We analyse the excitation of 114 rotational transitions of vinyl cyanide (a
crylonitrile), C2H3CN, in its upsilon(11) and upsilon(15) vibrational state
s, together with 98 transitions in the ground state. The data were taken fr
om the SEST line survey of Sgr B2(N) in the 1.3 mm band. For the lines with
energies above 200 K a rotational temperature of 440(-90)(+190) K, a C2H3C
N column density of 5.1(-2.5)(+7.2) x 10(18) cm(-2), and a source size in t
he range 0.025-0.037 pc are most consistent with observations. The resultin
g abundance of C2H3CN is about 6 x 10(-8). We argue that the high rotation
temperature of the high-energy lines is most likely due to direct radiative
excitation through far-infrared emission from hot dust. A Monte-Carlo anal
ysis was applied to the radiative transfer of the lines with upper-state en
ergies below 200 K. A good fit to the intensities of the a-type lines is ac
hieved by a model cloud with a fractional C2H3CN abundance of 4 x 10(-10).
By increasing the abundance to 6 x 10(-9) in the outer portion of the cloud
also the intensities of the b-type lines could be reasonably well fitted.
This model is, however, inconsistent with the low intensities of low-energy
a-type lines observed at longer wavelengths. Hence, we favour a constant C
2H3CN abundance of 4 x 10(-10) in the part of the cloud where the kinetic t
emperature is below 180 K, and regard the excitation of the intrinsically w
eak b-type lines as anomalous.