On the redshift distribution and physical properties of ACT-selected
  DSFGs
  We present multi-wavelength detections of nine candidate
gravitationally-lensed dusty star-forming galaxies (DSFGs) selected at 218GHz
(1.4mm) from the ACT equatorial survey. Among the brightest ACT sources, these
represent the subset of the total ACT sample lying in Herschel SPIRE fields,
and all nine of the 218GHz detections were found to have bright Herschel
counterparts. By fitting their spectral energy distributions (SEDs) with a
modified blackbody model with power-law temperature distribution, we find the
sample has a median redshift of $z=4.1^{+1.1}_{-1.0}$ (68 per cent confidence
interval), as expected for 218GHz selection, and an apparent total infrared
luminosity of $\log_{10}(\mu L_{\rm IR}/{\rm L}_\odot) =
13.86^{+0.33}_{-0.30}$, which suggests that they are either strongly lensed
sources or unresolved collections of unlensed DSFGs. The effective apparent
diameter of the sample is $\sqrt{\mu}d= 4.2^{+1.7}_{-1.0}$kpc, further evidence
of strong lensing or multiplicity, since the typical diameter of dusty
star-forming galaxies is $1.0$--$2.5$ kpc. We emphasize that the effective
apparent diameter derives from SED modelling without the assumption of
optically thin dust (as opposed to image morphology). We find that the sources
have substantial optical depth ($\tau = 4.2^{+3.7}_{-1.9}$) to dust around the
peak in the modified blackbody spectrum ($\lambda_{\rm obs} \le 500$ $\mu$m), a
result that is robust to model choice.
