Eric I. Barnes

The Role of the Radial Orbit Instability in Dark Matter Halo Formation and Structure

For a decade, N-body simulations have revealed a nearly universal dark matter density profile, which appears to be robust to changes in the overall density of the universe and the underlying power spectrum. Despite its universality, the physical origin of this profile has not yet been well understood. Semianalytic models by Barnes and coworkers have suggested that the density structure of dark matter halos is determined by the onset of the radial orbit instability (ROI). We have tested this hypothesis using N-body simulations of collapsing dark matter halos with a variety of initial conditions. For dynamically cold initial conditions, the resulting halo structures are triaxial in shape, due to the mild aspect of the instability. We examine how variations in initial velocity dispersion affect the onset of the instability, and find that an isotropic velocity dispersion can suppress the ROI entirely, while a purely radial dispersion does not. The quantity -->σ2/v2c is a criterion for instability, where regions with -->σ2/v2c 1 become triaxial due to the ROI or other perturbations. We also find that the radial orbit instability sets a scale length at which the velocity dispersion changes rapidly from isotropic to radially anisotropic. This scale length is proportional to the radius at which the density profile changes shape, as is the case in the semianalytic models; however, the coefficient of proportionality is different by a factor of ~2.5. We conclude that the radial orbit instability is likely to be a key physical mechanism responsible for the nearly universal profiles of simulated dark matter halos.

Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems

We investigate the connection between collisionless equilibria and the phase-space relation between density ρ and velocity dispersion σ found in simulations of dark matter halo formation, F = ρ/σ3 ∝ r-α. Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-free ρ/σ3 distributions when in equilibrium. We have also done a preliminary investigation of variables other than r that may match or supersede the correlation with F. In the same vein, we show that ρ/σm, where m = 3, is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law F distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the ρ/σ3 distributions of virialized systems.

Photometric Decomposition of Barred Galaxies

We present a non-parametric method for decomposition of the light of disk galaxies into disk, bulge and bar components. We have developed and tested the method on a sample of 68 disk galaxies for which we have acquired I-band photometry. The separation of disk and bar light relies on the single assumption that the bar is a straight feature with a different ellipticity and position angle from that of the projected disk. We here present the basic method, but recognise that it can be significantly refined. We identify bars in only 47% of the more nearly face-on galaxies in our sample. The fraction of light in the bar has a broad range from 1.3% to 40% of the total galaxy light. If low-luminosity galaxies have more dominant halos, and if halos contribute to bar stability, the luminosity functions of barred and unbarred galaxies should differ markedly; while our sample is small, we find only a slight difference of low significance.

Scale Lengths in Dark Matter Halos

We investigate a hypothesis regarding the origin of the scale length in halos formed in cosmological N-body simulations. This hypothesis can be viewed as an extension of an earlier idea put forth by Merritt and Aguilar. Our findings suggest that a phenomenon related to the radial orbit instability is present in such halos and is responsible for density profile shapes. This instability sets a scale length at which the velocity dispersion distribution changes rapidly from isotropic to radially anisotropic. This scale length is reflected in the density distribution as the radius at which the density profile changes slope. We have tested the idea that radially dependent velocity dispersion anisotropy leads to a break in density profile shape by manipulating the input of a semianalytic model to imitate the velocity structure imposed by the radial orbit instability. Without such manipulation, halos formed are approximated by single power-law density profiles and isotropic velocity distributions. Halos formed with altered inputs display density distributions featuring scale lengths and anisotropy profiles similar to those seen in cosmological N-body simulations.

THE RADIAL ORBIT INSTABILITY IN COLLISIONLESS N-BODY SIMULATIONS

Using a suite of self-gravitating, collisionless N-body models, we systematically explore a parameter space relevant to the onset and behavior of the radial orbit instability (ROI), whose strength is measured by the systemic axis ratios of the models. We show that a combination of two initial conditions, namely the velocity anisotropy and the virial ratio, determines whether a system will undergo ROI and exactly how triaxial the system will become. A third initial condition, the radial shape of the density profile, plays a smaller, but noticeable role. Regarding the dynamical development of the ROI, the instability (1) begins after systems collapse to their most compact configuration and (2) evolves fastest when a majority of the particles have radially anisotropic orbits, while there is a lack of centrally concentrated isotropic orbits. We argue that this is further evidence that self-reinforcing torques are the key to the onset of the ROI. Our findings support the idea that a separate orbit instability plays a role in halting the ROI.

