redshift distribution of radio-identified DSFGs, which have a
significantly lower mean redshift of <z>=2.3 and for which only 10-15% of the
population is expected to be at z>3. We discuss the effect of gravitational
lensing on the redshift distribution and compare our measured redshift
distribution to that of models in the literature.
