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 \sim 0.1 Z _ { \odot } .
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 , viz . { \log \Sigma _ { SFR } = 0.91 ^ { +0.23 } _ { -0.25 } \log \Sigma _ { gas,atomic } -3.84 ^ { +0.15 } _ % { -0.19 } } .
The corresponding gas consumption timescale is \sim 10 Gyr , i.e .
significantly smaller than the \sim 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 \sim 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 \sim 100 Gyr and \sim 2 Gyr estimated for the outer molecule poor and inner molecule rich regions of spiral disks .