  We use cosmological, chemo-dynamical, smoothed particle hydrodynamical
simulations of Milky-Way-analogue galaxies to find the expected present-day
distributions of both metal-free stars that formed from primordial gas and the
oldest star populations. We find that metal-free stars continue to form until
z~4 in halos that are chemically isolated and located far away from the biggest
progenitor of the final system. As a result, if the Population III initial mass
function allows stars with low enough mass to survive until z=0 (< 0.8 Msol),
they would be distributed throughout the Galactic halo. On the other hand, the
oldest stars form in halos that collapsed close to the highest density peak of
the final system, and at z=0 they are located preferentially in the central
region of the Galaxy, i.e., in the bulge. According to our models, these trends
are not sensitive to the merger histories of the disk galaxies or the
implementation of supernova feedback. Furthermore, these full hydrodynamics
results are consistent with our N-body results in Paper I, and lend further
weight to the conclusion that surveys of low-metallicity stars in the Galactic
halo can be used to directly constrain the properties of primordial stars. In
particular, they suggest that the current lack of detections of metal-free
stars implies that their lifetimes were shorter than a Hubble time, placing
constraints on the metal-free initial mass function.
