  We investigate the two-dimensional kpc-scale structure of the extinction in a
representative sample of local ULIRGs using the Halpha/Hbeta line ratio.We use
optical integral field spectroscopy obtained with the INTEGRAL instrument at
the William Herschel Telescope. Complementary optical and near-IR high angular
resolution HST images have also been used. The extinction exhibits a very
complex and patchy structure in ULIRGs on kpc scales, from basically
transparent regions to others deeply embedded in dust (Av~0.0 to Av~8.0 mag).
Nuclear extinction covers a broad range in Av from 0.6 to 6 mag, 69% of the
nuclei having Av>2.0 mag. Extinction in the external regions is substantially
lower than in the nuclei with 64% of the ULIRGs in the sample having median Av
of less than 2 mag for the entire galaxy. While post-coalescence nuclei tend to
cluster around Av values of 2 to 3 mag, pre-coalescence nuclei appear more
homogeneously distributed over the entire 0.4 mag <Av< 7.7 mag range. For the
average extinction (Av~2.0 derived for the ULIRGs of the sample, the ratio of
the de-reddened to observed SFR values is 6. The extinction-corrected,
Halpha-based SFR ranges from 10 to 300 Msun/yr. For only 28% of the cases the
de-reddened SFR is <20 Msun/yr, whereas for the observed SFR this percentage
increases to 72%. The IR-based SFR is always higher than the optical-based one,
with differences ranging from about 2 to up to 30. The nuclear observed SFR has
an average contribution to the total one of 16% for the entire sample. Once
corrected for extinction, the average value becomes 31%. Because of mostly
extinction effects, the optical (I-band) half-light radius in the sample
galaxies is on average a factor 2.3 larger than the corresponding near-IR
(H-band) value.
