We study the interstellar Na I $\lambda \lambda 5890, 5895$ (Na D) absorption-line doublet in a nearly-complete sample of $\sim$9900 nearby Seyfert 2 galaxies, in order to quantify the significance of optical AGN activity in driving kpc-scale outflows that can quench star formation. Comparison to a carefully matched sample of $\sim$44,000 control objects indicates that the Seyfert and control population have similar Na D detection rates ($\sim 5-6%$). Only 53 Seyferts (or 0.5% of the population) are found to potentially display galactic-scale winds, compared to 0.8% of the control galaxies. While nearly a third of the Na D outflows observed in our Seyfert 2 galaxies occur around the brightest AGN, both radio and infrared data indicate that star formation could play the dominant role in driving cold-gas outflows in an even higher fraction of the Na D-outflowing Seyfert 2s. Our results indicate that galactic-scale outflows at low redshift are no more frequent in Seyferts than they are in their non-active counterparts, that optical AGN are not significant contributors to the quenching of star formation in the nearby Universe, and that star-formation may actually be the principal driver of outflows even in systems that do host an AGN.
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