Models of cuspy triaxial stellar systems. I. Stability and chaoticity

TL;DR

This study constructs and analyzes stable, cuspy triaxial stellar models with high fractions of chaotic orbits, demonstrating their stability over cosmic timescales using N-body simulations and Lyapunov exponents.

Contribution

It provides the first detailed stability analysis of cuspy triaxial stellar systems with high chaotic orbit fractions using N-body simulations.

Findings

Models are highly stable over a Hubble time.

Less than 25% of orbits are regular, indicating high chaos.

Chaotic models can be physically stable.

Abstract

We used the N-body code of Hernquist and Ostriker (1992) to build a dozen cuspy ({\gamma}\approx 1) triaxial models of stellar systems through dissipationless collapses of initially spherical distributions of 10^6 particles. We chose four sets of initial conditions that resulted in models morphologically resembling E2, E3, E4 and E5 galaxies, respectively. Within each set, three different seed numbers were selected for the random number generator used to create the initial conditions, so that the three models of each set are statistically equivalent. We checked the stability of our models using the values of their central densities and of their moments of inertia, which turned out to be very constant indeed. The changes of those values were all less than 3 per cent over one Hubble time and, moreover, we show that the most likely cause of those changes are relaxation effects in the numerical code. We computed the six Lyapunov exponents of nearly 5,000 orbits in each model in order to recognize regular, partially and fully chaotic orbits. All the models turned out to be highly chaotic, with less than 25 per cent of their orbits being regular. We conclude that it is quite possible to obtain cuspy triaxial stellar models that contain large fractions of chaotic orbits and are highly stable. The difficulty to build such models with the method of Schwarzschild (1979) should be attributed to the method itself and not to physical causes.