The dynamical structure of broken power-law and double power-law models
  for dark matter haloes
  Galaxy kinematics and gravitational lensing are two complementary ways to
constrain the distribution of dark matter on galaxy scales. The typical dark
matter density profiles adopted in dynamical studies cannot easily be adopted
in lensing studies. Ideally, a mass model should be used that has the global
characteristics of realistic dark matter distributions, and that allows for an
analytical calculation of the magnifications and deflection angles. A simple
model with these properties, the broken-power-law (BPL) model, has very
recently been introduced. We examine the dynamical structure of the family of
BPL models. We derive simple closed expressions for basic dynamical properties,
and study the distribution function under the assumption of velocity isotropy.
We find that none of the BPL models with realistic parameters has an isotropic
distribution function that is positive over the entire phase space, implying
that the BPL models cannot be supported by an isotropic velocity distribution,
or models with a more radially anisotropic orbital structure. This result
limits the attractiveness of the BPL family as a tool for lensing studies to
some degree. More generally, we find that not all members of the general family
of double power-law or Zhao models, often used to model dark matter haloes, can
be supported by an isotropic or radially anisotropic distribution function. In
other words, the distribution function may become negative even for spherically
symmetric models with a well-behaved density profile.
