Stellar cusp and warm dust at the heart of NGC1068
  Establishing precisely how stars and interstellar medium distribute within
the central 100 pc area around an AGN, down to the pc scale, is key for
understanding how the very final transfer of matter from kpc scale to the
sub-parsec size of the accretion disc is achieved. Using AO-assisted
(SPHERE-VLT) near-IR images in H and Ks and narrow-band of the Seyfert 2 galaxy
NGC1068 we analyse the radial distribution of brightness in the central r < 100
pc area down to the pc scale. The median-averaged radial profiles are adjusted
by a cusp (power-law) plus a central point-source. A simple radiative transfer
model is used to interpret the data. We find that the fit of profiles beyond
10pc is done quite precisely at Ks by a cusp of exponent -2.0 plus a central
point-source and by a cusp of exponent -1.2 at H. The difference between H and
Ks can be explained by differential extinction, provided that the distribution
of dust is itself cuspy as r^-1. However, the required stellar density follows
a r^-4 cusp, much steeper than any other cusp theoretically predicted and the
mass of the cluster is unreasonable, even introducing a segregation in the
stellar population with an excess of giant stars inward. A much more acceptable
solution is found with a K profile dominated by warm dust emission, while the H
profile corresponds to a stellar cusp. NGC1068 is shown to satisfy a
relationship between half-light radius, cusp luminosity and exponent which
suggests that the cusp is the remnant of a recent starbust. We identify the
central point-like source with the very hot dust at the internal wall of the
putative torus and derive an intrinsic luminosity that requires an overall
extinction AK ~ 8, a value consistent with predictions by several models.
