Dwarf Galaxies in CDM, WDM, and SIDM: Disentangling Baryons and Dark
  Matter Physics
  We present a suite of FIRE-2 cosmological zoom-in simulations of isolated
field dwarf galaxies, all with masses of $M_\mathrm{halo} \approx
10^{10}\,$M$_\odot$ at $z=0$, across a range of dark matter models. For the
first time, we compare how both self-interacting dark matter (SIDM) and/or warm
dark matter (WDM) models affect the assembly histories as well as the central
density structure in fully hydrodynamical simulations of dwarfs. Dwarfs with
smaller stellar half-mass radii (r$_{1/2}<500$ pc) have lower
$\sigma_\star/V_\mathrm{max}$ ratios, reinforcing the idea that smaller dwarfs
may reside in halos that are more massive than is naively expected. The
majority of dwarfs simulated with self-interactions actually experience
contraction of their inner density profiles with the addition of baryons
relative to the cores produced in dark-matter-only runs, though the simulated
dwarfs are always less centrally dense than in $\Lambda$CDM. The
V$_{1/2}-$r$_{1/2}$ relation across all simulations is generally consistent
with observations of Local Field dwarfs, though compact objects such as Tucana
provide a unique challenge. Spatially-resolved rotation curves in the central
regions ($<400$ pc) of small dwarfs could provide a way to distinguish between
CDM, WDM, and SIDM, however: at the masses probed in this simulation suite,
cored density profiles in dwarfs with small r$_{1/2}$ values can only originate
from dark matter self-interactions.
