Orbital structure of self-consistent triaxial stellar systems

Abstract

We used a multipolar code to create, through the dissipationless collapses of systems of 1,000,000 particles, three self-consistent triaxial stellar systems with axial ratios corresponding to those of E4, E5 and E6 galaxies. The E5 and E6 models have small, but significant, rotational velocities although their total angular momenta are zero, that is, they exhibit figure rotation; the rotational velocity decreases with decreasing flattening of the models and for the E4 model it is essentially zero. Except for minor changes, probably caused by unavoidable relaxation effects, the systems are highly stable. The potential of each system was subsequently approximated with interpolating formulae yielding smooth potentials, stationary for the non-rotating model and stationary in the rotating frame for the rotating ones. The Lyapunov exponents could then be computed for randomly selected samples of the bodies that make up the different systems, allowing the recognition of regular and partially and fully chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using their locations on the frequency map. As it could be expected, the percentages of chaotic orbits increase with the flattening of the system. As one goes from E6 through E4, the fraction of partially chaotic orbits relative to that of fully chaotic ones increases, with the former surpassing the latter in model E4; the likely cause of this behavior is that 123 308 R. O. Aquilano et al. triaxiality diminishes from E6 through E4, the latter system being almost axially symmetric. We especulate that some of the partially chaotic orbits may obey a global integral akin to the long axis component of angular momentum. Our results show that is perfectly possible to have highly stable triaxial models with large fractions of chaotic orbits, but such systems cannot have constant axial ratios from center to border: a slightly flattened reservoir of highly chaotic orbits seems to be mandatory for those systems.

Análisis comparativo de la estructura orbital de modelos de galaxias triaxiales no cuspidales y cuspidales utilizando distintas expansiones para el potencial gravitatorio

“…Por ello, tanto Aquilano et al [2] como Muzzio et al [13] han usado como comparación las galaxias NGC1379 y NGC4697 que según Napolitano et al [14] tienen gradientes nulos de relación masa-luminosidad.…”

“…El modelo no cuspidal -que denominamos E6 de aquí en más-se construyó siguiendo el esquema descripto anteriormente y manteniendo fijo el parámetro de suavizado en = 0.010 [2].…”

“…Los modelos triaxiales seleccionados -E6 (no cuspidal) y E6c (cuspidal)-han sido caracterizados en detalle en trabajos previos y sus estructuras orbitales se obtuvieron siguiendo los esquema propuestos por Aquilano et al [2] y Muzzio et al [13].…”

“…A tal efecto, se utilizó la transformada modificada de Fourier implementada por D. Nesvorný, cuyo código nos fuera provisto oportunamente por el autor. Las frecuencias fundamentales nos permitieron clasificar lasórbitas regulares en tubos de eje mayor (LATs), tubos de eje menor (SATs), y cajas y cajitas (BBLs), usando el método propuesto por Kalapotharakos & Voglis [9], con sucesivos mejoramientos introducidos por Muzzio [11], Aquilano et al [2] y Muzzio et al [13].…”

“…La estructura orbital de modelos autoconsistentes de sistemas estelares triaxiales creados a través de colapsos no disipativos de partículas "frías" siguiendo su evolución con el código de N-cuerpos de L.A. Aguilar [1] ha sido investigada en varios trabajos anteriores ( [12], [11], [2] y [13]). Eĺ ultimo de ellos aborda el estudio de morfologías cuspidales puesto que constituyen una mejor representación de las galaxias elípticas que los modelos de densidad central constante usados en el pasado.…”