Context. Wide-field Spitzer surveys allow identification of thousands of potentially high-z submillimeter galaxies (SMGs) through their bright 24m emission and their mid-IR colors. Aims. We want to determine the average properties of such Spitzer-selected SMGs by combining millimeter, radio, and infrared photometry for a representative IR-flux (m) limited sample of SMG candidates. Methods. A complete sample of 33 sources believed to be starbursts (``5.8m-peakers'') was selected in the (0.5deg2) J1046+56 field with selection criteria 400Jy, the presence of a redshifted stellar emission peak at 5.8m, and 23.The field, part of the SWIRE Lockman Hole field, benefits from verydeep VLA/GMRT 20cm, 50cm, and 90cm radio data (all 33sources are detected at 50cm), and deep 160m and 70m Spitzer data. The 33 sources, with photometric redshifts 1.5-2.5, were observed at 1.2mm with IRAM-30m/MAMBO to an rms 0.7-0.8mJy in most cases. Their millimeter, radio, 7-band Spitzer, and near-IR properties were jointly analyzed. Results. The entire sample of 33sources has an average 1.2mm flux density of mJy and a median of 1.61mJy, so the majority of the sources can be considered SMGs. Four sources have confirmed 4detections, and nine were tentatively detected at the 3level. Because of its 24m selection, our sample shows systematically lower flux ratios than classical SMGs, probably because of enhanced PAHemission. A median FIR SED was built by stacking images at thepositions of 21 sources in the region of deepest Spitzer coverage. Its parameters are K, ,and SFR=450yr-1. The FIR-radio correlation provides another estimate of for each source, with an average value of ;however, this value may be overestimated because of some AGN contribution. Most of our targets are also luminous star-forming BzKgalaxies which constitute a significant fraction of weak SMGs at Conclusions. Spitzer 24m-selected starbursts and AGN-dominated ULIRGs can be reliably distinguished using IRAC-24m SEDs. Such ``5.8m-peakers'' with 400Jy have .They are thus ULIRGs, and the majority may be considered SMGs. However, they have systematically lower 1.2mm/24mflux density ratios than classical SMGs, warmer dust, comparable orlower IR/mm luminosities, and higher stellar masses. About 2000-3000``5.8m-peakers'' may be easily identifiable within SWIRE catalogues over 49deg2. Key words: galaxies: high-redshift - galaxies: starburst - galaxies: active - infrared: galaxies - submillimeter - radio continuum: galaxies
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