We have used the two-year Differential Microwave Radiometer data from the Cosmic Background Explorer (COBE) satellite to systematically search for millimetric (31-90 GHz) emission from the gamma-ray bursts (GRBs) in the Burst and Transient Source Experiment (BATSE) GRB 3B catalog. The large beam size of the COBE instrument (7° FWHM) allows for an efficient search of the large GRB positional error boxes, although it also means that fluxes from (point-source) GRB objects will be somewhat diluted. A likelihood analysis has been used to look for a change in the level of millimetric emission from the locations of 81 GRB events during the first two years (1990 and 1991) of the COBE mission. The likelihood analysis determined that we did not find any significant millimetric signal before or after the occurrence of the GRB. We found 95% confidence level upper limits of 175, 192, and 645 Jy or, in terms of fluxes, of 9.6, 16.3, and 54.8 × 10-13 erg cm-2 s, respectively at 31, 53, and 90 GHz. We also looked separately at three different classes of GRBs, including the top 10 (in peak flux), "short-burst," and "long-burst" subsets and found a similar upper limits for each subset. While these limits may be somewhat higher than one would like, we estimate that using this technique with future missions could push these limits down to ~1 mJy.
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