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

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 HI 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 $M_U=16M_{\odot }$. This top-light IMF is consistent with predictions of the Integrated Galaxy-wide IMF theory. Combining the HST images with HI data from The HI 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_{\odot} \ $\text{yr}$^{-1} \ $\text{kpc}$^{-2}$. This is depressed compared to the Kennicutt-Schmidt Star Formation Law, but consistent with weak star formation observed in diffuse HI environments. Extrapolating the SFL over the outer disc implies that there could be significant star formation occurring that is not detectable in H$\alpha$. Last, we determine the Toomre stability parameter $Q$ of the outer disc of DDO 154 using the THINGS HI rotation curve and velocity dispersion map. 72% of the HI in our field has $Q\le 4$ and this incorporates 96% of the observed MS stars. Hence 28% of the HI in the field is largely dormant.