We construct a new family of models of our Galaxy in which dark matter and disc stars are both represented by distribution functions that are analytic functions of the action integrals of motion .
The potential that is self-consistently generated by the dark matter , stars and gas is determined , and parameters in the distribution functions are adjusted until the model is compatible with observational constraints on the circular-speed curve , the vertical density profile of the stellar disc near the Sun , the kinematics of nearly 200 000 giant stars within 2 \mathrm { kpc } of the Sun , and estimates of the optical depth to microlensing of bulge stars .
We find that the data require a dark halo in which the phase-space density is approximately constant for actions | \mathrm { \textbf { J } } | \lesssim 140 \mathrm { kpc } { km s ^ { -1 } } .
In real space these haloes have core radii \simeq 2 \mathrm { kpc } .