By means of high-resolution cosmological hydrodynamical simulations of Milky
Way-like disc galaxies, we conduct an analysis of the associated stellar
metallicity distribution functions (MDFs). After undertaking a kinematic
decomposition of each simulation into spheroid and disc sub-components, we
compare the predicted MDFs to those observed in the solar neighbourhood and the
Galactic bulge. The effects of the star formation density threshold are visible
in the star formation histories, which show a modulation in their behaviour
driven by the threshold. The derived MDFs show median metallicities lower by
0.2-0.3 dex than the MDF observed locally in the disc and in the Galactic
bulge. Possible reasons for this apparent discrepancy include the use of low
stellar yields and/or centrally-concentrated star formation. The dispersions
are larger than the one of the observed MDF; this could be due to simulated
discs being kinematically hotter relative to the Milky Way. The fraction of low
metallicity stars is largely overestimated, visible from the more negatively
skewed MDF with respect to the observational sample. For our fiducial Milky Way
analog, we study the metallicity distribution of the stars born "in situ"
relative to those formed via accretion (from disrupted satellites), and
demonstrate that this low-metallicity tail to the MDF is populated primarily by
accreted stars. Enhanced supernova and stellar radiation energy feedback to the
surrounding interstellar media of these pre-disrupted satellites is suggested
as an important regulator of the MDF skewness.Comment: 20 pages, 14 figures, MNRAS, accepte