A Method For Determining Two-Dimensional Orbits In Galactic Disks

We propose a method for determining two-dimensional orbits of the interstellar matter (ISM) in galactic disks using observed line-of-sight velocity fields. Though four components, consisting of two of position and two of velocity, are necessary to determine two-dimensional orbits, the perpendicular velocity to line-of-sight can hardly be determined from observations. We show that the ISM’s orbits can be approximately determined by assuming that (i) the angular momentum is conserved along each orbit; (ii) all orbits are closed in a single rotating frame; and (iii) that the system is symmetric through the origin. As the angular momentum can be estimated on the major-axis of a disk, a perpendicular velocity to line-of-sight can be determined according to the conservation of the angular momentum, and thus two components of velocity are obtained. The ISM’s orbits can be calculated by solving differential equations given by an obtained twodimensional velocity field when a certain pattern speed is given. Typical deviation from correct orbit is less than observational resolution, according to our test calculations for modeled velocityfields. We applied this method to the observed data of NGC 4569, and obtained possible orbits for this galaxy. Furthermore, we calculated the mass distribution using our result. Subject headings: Galaxies: Kinematics and Dynamics, Galaxies: ISM, ISM: Kinematics and Dynamics, Methods: Data Analysis