Millimeter imaging of submillimeter galaxies in the COSMOS field: redshift distribution

We present new IRAM Plateau de Bure interferometer (PdBI) 1.3 mm continuum observations at similar to 1.5 '' resolution of 28 submillimeter galaxies (SMGs), previously discovered with the 870 mu m bolometer LABOCA at the APEX telescope from the central 0.7 deg(2) of the COSMOS field. Nineteen out of the 28 LABOCA sources were detected with PdBI at a greater than or similar to 3 sigma level of approximate to 1.4 mJy/beam. A combined analysis of this new sample with existing interferometrically identified SMGs in the COSMOS field yields the following results: i) greater than or similar to 15%, and possibly up to similar to 40% of single-dish detected SMGs consist of multiple sources; ii) statistical analysis of multi-wavelength counterparts to single-dish SMGs shows that only similar to 50% have real radio or IR counterparts; iii) similar to 18% of interferometric SMGs have either no multi-wavelength counterpart or only a radio-counterpart; and iv) similar to 50-70% of z greater than or similar to 3 SMGs have no radio counterparts (down to an rms of 7-12 mu Jy at 1.4 GHz). Using the exact interferometric positions to identify the multi-wavelength counterparts allows us to determine accurate photometric redshifts for these sources. The redshift distributions of the combined and the individual 1.1 mm and 870 mu m selected samples shows a higher mean and a broader width than those derived in previous studies. This study finds that on average brighter and/or mm-selected SMGs are located at higher redshifts, consistent with previous studies. The mean redshift for the 1.1 mm selected sample ((z) over bar = 3.1 +/- 0.4) is tentatively higher than that for the 870 mu m selected sample ((z) over bar = 2.6 +/- 0.4). Based on our nearly complete sample of AzTEC 1.1 mm SMGs in a 0.15 deg(2) area, we infer a higher surface density of z greater than or similar to 4 SMGs than predicted by current cosmological models. In summary, our findings imply that interferometric identifications at (sub-) millimeter wavelengths are crucial to build statistically complete and unbiased samples of SMGs.