Three-integral models of oblate elliptical galaxies

To investigate the possible intrinsic and observable kinematics of oblate elliptical galaxies, we construct self-consistent phase-space distribution functions (DFs), depending on three integrals of motion. Beginning with the two classical integrals E and L z , and an approximative third integral obtained by Hamiltonian perturbation theory, we devise normalized orbit shape invariants S i . Rewriting the DF in terms of energy and two such alternative integrals makes it easy to visualize the physical orbit distribution that a particular DF stands for. We build the desired anisotropy into a galaxy model by writing the DF as a product of an assigned function h(S i ) and a derived function g(E, S j ), selecting the assigned part of the DF, and solving for the derived part