arXiv subjects

Eric I. Barnes

Publications and source records attributed to Eric I. Barnes.

At least 19 recordsLinked to original sources

arXiv2019

Predicting Steady States of One-dimensional Collisionless Gravitating Systems

Building on the development of a Hermite-Legendre analysis of one-dimensional gravitating collisionless systems, we present a technique for determining the steady states of such systems. This provides an important component for understanding the physics involved in the relaxation of these kinds of systems. As the dark matter structures in the universe should have traits in common with these systems, insight into this relaxation can provide clues to larger astrophysical questions. For large perturbation strengths, we determine physically motivated parameter ranges for the simplest families of steady states as well as their stability. We also demonstrate that any set of initial conditions in the linear regime can be resolved into unique time-independent and time-dependent modes. Combinations of time-independent modes then describe the steady state of any system linearly perturbed from equilibrium. These results highlight the importance of initial conditions over relaxation mechanisms in the evolution of these systems.

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arXiv2019

Relaxation of One-dimensional Collisionless Gravitating Systems

In an effort to better understand collisionless relaxation processes in gravitational systems, we investigate one-dimensional models. Taking advantage of a Hermite-Legendre expansion of relevant distribution functions, we present analytical and numerical behaviors of Maxwell-Boltzmann entropy. In particular, we modestly perturb systems about a separable-solution equilibrium and observe their collisionless evolution to a steady state. We verify the time-independence of fine-grained entropy in these systems before turning our attention to the behavior of coarse-grained entropy. We also verify that there is no analogue to the collisional H-theorem for these systems. Competing terms in the second-order coarse-grained entropy make it impossible to guarantee continuously increasing entropy. However, over dynamical time-scales the coarse-grained entropy generally increases, with small oscillations occurring. The lack of substantive differences between the entropies in test-particle and self-gravitating cases suggests that phase mixing, rather than violent relaxation associated with potential changes, more significantly drives the coarse-grained entropy evolution. The effects of violent relaxation can be better quantified through analysis of energy distributions rather than phase-space distributions.

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arXiv2018

Triaxiality Inhibitors in N-Body Simulations

Numerous previous studies have investigated the phenomenon wherein initially spherical N-body systems are distorted to triaxial shapes. We report on an investigation of a previously described orbital instability that should oppose triaxiality. After verifying the instability with numerical orbit integrations that extend the original analysis, we search for evidence of the instability in N-body systems that become triaxial. Our results highlight the difficulty in separating dynamical process from finite-N effects. While we argue that our analysis points to the presence of the instability in simulated triaxial systems, discreteness appears to play a role in mimicking the instability. This suggests that predicting the shapes of real-world systems, such as dark matter halos around galaxies, based on such simulations involves more uncertainty than previously thought.

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arXiv2016

Comparing Extended System Interactions with Motions in Softened Potentials

Using an $N$-body evolution code that does not rely on softened potentials, I have created a suite of unbound interacting cluster pair simulations. The motions of the centers of mass of the clusters have been tracked and compared to the trajectories of point masses interacting via one of four different softened potential prescriptions. I find that the relationship between the impact parameter of the cluster interaction and the point-mass softening length that best approximates each cluster's center-of-mass motion depends on the adopted prescription. In general, the range of allowed softening lengths grows roughly linearly with the impact parameter, but zero softening is acceptable in the majority of situations. In an $N$-body simulation that adopts a fixed softening length, such relationships lead to the possibility of two-body effects, like dynamical friction, being either larger or smaller than the corresponding cluster situation. Further consideration of more specific $N$-body situations leads estimating that a very small fraction of point-mass encounters experience two-body effects significantly different than those of equivalent clusters.

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arXiv2015

Entropy Production in Collisionless Systems. III. Results from Simulations

The equilibria formed by the self-gravitating, collisionless collapse of simple initial conditions have been investigated for decades. We present the results of our attempts to describe the equilibria formed in $N$-body simulations using thermodynamically-motivated models. Previous work has suggested that it is possible to define distribution functions for such systems that describe maximum entropy states. These distribution functions are used to create radial density and velocity distributions for comparison to those from simulations. A wide variety of $N$-body code conditions are used to reduce the chance that results are biased by numerical issues. We find that a subset of initial conditions studied lead to equilibria that can be accurately described by these models, and that direct calculation of the entropy shows maximum values being achieved.

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arXiv2013

Dynamics of One-dimensional Self-gravitating Systems Using Hermite-Legendre Polynomials

The current paradigm for understanding galaxy formation in the universe depends on the existence of self-gravitating collisionless dark matter. Modeling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective nonlinear dynamics of many-particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyze the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase space distribution functions f(x,v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.

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arXiv2012

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 fit by King models. However, for many GCs, especially those with HST-resolved central regions, and `extra-tidal' features, King models provide poor fits. We suggest that this is partly because collisionless dynamics is also important and contribute to shaping the cluster properties. We show using time-scale and length-scale arguments that except for the very centers of clusters, collisionless dynamics should be more important than collisional. We then fit 38 GCs analyzed by Noyola and Gebhardt (2006) 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 ~5x better in term 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.)

