  The Nuker profile, characterised by an inner and outer power-law profile
smoothly merged around a break radius, is a very popular model to describe the
surface brightness profile of galactic nuclei. A disadvantage of this model for
dynamical studies is that the spatial density distribution that corresponds to
this surface brightness profile cannot be written in terms of elementary or
regular special functions. We derive a compact and elegant analytical
expression for the density of the Nuker model, based the Mellin integral
transform method. We use this expression to discuss the general behaviour and
asymptotic expansion of the density. We also discuss the special subclass of
Nuker models with an infinitely sharp break, and demonstrate that these models
are always characterised by non-monotonous and hence unphysical density
profile. We extend our study to the dynamical structure of spherical isotropic
galactic nuclei with a Nuker surface brightness profile. Based on this
analysis, we extend and refine the classification of spherical isotropic
galactic nuclei introduced by Tremaine et al. (1994). We demonstrate that both
the inner density slope and the sharpness of the break between the inner and
outer profiles critically determine the consistency and stability of the Nuker
models.
