We create a complete gravity torque map of the disk of the LINER/Seyfert 1.9 galaxy NGC4579. We quantify the efficiency of angular momentum transport and search for signatures of secular evolution in the fueling process from r~15kpc down to the inner r~50pc around the Active Galactic Nucleus (AGN). We use both the 1-0 and 2-1 line maps of CO obtained with the Plateau de Bure Interferometer (PdBI) as part of the NUclei of Galaxies-(NUGA)-project. We derive the stellar potential from a NIR (K band) wide field image of the galaxy. The K-band image, which reveals a stellar bar, together with a high resolution HI map of NGC4579 obtained with the Very Large Array (VLA), allow us to extend the gravity torque analysis to the outer disk. The bulk of the gas response traced by the CO PdBI maps follows the expected gas flow pattern induced by the bar potential in the presence of two Inner Lindblad Resonances (ILR). We also detect an oval distortion in the inner r~200pc of the K-band image. The oval is not aligned with the large-scale bar, a signature of dynamical decoupling. The morphology of the outer disk suggests that the neutral gas is currently piling up in a pseudo-ring formed by two winding spiral arms that are morphologically decoupled from the bar structure. In the outer disk, the decoupling of the spiral allows the gas to efficiently produce net gas inflow on intermediate scales. The corotation barrier seems to be overcome due to secular evolution processes. The gas in the inner disk is efficiently funneled by gravity torques down to r~300pc. Closer to the AGN, the two m=2 modes (bar and oval) act in concert to produce net gas inflow down to r~50pc, providing a clear smoking gun evidence of fueling with associated short dynamical time-scales.
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