Integral Field Spectroscopy based H\alpha\ sizes of local Luminous and
  Ultraluminous Infrared Galaxies. A Direct Comparison with high-z Massive Star
  Forming Galaxies
  Aims. We study the analogy between local U/LIRGs and high-z massive SFGs by
comparing basic H{\alpha} structural characteristics, such as size, and
luminosity (and SFR) surface density, in an homogeneous way (i.e. same tracer
and size definition, similar physical scales). Methods. We use Integral Field
Spectroscopy based H{\alpha} emission maps for a representative sample of 54
local U/LIRGs (66 galaxies). From this initial sample we select 26 objects with
H{\alpha} luminosities (L(H{\alpha})) similar to those of massive (i.e. M\ast
\sim 10^10 M\odot or larger) SFGs at z \sim 2, and observed on similar physical
scales. Results. The sizes of the H{\alpha} emitting region in the sample of
local U/LIRGs span a large range, with r1/2(H{\alpha}) from 0.2 to 7 kpc.
However, about 2/3 of local U/LIRGs with Lir > 10^11.4 L\odot have compact
H{\alpha} emission (i.e. r1/2 < 2 kpc). The comparison sample of local U/LIRGs
also shows a higher fraction (59%) of objects with compact H{\alpha} emission
than the high-z sample (25%). This gives further support to the idea that for
this luminosity range the size of the star forming region is a distinctive
factor between local and distant galaxies of similar SF rates. However, when
using H{\alpha} as a tracer for both local and high-z samples, the differences
are smaller than the ones recently reported using a variety of other tracers.
Despite of the higher fraction of galaxies with compact H{\alpha} emission, a
sizable group (\sim 1/3) of local U/LIRGs are large (i.e. r1/2 > 2 kpc). These
are systems showing pre-coalescence merger activity and they are
indistinguishable from the massive high-z SFGs galaxies in terms of their
H{\alpha} sizes, and luminosity and SFR surface densities.
