Accepted to the ApJ Preprint typeset using LATEX style emulateapj v. 5/2/11 GRAVITATIONAL LENS MODELS BASED ON SUBMILLIMETER ARRAY † IMAGING OF HERSCHEL††-SELECTED STRONGLY LENSED SUB-MILLIMETER GALAXIES AT Z> 1.5

Accepted to the ApJ Strong gravitational lenses are now being routinely discovered in wide-field surveys at (sub-)millimeter wavelengths. We present Submillimeter Array (SMA) high-spatial resolution imaging and Gemini-South and Multiple Mirror Telescope optical spectroscopy of strong lens candidates dis-covered in the two widest extragalactic surveys conducted by the Herschel Space Observatory: the Herschel-Astrophysical Terahertz Large Area Survey (H-ATLAS) and the Herschel Multi-tiered Ex-tragalactic Survey (HerMES). From a sample of 30 Herschel sources with S500> 100 mJy, 21 are strongly lensed (i.e., multiply imaged), 4 are moderately lensed (i.e., singly imaged), and the remain-der require additional data to determine their lensing status. We apply a visibility-plane lens modeling technique to the SMA data to recover information about the masses of the lenses as well as the in-trinsic (i.e., unlensed) sizes (rhalf) and far-infrared luminosities (LFIR) of the lensed submillimeter galaxies (SMGs). The sample of lenses comprises primarily isolated massive galaxies, but includes some groups and clusters as well. Several of the lenses are located at zlens> 0.7, a redshift regime that is inaccessible to lens searches based on Sloan Digital Sky Survey spectroscopy. The lensed SMGs are amplified by factors that are significantly below statistical model predictions given the 500µ