Previous studies have found that the Galactic rotation velocity-metallicity (V-[Fe/H]) relations for the thin and thick disk populations show negative and positive slopes, respectively. The first Gaia Data Release includes the Tycho-Gaia Astrometric Solution (TGAS) information, which we use to analyze the V-[Fe/H] relation for a strictly selected sample with high enough astrometric accuracy. We aim to arrive at an explanation for the slopes of the V-[Fe/H] relationship. We measure the V-[Fe/H] relation for thin and thick disk stars classified on the basis of their [$alpha$/Fe] and [Fe/H] abundances. We find dV/d[Fe/H]= -18 +/- 2 km/s/dex for stars in the thin disk and dV/d[Fe/H]= +23 +/- 10 km/s/dex for thick disk stars, so we confirm the different signs for the slopes. The negative value of dV/d[Fe/H] for thick disk stars is consistent with previous studies, but the combination of TGAS and APOGEE data provide higher precision, even though systematic errors could exceed +/-5 km/s/dex . Our average measurement of dV/d[Fe/H] for local thick disk stars shows a somewhat flatter slope than the previous studies, but we confirm a significant spread and a dependence of the slope on the [alpha/Fe] ratio of the stars. Using a simple N-body model, we demonstrate that the observed trend for the thick and thin disk can be explained by the observed radial metallicity gradients and the correlation between orbital eccentricity and metallicity in the thick disk.
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