Darwin Tames an Andromeda Dwarf: Unraveling the Orbit of Ngc 205 Using a Genetic Algorithm

NGC 205, a close satellite of the M31 galaxy, is our nearest example of a dwarf elliptical galaxy. Photometric and kinematic observations strongly suggest that NGC 205 is currently undergoing tidal distortion as a result of its interaction with M31. Despite earlier attempts, the orbit and progenitor properties of NGC 205 are not well known. In this paper, we present an optimized search for these unknowns by combining a genetic algorithm with restricted N -body simulations of the interaction. This approach, coupled with photometric and kinematic observations as constraints, allows for an effective exploration of a 10-dimensional parameter space. We represent the gravitational potential of M31 as a static analytic bulge-disk-halo model. NGC 205 is modeled as a static Hernquist potential with embedded mass-less test particles that serve as tracers of surface brightness. We explore three distinct, initially stable configurations of test particles: a cold rotating disk (no velocity dispersion), a warm rotating disk (small amount of velocity dispersion), and a hot, pressure-supported spheroid (isotropic velocity distribution with no rotation). Each of these models is able to reproduce some, but not all, of the observed features of NGC 205. This leads us to speculate that a rotating progenitor with substantial pressure support could match all of the observables. Furthermore, plausible combinations of mass and scale length for the pressure-supported spheroid model of the progenitor of NGC 205 reproduce the observed velocity dispersion profile. For all three models, we find that NGC 205’s lineof-sight distance and proper motion are well constrained by NGC 205’s kinematic profile and surface brightness distribution. Orbits that best match the observables place the satellite 11± 9 kpc behind M31 moving at very large velocities: 300 − 500 km s on primarily radial orbits. Given that the observed radial component is only 54 km s, this implies a large tangential motion for NGC 205, moving from the north-west towards the south-east, that translates into a predicted proper motion of ∼ 0.1 mas yr. These results suggest that NGC 205 is not associated with the stellar arc observed to the north of M31 and to the north-east of NGC 205. Furthermore, NGC 205’s velocity appears to be near or greater than its escape velocity, signifying that the satellite is likely on its first M31 passage. Subject headings: galaxies: dwarf — galaxies: kinematics and dynamics — galaxies: individual (NGC 205) — galaxies: interactions — methods: N -body simulations — methods: numerical