Chaos and secular evolution of triaxial N-body galactic models due to an imposed central mass

Free access article

Issue		A&A Volume 428, Number 3, December IV 2004


Page(s)		905 - 923
Section		Galactic structure, stellar clusters and populations
DOI		http://dx.doi.org/10.1051/0004-6361:20041492

A&A 428, 905-923 (2004)
DOI: 10.1051/0004-6361:20041492

Chaos and secular evolution of triaxial N-body galactic models due to an imposed central mass

C. Kalapotharakos^{1, 2}, N. Voglis¹ and G. Contopoulos¹

¹ Academy of Athens, Research Center for Astronomy, 4 Soranou Efesiou Str., Athens, 11527, Greece
e-mail: [ckalapot;nvogl;gcontop]@cc.uoa.gr
² University of Athens, Department of Physics, Section of Astrophysics, Greece

(Accepted 18 June 2004 / Accepted 20 August 2004 )

Abstract
We investigate the response of triaxial non-rotating N-body models of elliptical galaxies with smooth centers, initially in equilibrium, under the presence of a central mass assumed to be due mainly to a massive central black hole. We examine the fraction of mass in chaotic motion and the resulting secular evolution of the models. Four cases of the size of the central mass are investigated, namely m=0.0005, 0.0010, 0.0050, 0.0100 in units of the total mass of the galaxy. We find that a central mass with value m < 0.005 increases the mass fraction in chaotic motion from the level of $25{-}35\%$ (that appears in the case of smooth centers) to the level of $50{-}80\%$ depending on the value of m and on the initial maximum ellipticity of the system. However, most of this mass moves in chaotic orbits with Lyapunov numbers too small to develop chaotic diffusion in a Hubble time. Thus their secular evolution is so slow that it can be neglected in a Hubble time.

Larger central masses ( $m \ga 0.005$ ) give initially about the same fractions of mass in chaotic motion as for smaller m, but the Lyapunov numbers are concentrated to larger values, so that a secular evolution of the self-consistent models is prominent. These systems evolve in time tending to a new equilibrium. During their evolution they become self-organized by converting chaotic orbits to ordered orbits of the Short Axis Tube type. The mechanism of such a self-organization is investigated. The rate of this evolution depends on m and on the value of the initial maximum ellipticity of the system. For m=0.01 and a large initial maximum ellipticity $E_{\rm max}\approx 7$ , equilibrium can be achieved in one Hubble time, forming an oblate spheroidal configuration. For the same value of m and initial maximum elipticity $E_{\rm max}\approx 3.5$ , or for $E_{\rm max}\approx 7$ , but m=0.005, oblate equilibrium configurations can also be achieved, but in much longer times. Furthermore, we find that, for m=0.005 and $E_{\rm max}\approx 3.5$ , triaxial equilibrium configurations can be formed. The fraction of mass in chaotic motion in the equilibrium configurations is in the range of $12{-}25\%$ .

Key words: chaos -- stellar dynamics -- methods: N-body simulations -- galaxies: formation -- galaxies: evolution -- galaxies: kinematics and dynamics

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