Kinematics of gas in a triaxial galaxy

The morphology and kinematics of cold gas in a triaxial Stackel potential are discussed. Equilibrium gas disks are allowed in two planes: the plane perpendicular to the long axis and the plane perpendicular to the short axis. General expressions are derived for the projected density distribution and radial velocities. The determination of the aspect angles of the system from observations of the gas and the stellar light is discussed in detail. If a constant M/L is assumed, surface photometry of the stars and the kinematics of one single "ring" of gas suffice to restrict the three-dimensional solution space of the viewing angles to a curve. Observations of two rings in perpendicular planes allow the determination of all three viewing angles, even without the assumption that M/L is constant. If there is an extended gas disk in the plane perpendicular to the long axis, then the complete three-dimensional potential and mass distribution can be determined. Some of the results derived here apply also to gas orbits in nonseparable potentials. If the gas orbit is noncircular, then the geometry of the orbit will cause the locus of zero radial velocity to be different from the apparent minor axis of the gas ring. Such an observation puts direct constraints on the viewing angles and on the flattening of the potential. Further constraints can be found by numerical calculation of the simple periodic orbits in the deprojected potential, and by matching the projected orbit with the measured ring. These results show that allowing for a triaxial shape of the density makes the analysis of the deprojection of gas disks or rings laborious, but is not a major obstacle.