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arXiv2012

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 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 Lynden-Bell's 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 Lynden-Bell (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.

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arXiv2011

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.

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arXiv2009

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 a) begins after systems collapse to their most compact configuration and b) 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.

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arXiv2008

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. Semi--analytic models by Barnes et al. (2005) 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 sigma^2/vc^2 is a criterion for instability, where regions with sigma^2/vc^2 <~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 semi--analytic 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.

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arXiv2007

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.

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arXiv2007

Milgrom Relation Models for Spiral Galaxies from Two-Dimensional Velocity Maps

Using two-dimensional velocity maps and I-band photometry, we have created mass models of 40 spiral galaxies using the Milgrom relation (the basis of modified Newtonian dynamics, or MOND) to complement previous work. A Bayesian technique is employed to compare several different dark matter halo models to Milgrom and Newtonian models. Pseudo-isothermal dark matter halos provide the best statistical fits to the data in a majority of cases, while the Milgrom relation generally provides good fits as well. We also find that Milgrom models give mass-to-light ratios that roughly correlate with galaxy color, as predicted by stellar population models. A subsample of galaxies in the Hydra cluster follow a tight relation between mass-to-light and color, but one that is significantly different from relations found in previous studies. Ruling out the Milgrom relation with rotational kinematics is difficult due to systematic uncertainties in the observations as well as underlying model assumptions. We discuss in detail two galaxies for which the Milgrom relation appears to fail and find that relaxing the assumption of constant stellar mass-to-light ratio can maintain Milgrom models' viability.

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arXiv2006

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 rms-velocity distributions do not match one another. The nonextensive rms-velocity profile is either monotonically decreasing or displays little radial variation, each of which disagrees with the rms-velocity distributions seen in simulations. We conclude that the currently discussed nonextensive models require further modifications in order to corroborate dark matter halo simulations. (adapted from TeX)

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arXiv2006

Density Profiles of Collisionless Equilibria. II. Anisotropic Spherical Systems

It has long been realized that dark matter halos formed in cosmological N-body simulations are characterized by density profiles rho(r) that, when suitably scaled, have similar shapes. Additionally, combining the density and velocity dispersion profiles sigma(r), each of which have decidedly nonpower-law shapes, leads to quantity rho/(sigma^3) that is a power-law in radius over 3 orders of magnitude in radius. Halos' velocity anisotropy profiles beta(r) vary from isotropic near the centers of halos to quite radially anisotropic near the virial radius. Finally, there appears to be a nearly linear correlation between beta and the logarithmic density slope gamma for a wide variety of halos. This work is part of a continuing investigation of the above interrelationships and their origins using analytical and semi-analytical techniques. Our finding suggest that the nearly linear beta--gamma relationship is not just another expression of scale-free rho/(sigma^3) behavior. We also note that simultaneously reproducing density and anisotropy profiles like those found in simulations requires beta(r) and gamma(r) to have similar shapes, leading to nearly linear beta--gamma correlations. This work suggests that the beta--gamma and power-law rho/(sigma^3) relations have distinct physical origins.

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arXiv2006

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, $F=\psd \propto r^{-α}$. 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 \psd distributions when in equilibrium. We have also done a preliminary investigation of variables other than $r$ that may match or supercede the correlation with $F$. In the same vein, we show that $ρ/σ^m$, 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 \psd distributions of virialized systems.

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arXiv2005

Semi-analytical dark matter halos and the Jeans equation

Although N-body studies of dark matter halos show that the density profiles, rho(r), are not simple power-laws, the quantity rho/sigma^3, where sigma(r) is the velocity dispersion, is in fact a featureless power-law over ~3 decades in radius. In the first part of the paper we demonstrate, using the semi-analytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of rho/sigma^3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N-body and semi-analytic approaches, we argue that the scale-free nature of rho/sigma^3 cannot be the result of hierarchical merging, rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use rho/sigma^3 proportional to r^{-alpha} as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique ``periodic'' solution with alpha=1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of rho ~ r^{-0.78}, and rho ~ r^{-3.44}, respectively.

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arXiv2004

Mass Models for Spiral Galaxies from 2-D Velocity Maps

We model the mass distributions of 40 high surface brightness spiral galaxies inside their optical radii, deriving parameters of mass models by matching the predicted velocities to observed velocity maps. We use constant mass-to-light disk and bulge models, and we have tried fits with no halo and with three different halo density profiles. The data require a halo in most, but not all, cases, while in others the best fit occurs with negligible mass in the luminous component, which we regard as unphysical. All three adopted halo profiles lead to fits of about the same quality, and our data therefore do not constrain the functional form of the halo profile. The halo parameters display large degeneracies for two of the three adopted halo functions, but the separate luminous and dark masses are better constrained. However, the fitted disk and halo masses vary substantially between the adopted halo models, indicating that even high quality 2-D optical velocity maps do not provide significant constraints on the dark matter content of a galaxy. We demonstrate that data from longslit observations are likely to provide still weaker constraints. We conclude that additional information is needed in order to constrain the separate disk and halo masses in a galaxy.

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