The disk averaged star formation relation for Local Volume dwarf
  galaxies
  Spatially resolved HI studies of dwarf galaxies have provided a wealth of
precision data. However these high-quality, resolved observations are only
possible for handful of dwarf galaxies in the Local Volume. Future HI surveys
are unlikely to improve the current situation. We therefore explore a method
for estimating the surface density of the atomic gas from global HI parameters,
which are conversely widely available. We perform empirical tests using
galaxies with resolved HI maps, and find that our approximation produces values
for the surface density of atomic hydrogen within typically 0.5dex of the true
value. We apply this method to a sample of 147 galaxies drawn from modern
near-infrared stellar photometric surveys. With this sample we confirm a strict
correlation between the atomic gas surface density and the star formation rate
surface density, that is vertically offset from the Kennicutt-Schmidt relation
by a factor of 10-30, and significantly steeper than the classical N=1.4 of
Kennicutt (1998). We further infer the molecular fraction in the sample of low
surface brightness, predominantly dwarf galaxies by assuming that the star
formation relationship with molecular gas observed for spiral galaxies also
holds in these galaxies, finding a molecular-to-atomic gas mass fraction within
the range of 5-15%. Comparison of the data to available models shows that a
model in which the thermal pressure balances the vertical gravitational field
captures better the shape of the $\Sigma_{\rm SFR}-\Sigma_{\rm gas}$
relationship. However, such models fail to reproduce the data completely,
suggesting that thermal pressure plays an important role in the disks of dwarf
galaxies.
