Computer Science
Scientific paper
Jun 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt........10f&link_type=abstract
Thesis (PHD). RUTGERS THE STATE UNIVERSITY OF NEW JERSEY - NEW BRUNSWICK , Source DAI-B 57/12, p. 7569, Jun 1997, 166 pages.
Computer Science
1
Banana Orbits, Dehnen
Scientific paper
The gravitational potentials, orbital properties, and self-consistent equilibria of triaxial stellar systems with central density cusps are examined. Observations of the nuclei of early-type galaxies with the Hubble Space Telescope (HST) suggest that their surface brightness profiles fall into two categories: the 'cores' and the 'power laws.' We show that this dichotomy results from an optical illusion associated with projection onto the plane of the sky. Galaxies of both types have deprojected density profiles that are well-described as power-laws at small radii, with slopes 0≤γ<= 2, where ρ∝r-γ describes the central dependence of the luminosity density. Galaxies with 'cores' are found to have γ<=1, and this mild divergence produces a finite central density upon projection. The characteristics of periodic orbits in triaxial models with weak cusps, γ<=1, are investigated. Because of the weak central divergence of the density in these models, the gravitational force remains finite at the center. The stability of the long-axis orbit, which generates box orbits, and the shapes of the 2:1 'banana' orbits are examined. The long-axis orbit is unstable at most energies to lateral perturbations when the model is sufficiently flat, c/a/ ~< 0.7, or when the cusp is sufficiently steep, γ ~> 0.8. Regular box orbits, which depend for their existence on the stability of the long-axis orbit, do not exist in these models. The next-lowest resonance, the 2: 1 banana family, is present whenever the long-axis orbit is unstable. However the banana orbits have a very restricted range of shapes and are thicker than the model isodensity surfaces when c/a/ ~< 0.4. Motivated by these results, we attempt to construct self-consistent models of triaxial galaxies with Dehnen's (1993) density law. We consider central density cusps defined by γ = 1 (weak cusp) and γ = 2 (strong cusp). These values are representative of the nuclear density profiles of bright ('core') and faint ('power-law') galaxies as observed with HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. We compute libraries of ~7000 orbits in each of the models and map them as a function of energy. A large fraction of the orbits in both model potentials are stochastic, which diffuse relatively quickly through their allowed phase-space in the strong-cusp potential (~103 dynamical times) and more slowly in the weak-cusp potential (104 dynamical times or longer). Attempts to construct self-consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochastic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued diffusion of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space is uniformly populated at low energies and found these 'fully mixed' solutions only for the weak cusp potential. We made a conclusion that strong triaxiality can be inconsistent with a high central density. Our results suggest that chaos is a generic feature of motion in realistic triaxial potentials, but that the presence of chaos is not necessarily inconsistent with the existence of stationary triaxial configurations. Finally, we present a new family of cuspy triaxial mass models with continuous derivatives at the center that are convenient for numerical calculations.
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