We present accurate models of the gravitational potential produced by a radially exponential disk mass distribution. The models are produced by combining three separate Miyamoto-Nagai disks. Such models have been used previously to model the disk of the Milky Way, but here we extend this framework to allow its application to disks of any mass, scalelength, and a wide range of thickness from infinitely thin to near spherical (ellipticities from 0 to 0.9). The models have the advantage of simplicity of implementation, and we expect faster run speeds over a double exponential disk treatment. The potentials are fully analytical, and differentiable at all points. The mass distribution of our models deviates from the radial mass distribution of a pure exponential disk by <0.4% out to 4 disk scalelengths, and <1.9% out to 10 disk scalelengths. We tabulate fitting parameters which facilitate construction of exponential disks for any scalelength, and a wide range of disk thickness (a user-friendly, web-based interface is also available). Our recipe is well suited for numerical modelling of the tidal effects of a giant disk galaxy on star clusters or dwarf galaxies. We consider three worked examples; the Milky Way thin and thick disk, and a disky dwarf galaxy.
The dynamics of globular cluster systems (GCSs) around galaxies are often used to assess the total enclosed mass, and even to constrain the dark matter distribution. The globular cluster system of a galaxy is typically assumed to be in dynamical equilibrium within the potential of the host galaxy. However cluster galaxies are subjected to a rapidly evolving and, at times, violently destructive tidal field. We investigate the impact of the harassment on the dynamics of GCs surrounding early type cluster dwarfs, using numerical simulations. We find that the dynamical behaviour of the GCS is strongly influenced by the fraction of bound dark matter f_{DM} remaining in the galaxy. Only when f_{DM} falls to ~15%, do stars and GCs begin to be stripped. Still the observed GC velocity dispersion can be used to measure the true enclosed mass to within a factor of 2, even when f_{DM} falls as low as ~3%. This is possible partly because unbound GCs quickly separate from the galaxy body. However even the distribution of {it{bound}} GCs may spatially expand by a factor of 2-3. Once f_{DM} falls into the <3% regime, the galaxy is close to complete disruption, and GCS dynamics can no longer be used to reliably estimate the enclosed mass. In this regime, the remaining bound GCS may spatially expand by a factor of 4 to 8. It may be possible to test if a galaxy is in this regime by measuring the dynamics of the stellar disk. We demonstrate that if a stellar disk is rotationally supported, it is likely that a galaxy has sufficient dark matter, that the dynamics of the GCS can be used to reliably estimate the enclosed mass.
We examine the effects of gas expulsion on initially sub-structured and out-of-equilibrium star clusters. We perform N-body simulations of the evolution of star clusters in a static background potential before adjusting that potential to model gas expulsion. We investigate the impact of varying the rate at which the gas is removed, and the instant at which gas removal begins. Reducing the rate at which the gas is expelled results in an increase in cluster survival. Quantitatively, this dependency is approximately in agreement with previous studies, despite their use of smooth, and virialised initial stellar distributions. However, the instant at which gas expulsion occurs is found to have a strong effect on cluster response to gas removal. We find if gas expulsion occurs prior to one crossing time, cluster response is poorly described by any global parameters. Furthermore in real clusters the instant of gas expulsion is poorly constrained. Therefore our results emphasis the highly stochastic and variable response of star clusters to gas expulsion.
The last few years have seen the discovery of many faint and ultra-faint dwarf spheroidal galaxies around the Milky Way. Among these is a pair of satellites called Leo IV and Leo V. This pair is found at large distances from the Milky Way (154 and 175 kpc respectively). The rather small difference in radial distance, and the fact that they also show a close projected distance on the sky, has led to the idea that we might be seeing a new pair of bound galaxies - like the Magellanic Clouds. In this paper we investigate this speculation by means of a simple integration code (confirming the results with full N-body simulations). As the luminous mass of both faint dwarfs is far too low to allow them to be bound, we simulate the pair assuming extended dark matter haloes. Our results show that the minimum dark matter mass required for the pair to be bound is rather high - ranging from 1.6 x 10^10 Msun to 5.4 x 10^10 Msun (within the virial radii). Computing the mass of dark matter within a commonly adopted radius of 300 pc shows that our models are well within the predicted range of dark matter content for satellites so faint. We therefore conclude that it could be possible that the two galaxies constitute a bound pair.
We model the formation of Aurigas Wheel - a recently discovered collisional ring galaxy. Aurigas Wheel has a number of interesting features including a bridge of stars linking the neighbouring elliptical to the ring galaxy, and evidence for components of expansion and rotation within the ring. Using N-body/SPH modelling, we study collisions between an elliptical galaxy and a late-type disk galaxy. A near direct collision, with a mildy inclined disk, is found to reasonably reproduce the general system morphology ~50 Myr following the collision. The collision must have a relatively low velocity (initially ~150 km s^{-1}) in order to form the observed bridge, and simultaneously match the galaxies separation. Our best-match model suggests the total disk galaxy is ~5 times more massive than the elliptical. We find that the velocity of expansion of the ring is sensitive to the mass of the elliptical, while insensitive to the encounter velocity. We evolve our simulation beyond the current epoch to study the future destiny of the galaxy pair. In our model, the nucleus moves further away from the plane of the ring in the direction of the stellar bridge. The nucleus eventually merges with the elliptical galaxy ~100 Myr after the present time. The ring continues to expand for ~200 Myr before collapsing back. The low initial relative velocity of the two galaxies will eventually result in a complete merger.
We examine the effects of gas expulsion on initially sub-structured and out-of-equilibrium star clusters. We perform $N$-body simulations of the evolution of star clusters in a static background potential before removing that potential to model gas expulsion. We find that the initial star formation efficiency is not a good measure of the survivability of star clusters. This is because the stellar distribution can change significantly, causing a large change in the relative importance of the stellar and gas potentials. We find that the initial stellar distribution and velocity dispersion are far more important parameters than the initial star formation efficiency, and that clusters with very low star formation efficiencies can survive gas expulsion. We suggest that it is variations in cluster initial conditions rather than in their star formation efficiencies that cause some clusters to be destroyed while a few survive.
