We present CO(1-0) and CO(2-1) observations of the SA(rs)bc Seyfert 2 galaxy NGC 3147, obtained with the IRAM interferometer at 1farcs9 $times$1farcs6 and 1farcs6 $times$1farcs4 resolutions, respectively. A central peak seen mainly in CO(2-1) and a ring-like structure at $r simeq 10$arcsec $sim$2 kpc dominate the CO maps. In CO(1-0) an outer spiral at $r simeq 20$arcsec $sim$4 kpc is also detected, not visible in CO(2-1) emission because it falls outside the field-of-view of the primary beam. The kinematics of the molecular structures are quite regular, although there is evidence for local non-circular or streaming motions. We show that the molecular gas distribution is similar but not exactly identical to those of star formation tracers. Using a NIR image obtained with adaptive optics at the CFHT Telescope, we identify a weak bar in NGC 3147, which is classified as non-barred galaxy in the optical. We then compute the gravity torques exerted by this stellar bar on the gas. We find that the gas inside the inner CO ring is subject to a net negative torque and loses angular momentum. This is expected for gas at the UHR, just inside the corotation resonance of the stellar bar. In contrast, the gas outside corotation, in the spiral arms comprising the outer spiral structure, suffers positive torques and is driven outwards. We conclude that some molecular gas is presently flowing into the central region, since we find negative torques down to the resolution limit of our images.
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