We present a comprehensive study of the Na I $lambda$5890, 5895 (Na I D) resonant lines in the Sloan Digital Sky Survey (SDSS, DR7) spectroscopic sample to look for neutral gas outflows in the local galaxies. Individual galaxy spectra are stacked in bins of M${star}$ and SFR to investigate the dependence of galactic wind occurrence and velocity as a function of the galaxy position in the SFR-$M{star}$ plane. In massive galaxies at the high SFR tail we find evidence of a significant blue-shifted Na I D absorption, which we interpret as evidence of neutral outflowing gas. The occurrence of the blue-shifted absorption is observed at the same significance for purely SF galaxies, AGN and composite systems at fixed SFR. In all classes of objects the blue-shift is the largest and the Na I D equivalent width the smallest for face-on galaxies while the absorption feature is at the systemic velocity for edge-on systems. This indicates that the neutral outflow is mostly perpendicular or biconical with respect to the galactic disk. We also compare the kinematics of the neutral gas with the ionized gas phase as traced by the [OIII]$lambda$5007, H$alpha$, [NII]$lambda6548$ and [NII]$lambda6584$ emission lines. Differently for the neutral gas phase, all the emission lines show evidence of perturbed kinematics only in galaxies with a significant level of nuclear activity and, they are independent from the disk inclination. In conclusion, we find that, in the local Universe, galactic winds show two faces which are related to two different ejection mechanisms, namely the neutral outflowing gas phase related to the SF activity along the galaxy disk and the ionized phase related to the AGN feedback. In both the neutral and ionized gas phases, the observed wind velocities suggest that the outflowing gas remains bound to the galaxy with no definitive effect on the gas reservoir.
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