We present Atacama Large Millimeter/submillimeter Array ( ALMA ) 860 \mu m 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″ resolution , the ALMA data reveal multiple images of each submillimeter source , separated by 1-3″ , 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 \times 10 ^ { 13 } L _ { \odot } and star formation surface density of 4200 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } .
We find magnification factors of 5 to 22 , with lens Einstein radii of 1.1 - 2.0″ and Einstein enclosed masses of 1.6-7.2 \times 10 ^ { 11 } M _ { \odot } .
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 .