The properties of molecular gas, the fuel that forms stars, inside the cavity
of the circumnuclear disk (CND) are not well constrained. We present results of
a velocity-resolved submillimeter scan (~480 to 1250 GHz}) and [CII]158um line
observations carried out with Herschel/HIFI toward Sgr A*; these results are
complemented by a ~2'x2' CO (J=3-2) map taken with the IRAM 30 m telescope at
~7'' resolution. We report the presence of high positive-velocity emission (up
to about +300 km/s) detected in the wings of CO J=5-4 to 10-9 lines. This wing
component is also seen in H2O (1_{1,0}-1_{0,1}) a tracer of hot molecular gas;
in [CII]158um, an unambiguous tracer of UV radiation; but not in [CI]492,806
GHz. This first measurement of the high-velocity CO rotational ladder toward
Sgr A* adds more evidence that hot molecular gas exists inside the cavity of
the CND, relatively close to the supermassive black hole (< 1 pc). Observed by
ALMA, this velocity range appears as a collection of CO (J=3-2) cloudlets lying
in a very harsh environment that is pervaded by intense UV radiation fields,
shocks, and affected by strong gravitational shears. We constrain the physical
conditions of the high positive-velocity CO gas component by comparing with
non-LTE excitation and radiative transfer models. We infer T_k~400 K to 2000 K
for n_H~(0.2-1.0)x10^5 cm^-3. These results point toward the important role of
stellar UV radiation, but we show that radiative heating alone cannot explain
the excitation of this ~10-60 M_Sun component of hot molecular gas inside the
central cavity. Instead, strongly irradiated shocks are promising candidates.Comment: Accepted for publication in A&A Letters ( this v2 includes
corrections by language editor