  Nuclear stellar cusps are defined as central excess light component in the
stellar light profiles of galaxies and are suggested to be stellar relics of
intense compact starbursts in the central ~100-500 pc region of gas-rich major
mergers. Here we probe the build-up of nuclear cusps during the actual
starburst phase for a complete sample of Luminous Infrared Galaxy systems (85
LIRGs, with 11.4<log[LIR/L_sun]<12.5) in the GOALS sample. Cusp properties are
derived via 2-dimensional fitting of the nuclear stellar light imaged in the
near-infrared by the Hubble Space Telescope and have been combined with mid-IR
diagnostics for AGN/starburst characterization. We find that nuclear stellar
cusps are resolved in 76% of LIRGs (merger and non-interacting galaxies). The
cusp strength and luminosity increases with far-IR luminosity (excluding AGN)
and merger stage, confirming theoretical models that starburst activity is
associated with the build-up of nuclear stellar cusps. Evidence for ultra
compact nuclear starbursts is found in ~13% of LIRGs, which have a strong
unresolved central NIR light component but no significant contribution of an
AGN. The nuclear near-IR surface density (measured within 1 kpc radius)
increases by a factor of ~5 towards late merger stages. A careful comparison to
local early-type galaxies with comparable masses reveals (a) that local
(U)LIRGs have a significantly larger cusp fraction and (b) that the majority of
the cusp LIRGs have host galaxy luminosities (H-band) similar to core
ellipticals which is roughly one order in magnitude larger than for cusp
ellipticals.
