We present a harmonic expansion of the observed line-of-sight velocity field as a method to recover and investigate spiral structures in the nuclear regions of galaxies .
Application to the emission-line velocity field within the circumnuclear starforming ring of NGC 1097 , obtained with the GMOS-IFU spectrograph , reveals a three -arm spiral in the non-circular motions , which agrees with a two -arm dust spiral in the surface brightness .
This nuclear spiral is consistent with a weak perturbation in the gravitational potential due to a two-arm logarithmic spiral , with a pitch angle of 52 \pm 4 ^ { \circ } derived directly from the harmonic expansion of the velocity field .
Next , we use a simple spiral perturbation model to constrain the fraction of the measured non-circular motions that is due to radial inflow .
We combine the resulting inflow velocity with the gas density in the spiral arms , inferred from emission line ratios , to estimate the mass inflow rate as a function of radius , which reaches about 0.011 M _ { \odot } yr ^ { -1 } at a distance of 70 pc from the center .
This corresponds to a fraction of about 4.2 \times 10 ^ { -3 } of the Eddington mass accretion rate onto the central black hole in NGC 1097 , and is fully consistent with previous mass accretion models fitted to the observed spectral energy distribution in the nucleus of this LINER/Seyfert1 galaxy .
We conclude that the line-of-sight velocity not only can provide a cleaner view of nuclear spirals than the associated dust , but that the presented method also allows the quantitative study of these possibly important links in fueling the centers of galaxies , including providing a handle on the mass inflow rate as a function of radius .