We have mapped the central region of the Seyfert 1 galaxy NGC 1097 in
12CO(J=2-1) with the Submillieter Array (SMA). The 12CO(J=2-1) map shows a
central concentration and a surrounding ring, which coincide respectively with
the Seyfert nucleus and a starburst ring. The line intensity peaks at the
nucleus, whereas in a previously published 12CO(J=1-0) map the intensity peaks
at the starburst ring. The molecular ring has an azimuthally averaged
12CO(J=2-1)/(J=1-0) intensity ratio (R21) of about unity, which is similar to
those in nearby active star forming galaxies, suggesting that most of the
molecular mass in the ring is involved in fueling the starburst. The molecular
gas can last for only about 1.2\times10^8 years without further replenishment
assuming a constant star formation rate and a perfect conversion of gas to
stars. The velocity map shows that the central molecular gas is rotating with
the molecular ring in the same direction, while its velocity gradient is much
steeper than that of the ring. This velocity gradient of the central gas is
similar to what is usually observed in some Seyfert 2 galaxies. To view the
active nucleus directly in the optical, the central molecular gas structure can
either be a low-inclined disk or torus but not too low to be less massive than
the mass of the host galaxy itself, be a highly-inclined thin disk or clumpy
and thick torus, or be an inner part of the galactic disk. The R21 value of
~1.9 of the central molecular gas component, which is significantly higher than
the value found at the molecular gas ring, indicates that the activity of the
Seyfert nucleus may have a significant influence on the conditions of the
molecular gas in the central component.Comment: 22 pages, 4 figures, accepted by Ap