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We have used the IRAM 30-m telescope and the Plateau de Bure Interferometer (PdBI), to map the star--forming regions surrounding the two ultracompact H{sc ii} regions G10.47+0.03 and G31.41+0.31. The $J$=6--5, $J$=8--7, and $J$=12--11 rotational transitions of methyl cyanide (CH$_3$CN), its isotopomer $^{13}$CH$_3$CN, and of vibrationally excited $v_8$=1 CH$_3$CN, were observed with the 30-m. With the PdBI, we produced maps of CH$_3$CN(6--5), CH$_3^{13}$CN(6--5), vibrationally excited $v_8$=1 CH$_3$CN(6--5), and of the 3~mm continuum emission.
Temperatures and column densities for the two sources were determined from the 30-m data, on the basis of the intensities of the optically thin lines, as well as employing the optically thick lines. From the single--dish data we also infer the existence of an extended envelope ($\ge 10''$), not detectable with the interferometer, and the velocity shift in G31.41+0.31 (see below) is detected. Our data suggest that in this source there are $\simeq 2200$ solar masses within a radius $<0.1$~pc. An abundance ratio [CH$_3$CN]/[NH$_3$] of order of $2\,10^{-3}$ is also found in both objects.
From the PdBI data, and in the case of G31.41+0.31, the core angular diameter as measured in both methyl cyanide and the 3~mm continuum is $\simeq 1''$, corresponding to $\simeq 0.04$~pc. G10.47+0.03 is basically unresolved in our maps. Velocity gradients are found in both sources, the most evident beeing in G31.41+0.31, where we observe $\sim 400$~km~s$^{-1}$\,$pc$^{-1}$ in the SW--NE direction. Therefore, these hot--cores are sites of high velocity motions. We also discuss the 3~mm continuum emission, which is likely to come mostly from heated dust in the case of G31.41+0.31, whereas in G10.47+0.03 contributions from both free--free and dust emission are likely to be observed. We discuss possible scenarios for these two sources.
