NIHAO XX: The impact of the star formation threshold on the cusp-core
  transformation of cold dark matter haloes
  We use cosmological hydrodynamical galaxy formation simulations from the
NIHAO project to investigate the impact of the threshold for star formation on
the response of the dark matter (DM) halo to baryonic processes. The fiducial
NIHAO threshold, $n=10\, {\rm cm}^{-3}$, results in strong expansion of the DM
halo in galaxies with stellar masses in the range $10^{7.5} < M_{star} <
10^{9.5} M_{\odot}$. We find that lower thresholds such as $n=0.1$ (as employed
by the EAGLE/APOSTLE and Illustris/AURIGA projects) do not result in
significant halo expansion at any mass scale. Halo expansion driven by
supernova feedback requires significant fluctuations in the local gas fraction
on sub-dynamical times (i.e., < 50 Myr at galaxy half-light radii), which are
themselves caused by variability in the star formation rate. At one per cent of
the virial radius, simulations with $n=10$ have gas fractions of $\simeq 0.2$
and variations of $\simeq 0.1$, while $n=0.1$ simulations have order of
magnitude lower gas fractions and hence do not expand the halo. The observed DM
circular velocities of nearby dwarf galaxies are inconsistent with CDM
simulations with $n=0.1$ and $n=1$, but in reasonable agreement with $n=10$.
Star formation rates are more variable for higher $n$, lower galaxy masses, and
when star formation is measured on shorter time scales. For example,
simulations with $n=10$ have up to 0.4 dex higher scatter in specific star
formation rates than simulations with $n=0.1$. Thus observationally
constraining the sub-grid model for star formation, and hence the nature of DM,
should be possible in the near future.
