The rate of secular evolution in elliptical galaxies with central masses

TL;DR

This study uses N-body simulations to analyze how central masses induce chaotic orbits and secular evolution in elliptical galaxies, identifying key factors like effective chaotic momentum that influence the evolution rate.

Contribution

It introduces the concept of effective chaotic momentum and quantifies the relationship between central mass, chaos, and secular evolution in elliptical galaxies.

Findings

Chaotic orbits scale with central mass as a power law with exponent close to 1/2.

Secular evolution correlates with the effective chaotic momentum.

Below a threshold of 0.004, systems show negligible secular evolution.

Abstract

We study a series of $N-$body simulations representing elliptical galaxies with central masses. Starting from two different systems with smooth centres, which have initially a triaxial configuration and are in equilibrium, we insert to them central masses of various values. Immediately after such an insertion a system presents a high fraction of particles moving in chaotic orbits, a fact causing a secular evolution towards a new equilibrium state. The chaotic orbits responsible for the secular evolution are identified. Their typical Lypaunov exponents are found to scale with the central mass as a power law $L\propto m^s$ with $s$ close to 1/2. The requirements for an effective secular evolution within a Hubble time are examined. These requirements are quantified by introducing a quantity called \emph{effective chaotic momentum} $\mathscr{L}$. This quantity is found to correlate well with the rate of the systems' secular evolution. In particular, we find that when $\mathscr{L}$ falls below a threshold value (0.004 in our $N-$body units) a system does no longer exhibit significant secular evolution.