In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to improve a
ccuracy, especially for nearly radial orbits. 1) It is found that moderately improved orbital fits can be achieved with higher order perturbation expansions (in eccentricity), with the addition of `harmonic terms to the solution. 2) Alternately, a matching of the extreme radial excursions of an orbit can be imposed, and a more accurate estimate of the eccentricity parameter is obtained. However, the error in the precession frequency is usually increased. 3) A correction function of small magnitude corrects the frequency problem. With this correction, even first order approximations yield excellent fits at quite high eccentricity over a range of potential indices that includes flat and falling rotation curve cases. 4) Adding a first harmonic term to fit the breadth of the orbital loops, and determining the fundamental and harmonic coefficients by matching to three orbital positions further improves the fit. With a couple of additional small corrections one obtains excellent fits to orbits with radial ranges of more than a thousand for some potentials. These simple corrections to the basic p-ellipse are basically in the form of several successive approximations, and can provide high accuracy. They suggest new results including that the apsidal precession rate scales approximately as $log(1-e)$ at very high eccentricities $e$. New insights are also provided on the occurrence of periodic orbits in various potentials, especially at high eccentricity.
We report the detection of strong, resolved emission from warm H2 in the Taffy galaxies and bridge. Relative to the continuum and faint PAH emission, the H2 emission is the strongest in the connecting bridge, approaching L(H2)/L(PAH8{mu}m) = 0.1 betw
een the two galaxies, where the purely rotational lines of H2 dominate the mid-infrared spectrum in a way very reminiscent of the group-wide shock in the interacting group Stephans Quintet. The surface brightness in the 0-0 S(0) and S(1) H2 lines in the bridge is more than twice that observed at the center of the Stephans Quintet shock. We observe a warm H2 mass of 4.2 times 108 Modot in the bridge, but taking into account the unobserved bridge area, the total warm mass is likely to be twice this value. We use excitation diagrams to characterize the warm molecular gas, finding an average surface mass of 5 times 106 Modot kpc-2 and typical excitation temperatures of 150-175 K. H2 emission is also seen in the galaxy disks, although there the emission is more consistent with normal star forming galaxies. We investigate several possible heating mechanisms for the bridge gas, but favor the conversion of kinetic energy from the head-on collision via turbulence and shocks as the main heating source. Since the cooling time for the warm H2 is short (5000 yr), shocks must be permeating the molecular gas in bridge region in order to continue heating the H2.
We present smoothed particle hydrodynamic models of the interactions in the compact galaxy group, Stephans Quintet. This work is extension of the earlier collisionless N-body simulations of Renaud et al. in which the large-scale stellar morphology of
the group was modeled with a series of galaxy-galaxy interactions in the simulations. Including thermohydrodynamic effects in this work, we further investigate the dynamical interaction history and evolution of the intergalactic gas of Stephans Quintet. The major features of the group, such as the extended tidal features and the group-wide shock, enabled us to constrain the models reasonably well, while trying to reproduce multiple features of the system. We found that reconstructing the two long tails extending from NGC 7319 toward NGC 7320c one after the other in two separate encounters is very difficult and unlikely, because the second encounter usually destroys or distorts the already-generated tidal structure. Our models suggest the two long tails may be formed simultaneously from a single encounter between NGC 7319 and 7320c, resulting in a thinner and denser inner tail than the outer one. The tails then also run parallel to each other as observed. The model results support the ideas that the group-wide shock detected in multi-wavelength observations between NGC 7319 and 7318b and the starburst region north of NGC 7318b are triggered by the high-speed collision between NGC 7318b and the intergalactic gas. Our models show that a gas bridge is formed by the high-speed collision and clouds in the bridge continue to interact for some tens of millions of years after the impact. This produces many small shocks in that region, resulting a much longer cooling time than that of a single impact shock.
We have discovered long-lived waves in two sets of numerical models of fast (marginally bound or unbound) flyby galaxy collisions, carried out independently with two different codes. In neither simulation set are the spirals the result of a collision
-induced bar formation. Although there is variation in the appearance of the waves with time, they do not disappear and reform recurrently, as seen in other cases described in the literature. We also present an analytic theory that can account for the wave structure, not as propagating transients, nor as a fixed pattern propagating through the disc. While these waves propagate through the disc, they are maintained by the coherent oscillations initiated by the impulsive disturbance. Specifically, the analytic theory suggests that they are caustic waves in ensembles of stars pursuing correlated epicyclic orbits after the disturbance. This theory is an extension of that developed by Struck and collaborators for colliding ring galaxies. The models suggest that this type of wave may persist for a couple of Gyr., and galaxy interactions occur on comparable timescales, so waves produced by the mechanism may be well represented in observed spirals. In particular, this mechanism can account for the tightly wound, and presumably long-lived spirals, seen in some nearby early-type galaxies. These spirals are also likely to be common in groups and clusters, where fast encounters between galaxies occur relatively frequently. However, as the spirals become tightly wound, and evolve to modest amplitudes, they may be difficult to resolve unless they are nearby. Nonetheless, the effect may be one of several processes that result from galaxy harassment, and via wave-enhanced star formation contribute to the Butcher-Oemler effect.
We use smoothed particle hydrodynamics (SPH) models to study the large-scale morphology and dynamical evolution of the intergalactic gas in Stephans Quintet, and compare to multiwavelength observations. Specifically, we model the formation of the hot
X-ray gas, the large-scale shock, and emission line gas as the result of NGC 7318b colliding with the group. We also reproduce the N-body model of Renaud and Appleton for the tidal structures in the group.
The existence of partially ionized, diffuse gas and dust clouds at kiloparsec scale distances above the central planes of edge-on, galaxy discs was an unexpected discovery about 20 yrs ago. Subsequent observations showed that this EDIG (extended or e
xtraplanar diffuse interstellar gas) has rotation velocities approximately 10-20% lower than those in the central plane, and have been hard to account for. Here we present results of hydrodynamic models, with radiative cooling and heating from star formation. We find that in models with star formation generated stochastically across the disc an extraplanar gas layer is generated as long as the star formation is sufficiently strong. However, this gas rotates at nearly the same speed as the mid-plane gas. We then studied a range of models with imposed spiral or bar waves in the disc. EDIG layers were also generated in these models, but primarily over the wave regions, not over the entire disc. Because of this partial coverage, the EDIG clouds move radially, as well as vertically, with the result that observed kinematic anomalies are reproduced. The implication is that the kinematic anomalies are the result of three-dimensional motions when the cylindrical symmetry of the disc is broken. Thus, the kinematic anomalies are the result of bars or strong waves, and more face-on galaxies with such waves should have an asymmetric EDIG component. The models also indicate that the EDIG can contain a significant fraction of cool gas, and that some star formation can be triggered at considerable heights above the disc midplane. We expect all of these effects to be more prominent in young, forming discs, to play a role in rapidly smoothing disc asymmetries, and in working to self-regulate disc structure.
