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.
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