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I present a self-consistent stellar dynamical model for the bar of our Galaxy. The model fits the density profile fits the COBE light distribution, the observed solid body stllar rotation curve, the fall-off of minor axis velocity dispersion and the velocity ellipsoid at Baade's window. The fully self-consistent model was constructed using quadratic programming to assign weights to several thousand orbits running in a rotating bar potential. This model is {\sl the first} self-consistent rapidly rotating bar model built using an extension of Schwarzchild's orbit technique. The bar is smooth in phase space with the direct boxy orbits being the dominant orbit family. I have explored the range of models consist with current data and can suggest future observations that will distinguish between models. These techniques can easily be applied to external bulges and galactic nuclei.
We also use the self-consistent bar to build {\sl a microlensing model} for the Galactic Bulge. Comparing with the OGLE observations, we find that the observed large optical depth and long microlensing event duration towards the Bulge are consistent with a $2\times 10^{10}M\odot$ bar elongated along our line-of-sight and with lenses being ordinary stars; the model predicts 5-7 events with typical time scale of 20 days for the OGLE.
The thesis results also include finding a very general family of {\sl analytical density-potential pairs} for bulges and nuclei of general shape and radial profile. Most of the well-known spherical density-potential pairs are its special cases, including the $\eta$-models by Tremaine et al. (1994), Plummer model, the Perfect Sphere model, the modified Hubble profile. We demonstrate its application to study dynamics of both spherical and non-spherical systems.
