The distribution of star formation in galactic bars as seen with
  H$\alpha$ and stacked GALEX UV imaging
  We investigate the spatial distribution of star formation (SF) within bars of
nearby disk galaxies (inclination $< 65^{\circ}$) from the S$^4$G survey. We
use archival GALEX far- and near-UV imaging for 772 barred galaxies. We also
assemble a compilation of continuum-subtracted H$\alpha$ images for 433 barred
galaxies, of which 70 are produced by ourselves from ancillary photometry and
MUSE/CALIFA IFU data cubes. We employ two complementary approaches: i) the
analysis of bar/disk stacks built from co-added UV images of hundreds of
galaxies; and ii) the classification of the morphology of ionised regions in
galaxies into three main SF classes: A) only circumnuclear SF, B) SF at the bar
ends, but not along the bar, and C) SF along the bar. Lenticular galaxies
typically belong to SF class A: this is probably related to bar-induced SF
quenching. The distribution of SF class B peaks for early- and
intermediate-type spirals: this most likely results from the interplay of gas
flow, shocks, and enhanced shear in centrally concentrated galaxies with large
bar amplitudes. Late-type galaxies are mainly assigned to SF class C: we argue
that this is a consequence of low shear. In bar stacks of spirals, the UV
emission traces the stellar bars and dominates on their leading side, as
witnessed in simulations. For early-types, the central UV emission is $\sim$0.5
mag brighter in strongly barred galaxies, relative to their weakly barred
counterparts: this is related to the efficiency of strong bars sweeping the
disk gas and triggering central starbursts. We also show that the distributions
of SF in inner ringed galaxies are broadly the same in barred and non-barred
galaxies, including a UV/H$\alpha$ deficit in the middle part of the bar: this
hints at the effect of resonance rings trapping gas. Distinct distributions of
SF within bars are reported in galaxies of different morphological types
(Abridged).