ENTROPY PRODUCTION IN COLLISIONLESS SYSTEMS. II. ARBITRARY PHASE-SPACE OCCUPATION NUMBERS

We present an analysis of two thermodynamic techniques for determining equilibria of self-gravitating systems. One is the Lynden-Bell (LB) entropy maximization analysis that introduced violent relaxation. Since we do not use the Stirling approximation, which is invalid at small occupation numbers, our systems have finite mass, unlike LBs isothermal spheres. (Instead of Stirling, we utilize a very accurate smooth approximation for ln x!.) The second analysis extends entropy production extremization to self-gravitating systems, also without the use of the Stirling approximation. In addition to the LB statistical family characterized by the exclusion principle in phase space, and designed to treat collisionless systems, we also apply the two approaches to the Maxwell-Boltzmann (MB) families, which have no exclusion principle and hence represent collisional systems. We implicitly assume that all of the phase space is equally accessible. We derive entropy production expressions for both families and give the extremum conditions for entropy production. Surprisingly, our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy, in both LB and MB statistics. In other words, both thermodynamic approaches lead to the same equilibrium structures.

Collisionless dynamics in globular clusters

Since globular clusters (GCs) are old, low-N systems their dynamics is widely believed to be fully dominated by collisional two-body processes and their surface brightness profiles are fitted by King models. However, for many GCs, especially those with Hubble Space Telescope-resolved central regions and ‘extratidal’ features, King models provide poor fits. We suggest that this is partly because collisionless dynamics is also important and contributes to shaping the cluster properties. We show using time-scale and length-scale arguments that except for the very centres of clusters, collisionless dynamics should be more important than collisional. We then fit 38 GCs analysed by Noyola & Gebhardt with (collisional) King and (collisionless) DARKexp models over the full available radial range, and find that the latter provide a better fit to 29 GCs; for six of these the fit is at least approximately five times better in terms of rms. DARKexp models are theoretically derived maximum entropy equilibrium states of self-gravitating collisionless systems and have already been shown to fit the results of dark matter N-body simulations. (We do not attempt fits with ad hoc fitting functions.)

Entropy production in collisionless systems. I. Large phase-space occupation numbers

Certain thermal non-equilibrium situations, outside of the astrophysical realm, suggest that entropy production extrema, instead of entropy extrema, are related to stationary states. In an effort to better understand the evolution of collisionless self-gravitating systems, we investigate the role of entropy production and develop expressions for the entropy production rate in two particular statistical families that describe self-gravitating systems. From these entropy production descriptions, we derive the requirements for extremizing the entropy production rate in terms of specific forms for the relaxation function in the Boltzmann equation. We discuss some implications of these relaxation functions and point to future work that will further test this novel thermodynamic viewpoint of collisionless relaxation.

Velocity Distributions from Nonextensive Thermodynamics

There is no accepted mechanism that explains the equilibrium structures that form in collisionless cosmological N-body simulations. Recent work has identified nonextensive thermodynamics as an innovative approach to the problem. The distribution function that results from adopting this framework has the same form as for polytropes, but the polytropic index is now related to the degree of nonextensiveness. In particular, the nonextensive approach can mimic the equilibrium structure of dark matter density profiles found in simulations. We extend the investigation of this approach to the velocity structures expected from nonextensive thermodynamics. We find that the nonextensive and simulated N-body vrms distributions do not match one another. The nonextensive vrms profile is either monotonically decreasing or displays little radial variation, each of which disagrees with the vrms distributions seen in simulations. We conclude that the currently discussed nonextensive models require further modifications in order to corroborate dark matter halo simulations.

COMPARING EXTENDED SYSTEM INTERACTIONS WITH MOTIONS IN SOFTENED POTENTIALS

Using an