We present an analysis of the morphological classification of 89 luminous
infrared galaxies (LIRGs) from the Great Observatories All-sky LIRG Survey
(GOALS) sample using non-parametric coefficients and compare their morphology
as a function of wavelength. We rely on images obtained in the optical (B- and
I-band) as well as in the infrared (H-band and 5.8μm). Our classification
is based on the calculation of Gini and the second order of light (M20)
non-parametric coefficients which we explore as a function of stellar mass
(M⋆), infrared luminosity (LIR) and star formation rate (SFR). We
investigate the relation between M20, the specific SFR (sSFR) and the dust
temperature (Tdust) in our galaxy sample. We find that M20 is a
better morphological tracer than Gini, as it allows to distinguish systems
formed by double systems from isolated and post-merger LIRGs. The
multi-wavelength analysis allows us to identify a region in the Gini-M20
parameter space where ongoing mergers reside, regardless of the band used to
calculate the coefficients. In particular when measured in the H-band, this
region can be used to identify ongoing mergers, with a minimal contamination
from LIRGs in other stages. We also find that while the sSFR is positively
correlated with M20 when measured in the mid-infrared, i.e. star-bursting
galaxies show more compact emission, it is anti-correlated with the B-band
based M20. We interpret this as the spatial decoupling between obscured
and un-obscured star formation, whereby the ultraviolet/optical size of a LIRGs
experience an intense dust enshrouded central starburst is larger than in the
one in the mid-infrared since the contrast between the nuclear to the extended
disk emission is smaller in the mid-infrared. This has important implications
for high redshift surveys of dusty sources. [abridged]Comment: ( 18 pages, 12 figures, Accepted for publication in A&A