  We use a sample of 9397 low z galaxies with a close companion to investigate
the connection between mergers and luminous infra-red (IR) galaxies (LIRGs).
The pairs are selected from the SDSS and have projected separations rp < 80
kpc, relative velocities dv < 300 km/s and stellar mass ratios within a factor
1:10. The IR luminosities (LIR) of galaxies in the pair and (mass, z and
environment-matched) control samples are determined from the SDSS -- IRAS
matched catalog of Hwang et al. (2010). We find a trend for increasing LIRG
fraction towards smaller pair separations, peaking at a factor of ~ 5--10 above
the median control fraction at the smallest separations (rp < 20 kpc), but
remaining elevated by a factor ~ 2--3 even out to 80 kpc (the widest
separations in our sample). We also find that LIRGs are most likely to be found
in high mass galaxies which have an approximately equal mass companion. We
confirm the results of previous studies that both the active galactic nucleus
(AGN) fraction and merger fraction increase strongly as a function of IR
luminosity. About 7% of LIRGs are associated with major mergers, as defined
within the criteria and mass completion of our sample. Finally, we quantify a
SFR offset (Delta SFR) as the enhancement (or decrement) relative to
star-forming galaxies of the same mass and redshift. We demonstrate that there
is a clear connection between the Delta SFR and the classification of a galaxy
as a LIRG that is mass dependent. Most of the LIRGs in our merger sample are
relatively high mass galaxies (log M* > 10.5), likely because the SFR
enhancement required to produce LIRG luminosities is more modest than at low
masses. The Delta SFR offers a redshift-independent metric for the
identification of the galaxies with the most enhanced star forming rates that
does not rely on fixed LIR boundaries.
