Orbital Instabilities in a Triaxial Cusp Potential

Abstract

This paper constructs an analytic form for a triaxial potential that describes the dynamics of a wide variety of astrophysical systems, including the inner portions of dark matter halos, the central regions of galactic bulges, and young embedded star clusters. Specifically, this potential results from a density profile of the form $\rho (m)\propto m^{-1}$, where the radial coordinate is generalized to triaxial form so that $m^2=x^2/a^2+y^2/b^2+z^2/c^2$. Using the resulting analytic form of the potential, and the corresponding force laws, we construct orbit solutions and show that a robust orbit instability exists in these systems. For orbits initially confined to any of the three principal planes, the motion in the perpendicular direction can be unstable. We discuss the range of parameter space for which these orbits are unstable, find the growth rates and saturation levels of the instability, and develop a set of analytic model equations that elucidate the essential physics of the instability mechanism. This orbit instability has a large number of astrophysical implications and applications, including understanding the formation of dark matter halos, the structure of galactic bulges, the survival of tidal streams, and the early evolution of embedded star clusters.

50 pages, accepted for publication in ApJ

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• Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars
• The fine-grained phase-space structure of Cold Dark Matter halos
• What's Up in the Milky Way? The Orientation of the Disc Relative to the Triaxial Halo
• Does sub-cluster merging accelerate mass segregation in local star formation?
• Kinematic Signatures of Subvirial Initial Conditions in Young Clusters
• Tidal disruption of globular clusters in dwarf galaxies with triaxial dark matter haloes
• A unified framework for the orbital structure of bars and triaxial ellipsoids
• The Radial Orbit Instability in Collisionless N-Body Simulations
• Milking the spherical cow: on aspherical dynamics in spherical coordinates
• Internal Alignments of Red Versus Blue Discs in Dark Matter Halos
• Strong Lensing by Galaxies
• SMART: A new implementation of Schwarzschild's Orbit Superposition technique for triaxial galaxies and its application to an N-body merger simulation
• The Orbital Structure of Triaxial Galaxies with Figure Rotation
• Light versus dark in strong-lens galaxies: Dark matter haloes that are rounder than their stars
• Detecting the Figure Rotation of Dark Matter Halos with Tidal Streams
• Hill's Equation with Random Forcing Parameters: The Limit of Delta Function Barriers
• On the Apparent Power Law in CDM Halo Pseudo Phase Space Density Profiles
• Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices
• A three dimensional investigation of two dimensional orbits
• Analytical galactic models with mild stellar cusps
• Hill's Equation with Small Fluctuations: Cycle to Cycle Variations and Stochastic Processes
• Triaxiality Inhibitors in N-Body Simulations
• Investigating the relation between environment and internal structure of massive elliptical galaxies using strong lensing