  Feedback from supernovae is essential to understanding the self-regulation of
star formation in galaxies. However, the efficacy of the process in a
cosmological context remains unclear due to excessive radiative losses during
the shock propagation. To better understand the impact of SN explosions on the
evolution of galaxies, we perform a suite of high-resolution (12 pc), zoom-in
cosmological simulations of a Milky Way-like galaxy at z=3 with adaptive mesh
refinement. We find that SN explosions can efficiently regulate star formation,
leading to the stellar mass and metallicity consistent with the observed
mass-metallicity relation and stellar mass-halo mass relation at z~3. This is
achieved by making three important changes to the classical feedback scheme: i)
the different phases of SN blast waves are modelled directly by injecting
radial momentum expected at each stage, ii) the realistic time delay of SNe,
commencing at as early as 3 Myr, is required to disperse very dense gas before
a runaway collapse sets in at the galaxy centre via mergers of gas clumps, and
iii) a non-uniform density distribution of the ISM is taken into account below
the computational grid scale for the cell in which SN explodes. The last
condition is motivated by the fact that our simulations still do not resolve
the detailed structure of a turbulent ISM in which the fast outflows can
propagate along low-density channels. The simulated galaxy with the SN feedback
model shows strong outflows, which carry approximately ten times larger mass
than star formation rate, as well as smoothly rising circular velocity. Other
feedback models that do not meet the three conditions form too many stars,
producing a peaked rotation curve. Our results suggest that understanding the
structure of the turbulent ISM may be crucial to assess the role of SN and
other feedback processes in galaxy formation theory.
