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 $M_U = 16\ M_{\odot}$. 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 $N = 2.92 \pm0.22$ and zero point $A=4.47 \pm 0.65 \times 10^{-7} \
M_{\odot} \ \text{yr}^{-1} \ \text{kpc}^{-2}$. This is depressed compared 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 $Q\leq 4$ and this
incorporates 96% of the observed MS stars. Hence 28% of the HI in the field is
largely dormant.
