Dissipation and Extra Light in Galactic Nuclei. III. "Core" Ellipticals and "Missing" Light

We investigate how "extra" or "excess" central light in the surface brightness profiles of cusp or power-law elliptical galaxies relates to the profiles of ellipticals with cores. The envelopes of cusp ellipticals are established by violent relaxation in mergers acting on stars present in gas-rich progenitor disks, while their centers are structured by the relics of dissipational, compact starbursts. Ellipticals with cores are formed by the subsequent merging of the now gas-poor cusp ellipticals, with the fossil starburst components combining to preserve a dense, compact component in these galaxies as well (although mixing of stars smooths the transition from the outer to inner components in the profiles). By comparing extensive hydrodynamical simulations to observed profiles spanning a broad mass range, we show how to observationally isolate and characterize the relic starburst component in core ellipticals. Our method recovers the younger starburst population, demonstrating that these dense concentrations survive spheroid-spheroid mergers and reflect the degree of dissipation in the initial mergers that formed the penultimate galaxy progenitors. The degree of dissipation in the mergers that produced the cusp ellipticals is a strong function of stellar mass, roughly tracing the observed gas fractions of disks of the same mass over redshifts z ~ 0-2. The strength of this component strongly correlates with effective radius at fixed mass: systems with more dissipation are more compact, sufficient to explain the discrepancy in the maximum phase-space densities of ellipticals and their progenitor spirals. The survival of this component together with scattering of stars into the envelope in re-mergers naturally explain the high-Sersic index profile shapes characteristic of very massive core ellipticals. This is also closely related to the kinematics and isophotal shapes: only systems with matched starburst components from their profile fits also reproduce the observed kinematics of boxy/core ellipticals. The final "core-scouring" phase of core formation occurs when a black hole binary formed in the merger scatters stars out of the innermost regions of the extra-light component. It is therefore critical to adopt a physically motivated profile decomposition that accounts for the fossil starburst component when attempting to quantify scouring. We show that estimates of the scoured mass that employ single-component forms fitted to the entire galaxy profile can be strongly biased.