The observed radial and vertical metallicity distribution of old stars in the Milky Way disk provides a powerful constraint on the chemical enrichment and dynamical history of the disk .
We present the radial metallicity gradient , \Delta { [ Fe / H ] } / \Delta R , as a function of height above the plane , |Z| , using 7010 main sequence turnoff stars observed by the Sloan Extension for Galactic Understanding and Exploration ( SEGUE ) survey .
The sample consists of mostly old thin and thick disk stars , with a minimal contribution from the stellar halo , in the region 6 < R < 16 kpc , 0.15 < |Z| < 1.5 kpc .
The data reveal that the radial metallicity gradient becomes flat at heights |Z| > 1 kpc .
The median metallicity at large |Z| is consistent with the metallicities seen in outer disk open clusters , which exhibit a flat radial gradient at [ Fe/H ] \sim - 0.5 .
We note that the outer disk clusters are also located at large |Z| ; because the flat gradient extends to small R for our sample , there is some ambiguity in whether the observed trends for clusters are due to a change in R or |Z| .
We therefore stress the importance of considering both the radial and vertical directions when measuring spatial abundance trends in the disk .
The flattening of the gradient at high |Z| also has implications on thick disk formation scenarios , which predict different metallicity patterns in the thick disk .
A flat gradient , such as we observe , is predicted by a turbulent disk at high redshift , but may also be consistent with radial migration , as long as mixing is strong .
We test our analysis methods using a mock catalog based on the model of Schönrich & Binney , and we estimate our distance errors to be \sim 25 \% .
We also show that we can properly correct for selection biases by assigning weights to our targets .