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We present optical photometry of Hubble Space Telescope (HST) ACS/WFC data ofthe resolved stellar populations in the outer disc of the dwarf irregulargalaxy DDO 154. The photometry reveals that young main sequence stars arealmost absent from the outermost HI disc. Instead, most are clustered near themain stellar component of the galaxy. We constrain the stellar initial massfunction (IMF) by comparing the luminosity function of the main sequence starsto simulated stellar populations assuming a constant star formation rate overthe dynamical timescale. The best-fitting IMF is deficient in high mass starscompared to a canonical Kroupa IMF, with a best-fit slope $\alpha = -2.45$ andupper mass limit $M_U = 16\ M_{\odot}$. This top-light IMF is consistent withpredictions of the Integrated Galaxy-wide IMF theory. Combining the HST imageswith HI data from The HI Nearby Galaxy Survey Treasury (THINGS) we determinethe star formation law (SFL) in the outer disc. The fit has a power lawexponent $N = 2.92 \pm0.22$ and zero point $A=4.47 \pm 0.65 \times 10^{-7} \M_{\odot} \ \text{yr}^{-1} \ \text{kpc}^{-2}$. This is depressed compared tothe Kennicutt-Schmidt Star Formation Law, but consistent with weak starformation observed in diffuse HI environments. Extrapolating the SFL over theouter disc implies that there could be significant star formation occurringthat is not detectable in H$\alpha$. Last, we determine the Toomre stabilityparameter $Q$ of the outer disc of DDO 154 using the THINGS HI rotation curveand velocity dispersion map. 72% of the HI in our field has $Q\leq 4$ and thisincorporates 96% of the observed MS stars. Hence 28% of the HI in the field islargely dormant.

Star formation in the outskirts of DDO 154: A top-light IMF in a nearly dormant disc