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Register a new userOn the deprojection of triaxial galaxies with Stackel potentials
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A family of triaxial Stackel potential-density pairs is introduced. With the help of a Quadratic Programming method, a linear combination of potential-density pairs of this family which fits a given projected density distribution can be built. This deprojection strategy can be used to model the potentials of triaxial elliptical galaxies with or without dark halos. Besides, we show that the expressions for the Stackel triaxial density and potential are considerably simplified when expressed in terms of divided differences, which are convenient numerically. We present an example of triaxial deprojection for the galaxy NGC~5128 whose photometry follows the de Vaucouleurs law.
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We present a grid-based non-parametric approach to obtain a triaxial three-dimensional luminosity density from its surface brightness distribution. Triaxial deprojection is highly degenerate and our approach illustrates the resulting difficulties. Fortunately, for massive elliptical galaxies, many deprojections for a particular line of sight can be discarded, because their projection along other lines of sight does not resemble elliptical galaxies. The near-elliptical isophotes of these objects imply near ellipsoidal intrinsic shapes. In fact, deprojection is unique for densities distributed on ellipsoidal shells. The constrained non-parametric deprojection method we present here relaxes this constraint and assumes that the contours of the luminosity density are boxy/discy ellipsoids with radially varying axis ratios. With this approach we are able to reconstruct the intrinsic triaxial densities of our test models, including one drawn from an $N$-body simulation. The method also allows to compare the relative likelihood of deprojections at different viewing angles. We show that the viewing orientations of individual galaxies with nearly ellipsoidal isophotal shapes can be constrained from photometric data alone.
Photometric deprojection is used to determine the stellardisk and bulge parameters for several edgeon galaxies from the FGC catalog. The assumption that the galaxies of our sample belonging to the fourth (i.e., lowest) surfacebrightness class in the FGC are edgeon, lowsurfacebrightness (LSB) galaxies is considered.
Cuspy triaxial potentials admit a large number of chaotic orbits, which moreover exhibit extreme stickiness that makes the process of chaotic mixing surprisingly inefficient. Environmental effects, modeled as noise and/or periodic driving, help accelerate phase space transport but probably not as much as in simpler potentials. This could mean that cuspy triaxial ellipticals cannot exist as time-independent systems.
We construct self-consistent dynamical models for disk galaxies with triaxial, cuspy halos. We begin with an equilibrium, axisymmetric, disk-bulge-halo system and apply an artificial acceleration to the halo particles. By design, this acceleration conserves energy and thereby preserving the systems differential energy distribution even as its phase space distribution function is altered. The halo becomes triaxial but its spherically-averaged density profile remains largely unchanged. The final system is in equilibrium, to a very good approximation, so long as the halos shape changes adiabatically. The disk and bulge are ``live while the halo is being deformed; they respond to the changing gravitational potential but also influence the deformation of the halo. We test the hypothesis that halo triaxiality can explain the rotation curves of low surface brightness galaxies by modelling the galaxy F568-3.
This paper investigates chaos and chaotic phase mixing in triaxial Dehnen potentials which have been proposed to describe realistic ellipticals. Earlier work is extended by exploring the effects of (1) variable axis ratios, (2) `graininess associated with stars and bound substructures, idealised as friction and white noise, and (3) large-scale organised motions presumed to induce near-random forces idealised as coloured noise with finite autocorrelation time. Three important conclusions are: (1) not all the chaos can be attributed to the cusp; (2) significant chaos can persist even for axisymmetric systems; and (3) introducing a supermassive black hole can increase both the relative number of chaotic orbits and the size of the largest Lyapunov exponent. Sans perturbations, distribution functions associated with initially localised chaotic ensembles evolve exponentially towards a nearly time-independent form at a rate L that correlates with the finite time Lyapunov exponents associated with the evolving orbits. Perturbations accelerate phase space transport by increasing the rate of phase mixing in a given phase space region and by facilitating diffusion along the Arnold web that connects different phase space regions, thus facilitating an approach towards a true equilibrium. The details of the perturbation appear unimportant. All that matters are the amplitude and the autocorrelation time, upon which there is a weak logarithmic dependence. Even comparatively weak perturbations can increase L by a factor of three or more, a fact that has potentially significant implications for violent relaxation.
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