We present single dish and interferometric maps of several rotational trans
itions of HC3N vibrationally excited levels towards Sgr B2. HC3N is a very
suitable molecule to probe hot and dense regions (hot cores) affected by hi
gh extinction since its vibrational levels are mainly excited by mid-IR rad
iation. The single dish maps show, for the first time, that the HC3N vibrat
ionally excited emission (HC3N*) is not restricted to Sgr B2M and N but ext
ended over an area 40 " x 20 " in extent. We distinguish four bright clumps
(Sgr B2R1 to B2R4) in the ridge connecting the main cores Sgr B2M and Sgr
B2N, and a low brightness extended region to the west of the ridge (Sgr B2W
). The physical properties and the kinematics of all hot cores have been de
rived from the HC3N* lines. Our high angular resolution images show that th
e Sgr B2N hot core breaks in two different hot cores, Sgr B2N1 and N2, with
different radial velocities and separated by similar to 2 " in declination
. We find that the excitation of the HC3N* emission in all hot cores can be
represented by a single temperature and that the linewidth of the HC3N* ro
tational lines arising from different vibrational levels systematically dec
reases as the energy of the vibrational level increases. The systematic tre
nd in the linewidth is likely related to the increase of the velocity as th
e distance to the exciting source increases. We have developed a simple mod
el to study the excitation of the HC3N vibrational levels by IR radiation.
We find that the single excitation temperature can be explained by high lum
inosities of embedded stars (similar to 10(7) L-circle dot) and small sourc
e sizes (similar to 2 - 3 "). The estimated clump masses are 500 M-circle d
ot for Sgr B2M, 800 M-circle dot for Sgr B2N and 10-30 M-circle dot for Sgr
B2R1 to B2R4. Luminosities are 1 - 2 10(6) L-circle dot for Sgr B2R1-B2R4
and Sgr B2M and 10(7) L-circle dot for Sgr B2N. We estimate HC3N abundances
of 5 10(-9) for Sgr B2M and Sgr B2N2 and 10(-7) for the rest of the hot co
res. The different HC3N abundances in the hot cores reflect different stage
s of evolution due to time dependent chemistry and/or photo-dissociation by
UV radiation from nearby HII regions. According to the mass and the lumino
sity of the different hot cores, we propose that Sgr B2M and B2N contain a
cluster of 20-30 hot cores, each like that in Orion A, a number similar to
the UC HII regions already detected in the region. The Sgr B2R1-B2R4 hot co
res represent isolated formation of massive stars.