We present Atacama Large Millimeter/submillimeter Array (ALMA) 860 micrometer imaging of four high-redshift (z=2.8-5.7) dusty sources that were detected using the South Pole Telescope (SPT) at 1.4 mm and are not seen in existing radio to far-infrared
catalogs. At 1.5 arcsec resolution, the ALMA data reveal multiple images of each submillimeter source, separated by 1-3 arcsec, consistent with strong lensing by intervening galaxies visible in near-IR imaging of these sources. We describe a gravitational lens modeling procedure that operates on the measured visibilities and incorporates self-calibration-like antenna phase corrections as part of the model optimization, which we use to interpret the source structure. Lens models indicate that SPT0346-52, located at z=5.7, is one of the most luminous and intensely star-forming sources in the universe with a lensing corrected FIR luminosity of 3.7 X 10^13 L_sun and star formation surface density of 4200 M_sun yr^-1 kpc^-2. We find magnification factors of 5 to 22, with lens Einstein radii of 1.1-2.0 arcsec and Einstein enclosed masses of 1.6-7.2x10^11 M_sun. These observations confirm the lensing origin of these objects, allow us to measure the their intrinsic sizes and luminosities, and demonstrate the important role that ALMA will play in the interpretation of lensed submillimeter sources.
We investigate how strong lensing of dusty, star-forming galaxies by foreground galaxies can be used as a probe of dark matter halo substructure. We find that spatially resolved spectroscopy of lensed sources allows dramatic improvements to measureme
nts of lens parameters. In particular we find that modeling of the full, three-dimensional (angular position and radial velocity) data can significantly facilitate substructure detection, increasing the sensitivity of observables to lower mass subhalos. We carry out simulations of lensed dusty sources observed by early ALMA (Cycle 1) and use a Fisher matrix analysis to study the parameter degeneracies and mass detection limits of this method. We find that, even with conservative assumptions, it is possible to detect galactic dark matter subhalos of ~ 10^8 M_{odot} with high significance in most lensed DSFGs. Specifically, we find that in typical DSFG lenses, there is a ~ 55 % probability of detecting a substructure with M>10^8 M_{odot} with more than 5 sigma detection significance in each lens, if the abundance of substructure is consistent with previous lensing results. The full ALMA array, with its significantly enhanced sensitivity and resolution, should improve these estimates considerably. Given the sample of ~100 lenses provided by surveys like the South Pole Telescope, our understanding of dark matter substructure in typical galaxy halos is poised to improve dramatically over the next few years.
We study the effects of strong lensing on the observed number counts of mm sources using a ray tracing simulation and two number count models of unlensed sources. We employ a quantitative treatment of maximum attainable magnification factor depending
on the physical size of the sources, also accounting for effects of lens halo ellipticity. We calculate predicted number counts and redshift distributions of mm galaxies including the effects of strong lensing and compare with the recent source count measurements of the South Pole Telescope (SPT). The predictions have large uncertainties, especially the details of the mass distribution in lens galaxies and the finite extent of sources, but the SPT observations are in good agreement with predictions. The sources detected by SPT are predicted to largely consist of strongly lensed galaxies at z>2. The typical magnifications of these sources strongly depends on both the assumed unlensed source counts and the flux of the observed sources.
