  (Abridged) We combine data from The HI Nearby Galaxy Survey and the GALEX
Nearby Galaxy Survey to study the relationship between atomic hydrogen (HI) and
far-ultraviolet (FUV) emission outside the optical radius (r25) in 17 spiral
and 5 dwarf galaxies. In this regime, HI is likely to represent most of the ISM
and FUV emission to trace recent star formation with little bias due to
extinction, so that the two quantities closely trace the underlying
relationship between gas and star formation rate (SFR). The azimuthally
averaged HI and FUV intensities both decline with increasing radius in this
regime, with the scale length of the FUV profile typically half that of the HI
profile. Despite the mismatch in profiles, there is a significant spatial
correlation (at 15" resolution) between local FUV and HI intensities; near r25
this correlation is quite strong, in fact stronger than anywhere inside r25,
and shows a decline towards larger radii. The star formation efficiency (SFE) -
defined as the ratio of FUV/HI and thus the inverse of the gas depletion time -
decreases with galactocentric radius across the outer disks, though much
shallower than across the optical disks. On average, we find the gas depletion
times to be well above a Hubble time (~10^11 yr). We observe a clear
relationship between FUV/HI and HI column in the outer disks, with the SFE
increasing with increasing HI column. Despite observing systematic variations
in FUV/HI, we find no clear evidence for step-function type star formation
thresholds. When compared with results from inside r25, we find outer disk star
formation to be distinct in several ways: it is extremely inefficient
(depletion times of many Hubble times) with column densities and SFRs lower
than found anywhere inside the optical disks. It appears that the HI column is
one of, perhaps even the key environmental factor in setting the SFR in outer
galaxy disks.
