The ATLAS3D Project -- XXIII. Angular momentum and nuclear surface
  brightness profiles
  [Abridged and Edited] We investigate nuclear light profiles in 135 ATLAS3D
galaxies for which the Hubble Space Telescope (HST) imaging is available and
compare them to the large scale kinematics obtained with the SAURON
integral-field spectrograph. Specific angular momentum, lambda_R, correlates
with the shape of nuclear light profiles, where cores are typically found in
slow rotators and core-less galaxies are fast rotators. Cores are found only in
massive galaxies and only in systems with the stellar mass M>8x10^10 Msun.
Based on our sample, we, however, see no evidence for a bimodal distribution of
nuclear slopes. The best predictor for finding a core is based on the stellar
velocity dispersion within an effective radius, sigma_e, and specific angular
momentum, where cores are found for lambda_R<0.25 and sigma_e>160 km/s. We
estimate that only about 10% of nearby early-type galaxies contain cores.
Furthermore, we show that there is a genuine population of fast rotators with
cores. We also show that core fast rotators are morphologically, kinematically
and dynamically different from core slow rotators. The cores of fast rotators
could harbour black holes of similar masses to those in core slow rotators, but
typically more massive than those found in core-less fast rotators. Core-less
galaxies, and especially core-less fast rotators, are under-luminous in the
diffuse X-ray emission, but the presence of a core does not imply high X-ray
luminosities. We postulate a possible population of core-less galaxies among
slow rotators, which can not be explained as face-on discs, but comprise a
genuine sub-population of slow rotators. These galaxies are typically less
massive and flatter than core slow rotators, and show evidence for dynamical
cold structures and exponential photometric components. We discuss possible
processes for formation of cores and their subsequent preservation.
