SH$\alpha$DE: Survey description and mass-kinematics scaling relations
  for dwarf galaxies
  The Study of H$\alpha$ from Dwarf Emissions (SH$\alpha$DE) is a high spectral
resolution (R=13500) H$\alpha$ integral field survey of 69 dwarf galaxies with
stellar masses $10^6<M_\star<10^9 \,\rm{M_\odot}$. The survey used FLAMES on
the ESO Very Large Telescope. SH$\alpha$DE is designed to study the kinematics
and stellar populations of dwarf galaxies using consistent methods applied to
massive galaxies and at matching level of detail, connecting these mass ranges
in an unbiased way. In this paper we set out the science goals of SH$\alpha$DE,
describe the sample properties, outline the data reduction and analysis
processes. We investigate the $\log{M_{\star}}-\log{S_{0.5}}$ mass-kinematics
scaling relation, which have previously shown potential for combining galaxies
of all morphologies in a single scaling relation. We extend the scaling
relation from massive galaxies to dwarf galaxies, demonstrating this relation
is linear down to a stellar mass of $M_{\star}\sim10^{8.6}\,\rm{M_\odot}$.
Below this limit, the kinematics of galaxies inside one effective radius appear
to be dominated by the internal velocity dispersion limit of the
H$\alpha$-emitting gas, giving a bend in the $\log{M_{\star}}-\log{S_{0.5}}$
relation. Replacing stellar mass with total baryonic mass using gas mass
estimate reduces the severity but does not remove the linearity limit of the
scaling relation. An extrapolation to estimate the galaxies' dark matter halo
masses, yields a $\log{M_{h}}-\log{S_{0.5}}$ scaling relation that is free of
any bend, has reduced curvature over the whole mass range, and brings galaxies
of all masses and morphologies onto the virial relation.
