COLDz: A High Space Density of Massive Dusty Starburst Galaxies ~1
  Billion Years after the Big Bang
  We report the detection of CO($J$=2$\to$1) emission from three massive dusty
starburst galaxies at $z$$>$5 through molecular line scans in the NSF's Karl G.
Jansky Very Large Array (VLA) CO Luminosity Density at High Redshift (COLDz)
survey. Redshifts for two of the sources, HDF 850.1 ($z$=5.183) and AzTEC-3
($z$=5.298), were previously known. We revise a previous redshift estimate for
the third source GN10 ($z$=5.303), which we have independently confirmed
through detections of CO $J$=1$\to$0, 5$\to$4, 6$\to$5, and [CII] 158 $\mu$m
emission with the VLA and the NOrthern Extended Milllimeter Array (NOEMA). We
find that two currently independently confirmed CO sources in COLDz are
"optically dark", and that three of them are dust-obscured galaxies at $z$$>$5.
Given our survey area of $\sim$60 arcmin$^2$, our results appear to imply a
$\sim$6-55 times higher space density of such distant dusty systems within the
first billion years after the Big Bang than previously thought. At least two of
these $z$$>$5 galaxies show star-formation rate surface densities consistent
with so-called "maximum" starbursts, but we find significant differences in CO
excitation between them. This result may suggest that different fractions of
the massive gas reservoirs are located in the dense, star-forming nuclear
regions - consistent with the more extended sizes of the [CII] emission
compared to the dust continuum and higher [CII]-to-far-infrared luminosity
ratios in those galaxies with lower gas excitation. We thus find substantial
variations in the conditions for star formation between $z$$>$5 dusty
starbursts, which typically have dust temperatures $\sim$57%$\pm$25% warmer
than starbursts at $z$=2-3 due to their enhanced star formation activity.
