We present optical photometry of Hubble Space Telescope ( HST ) ACS/WFC data of the resolved stellar populations in the outer disc of the dwarf irregular galaxy DDO 154 .
The photometry reveals that young main sequence stars are almost absent from the outermost H i disc .
Instead , most are clustered near the main stellar component of the galaxy .
We constrain the stellar initial mass function ( IMF ) by comparing the luminosity function of the main sequence stars to simulated stellar populations assuming a constant star formation rate over the dynamical timescale .
The best-fitting IMF is deficient in high mass stars compared to a canonical Kroupa IMF , with a best-fit slope \alpha = -2.45 and upper mass limit M _ { U } = 16 M _ { \sun } .
This top-light IMF is consistent with predictions of the Integrated Galaxy-wide IMF theory .
Combining the HST images with H i data from The H i Nearby Galaxy Survey Treasury ( THINGS ) we determine the star formation law ( SFL ) in the outer disc .
The fit has a power law exponent N = 2.92 \pm 0.22 and zero point A = 4.47 \pm 0.65 \times 10 ^ { -7 } M _ { \sun } \text { yr } ^ { -1 } \text { kpc } ^ { -2 } .
This is depressed compared to the Kennicutt-Schmidt Star Formation Law , but consistent with weak star formation observed in diffuse H i environments .
Extrapolating the SFL over the outer disc implies that there could be significant star formation occurring that is not detectable in H \alpha .
Last , we determine the Toomre stability parameter Q of the outer disc of DDO 154 using the THINGS H i rotation curve and velocity dispersion map .
72 % of the H i in our field has Q \leq 4 and this incorporates 96 % of the observed MS stars .
Hence 28 % of the H i in the field is largely dormant .