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Rotational spectroscopy of isotopic vinyl cyanide, H$_2$C=CH$-$C$\equiv$N, in the laboratory and in space

The rotational spectra of singly substituted $^{13}$C and $^{15}$N isotopic species of vinyl cyanide have been studied in natural abundances between 64 and 351 GHz. In combination with previous results, greatly improved spectroscopic parameters have been obtained which in turn helped to identify transitions of the $^{13}$C species for the first time in space through a molecular line survey of the extremely line-rich interstellar source Sagittarius B2(N) in the 3 mm region with some additional observations at 2 mm. The $^{13}$C species are detected in two compact ($\sim 2.3''$), hot (170 K) cores with a column density of $\sim 3.8 \times 10^{16}$ and $1.1 \times 10^{16}$ cm$^{-2}$, respectively. In the main source, the so-called ``Large Molecule Heimat'', we derive an abundance of $2.9 \times 10^{-9}$ for each $^{13}$C species relative to H$_2$. An isotopic ratio $^{12}$C/$^{13}$C of 21 has been measured. Based on a comparison to the column densities measured for the $^{13}$C species of ethyl cyanide also detected in this survey, it is suggested that the two hot cores of Sgr B2(N) are in different evolutionary stages. Supplementary laboratory data for the main isotopic species recorded between 92 and 342 GHz permitted an improvement of its spectroscopic parameters as well.