  We use data for faint (M_B > -14.5) dwarf irregular galaxies drawn from the
FIGGS survey to study the correlation between the atomic gas density
(Sigma_gas,atomic) and star formation rate (Sigma_SFR) in the galaxies. The
estimated gas phase metallicity of our sample galaxies is Z ~ 0.1 Z_sun.
Understanding star formation in such molecule poor gas is of particular
importance since it is likely to be of direct relevance to simulations of early
galaxy formation. For about 20% (9/43) of our sample galaxies, we find that the
HI distribution is significantly disturbed, with little correspondence between
the optical and HI distributions. We exclude these galaxies from the
comparison. We also exclude galaxies with very low star formation rates, for
which stochastic effects make it difficult to estimate the true star formation
rates. For the remaining galaxies we compute the Sigma_gas,atomic and Sigma_SFR
averaged over the entire star forming disk of the galaxy. For these galaxies we
find a nearly linear relation between the star formation rate and the atomic
gas surface densities. The corresponding gas consumption timescale is ~ 10 Gyr,
i.e. significantly smaller than the ~ 100 Gyr estimated for the outer regions
of spiral galaxies. We also estimate the gas consumption timescale computed
using the global gas content and the global star formation rate for all
galaxies with a reliable measurement of the star formation rate, regardless of
whether the HI distribution is disturbed or not. The mean gas consumption
timescale computed using this entire gas reservoir is ~ 18 Gyr, i.e. still
significantly smaller than that estimated for the outer parts of spirals. The
gas consumption timescale for dwarfs is intermediate between the values of ~
100 Gyr and ~ 2 Gyr estimated for the outer molecule poor and inner molecule
rich regions of spiral disks.
