Abstract
We have developed a novel Markov Chain Monte Carlo chemical 'painting' technique to explore possible radial and vertical metallicity gradients for the thick disc progenitor. In our analysis, we match an N-body simulation to the data from the Apache Point Observatory Galactic Evolution Experiment survey. We assume that the thick disc has a constant scaleheight and has completed its formation at an early epoch, after which time radial mixing of its stars has taken place. Under these assumptions, we find that the initial radial metallicity gradient of the thick disc progenitor should not be negative, but either flat or even positive, to explain the current negative vertical metallicity gradient of the thick disc. Our study suggests that the thick disc was built-up in an inside-out and upside-down fashion, and older, smaller and thicker populations are more metal poor. In this case, star-forming discs at different epochs of the thick disc formation are allowed to have different radial metallicity gradients, including a negative one, which helps to explain a variety of slopes observed in high-redshift disc galaxies. This scenario helps to explain the positive slope of the metallicity-rotation velocity relation observed for the Galactic thick disc. On the other hand, radial mixing flattens the slope of an existing gradient.