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We have surveyed molecular line emission from Sgr B2 over the range from 330 to 355 GHz at the position designated Sgr B2(M). This position is prominent in millimeter continuum maps of the region and is associated with a compact H II region, a hot NH_3 core, and sources of H_2O and OH maser emission. We have also obtained observations contrasting the submillimeter molecular emission from Sgr B2(M) and Sgr B2(N), an additional center of activity thought to be a dense protostellar core. The picture of the interstellar chemistry of these regions which we derive is substantially different from that determined from previous observations at lower frequencies and with lower spatial resolution. In particular, molecules such as SO_2 and CH_3OH dominate the submillimeter spectrum to a much greater extent than they do the low-frequency observations. Much of this difference is due to the higher spatial resolution of the submillimeter observations, which makes them much more sensitive to emission from compact, dense cores. The millimeter data were most effective at sampling material in the surrounding lower density regions. The chemistry of the core sources in Sgr B2 appears similar to that of other dense cores, such as the core of the Orion molecular cloud. The spectral differences between Sgr B2(M) and Sgr B2(N) primarily relate to differences in excitation and column density. For most molecular species the northern source (N) has a column density significantly higher than that found in the middle source (M), often by a factor of about 5. The principal exceptions are the species SO and SO_2 which seem to be substantially more abundant in the middle source. Generally excitation seems to be higher in the northern source, suggesting a somewhat higher density core, although there are some departures indicating that the excitation situation is more complicated. High optical depths in many of the submillimeter transitions systematically bias the interpretation of both column densities and excitation. Many of the millimeter lines may also have high optical depths, particularly those lines arising from the compact core sources.

Molecular line survey of Sagittarius B2(M) from 330 to 355 GHz and comparison with Sagittarius B2(N)