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

Abstract

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 > ∼ 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 max ≈ 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 max ≈ 3.5, or for E max ≈ 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 max ≈ 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%.

Dynamics of galaxy cores and supermassive black holes

“…There is however a large body of work addressing the large-scale effects of central mass concentrations on triaxial spheroids or bars (e.g. Norman et al 1985, Hasan et al 1993, Dubinski 1994, Merritt & Quinlan 1998, Holley-Bockelmann et al 2002, Kalapotharakos et al 2004, Kalapotharakos & Voglis 2005, Athanassoula et al 2005. These studies generally proceed by first constructing an N-body model for the bar or triaxial spheroid, then a compact mass is inserted or grown at the center and the model is integrated forward.…”

Special Features of Galactic Dynamics

“…The distribution of the real particles with respect to values of log Lj in four models with CMCs. For larger values of the mass m, the maximum of the distributions is shifted at larger values of log Lj (after Kalapotharakos et al 2004).…”

“…A extended study of global dynamics in N-Body systems was made by Voglis et al (2002), Kalapotharakos et al (2004) and Kalapotharakos and Voglis (2005). This is a study of N-Body systems in equilibrium resulting from the cosmological simulations described in subsection 2.5.…”

“…part of the portrait. A dot is plotted after the moment when the orbit is captured in the regular domain (after Kalapotharakos et al 2004). …”

“…At the equilibrium position there are only regular orbits of SAT type and chaotic orbits. Kalapotharakos et al (2004) concluded that a system must have a CMC of at least m ≈ 0.01, in order to complete its evolution and reach a new equilibrium state within a Hubble time. For smaller mass parameters the evolution to equilibrium is prolonged over many Hubble times.…”