The distribution function of the Galaxy's dark halo

Starting from the hypothesis that the Galaxy's dark halo responded adiabatically to the infall of baryons, we have constructed a self-consistent dynamical model of the Galaxy that satisfies a large number of observations, including measurements of gas terminal velocities and masers, the kinematics of 180 000 giant stars from the RAVE (RAdial Velocity Experiment) survey and star-count data from the Sloan Digital Sky Survey. The stellar disc and the dark halo are both specified by distribution functions of the action integrals. The model is obtained by extending the work of Piffl et al. from the construction of a single model to a systematic search of model space. Whereas the model of Piffl et al. violated constraints on the terminal-velocity curve, our model respects these constraints by adopting a long scalelength R-d = 3.66 kpc for the thin and thick discs. The model is, however, inconsistent with the measured optical depth for microlensing of bulge stars because it attributes too large a fraction of the density at R less than or similar to 3 kpc to dark matter rather than stars. Moreover, it now seems likely that the thick disc's scalelength is significantly shorter than the model implies. Shortening this scalelength would cause the constraints from the rotation curve to be violated anew. We conclude that we can now rule out adiabatic compression of our Galaxy's dark halo.