Metallicity Gradient of the Thick Disc Progenitor at High Redshift
  We have developed a novel Markov Chain Mote Carlo (MCMC) 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 (APOGEE)
survey. We assume that the thick disc has a constant scale-height 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.
