  Cosmological simulations of dark matter structures have identified a set of
universal profiles, and similar characteristics have been seen in
non-cosmological simulations. It has therefore been speculated whether these
profiles of collisionless systems relate to accretion and merger history, or if
there is an attractor for the dark matter systems. Here we identify such a
1-dimensional attractor in the 3-dimensional space spanned by the 2 radial
slopes of the density and velocity dispersion, and the velocity anisotropy.
This attractor effectively removes one degree of freedom from the Jeans
equation. It also allows us to speculate on a new fluid interpretation for the
Jeans equation, with an effective polytropic index for the dark matter
particles between 1/2 and 3/4. If this attractor solution holds for other
collisionless structures, then it may hold the key to break the mass-anisotropy
degeneracy, which presently prevents us from measuring the mass profiles in
dwarf galaxies uniquely.
