Balsa Terzic

Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models

We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N-body dark matter halos. We consider halos generated from ΛCDM simulations of gravitational clustering, as well as isolated spherical collapses. The logarithmic density slopes γ ≡ d log ρ/d log r of the ΛCDM halos are found to vary as power laws in radius, reaching values of γ ≈ -1 at the innermost resolved radii, ~10-2rvir. This behavior is significantly different from that of broken-power-law models like the Navarro-Frenk-White (NFW) profile but similar to that of models like de Vaucouleurss. Accordingly, we compare the N-body density profiles with various parametric models to find which provide the best fit. We consider an NFW-like model with arbitrary inner slope; Dehnen & McLaughlins anisotropic model; Einastos model (identical in functional form to Sersics model but fitted to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sersics R1/n law. Overall, the best-fitting model to the ΛCDM halos is Einastos, although the Prugniel-Simien and Dehnen-McLaughlin models also perform well. With regard to the spherical-collapse halos, both the Prugniel-Simien and Einasto models describe the density profiles well, with an rms scatter some 4 times smaller than that obtained with either the NFW-like model or the three-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass.

Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ρ/σ 3

We have recently shown that both the Prugniel-Simien model and Sersics function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than a Navarro-Frenk-White-like model with an equal number of parameters. Here we provide analytical expressions for the logarithmic slopes of these models and compare them with data from real galaxies. Depending on the Einasto parameters of the dark matter halo, one can expect an extrapolated inner (0.01-1 kpc) logarithmic profile slope ranging from approximately -0.2 to approximately -1.5, with a typical value at 0.1 kpc around -0.7. Application of this (better fitting) model therefore alleviates some of the past disagreement with observations on this issue. In addition, we provide useful expressions for the concentration and assorted scale radii: rs, r-2, re, Re, rvir, and rmax, the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of ρ(r)/σ(r)3 for both the Einasto and Prugniel-Simien models, where σ(r) is the velocity dispersion associated with the density profile ρ(r). We find this representation of the phase-space density profile to be well approximated by a power law with a slope slightly shallower than -2 near r = r-2.

Empirical Models for Dark Matter Halos. III. The Kormendy Relation and the log ρ e -log R e Relation

We have recently shown that the three-parameter density profile model from Prugniel & Simien provides a better fit to simulated galaxy- and cluster-sized dark matter halos than an Navarro-Frenk-White-like model with arbitrary inner profile slope γ (Paper I). By construction, the parameters of the Prugniel-Simien model equate to those of the Sersic R1/n function fitted to the projected distribution. Using the Prugniel-Simien model we are therefore able to show that the location of simulated (1012 M⊙) galaxy-sized dark matter halos in the μe- log Re diagram coincides with that of the brightest cluster galaxies, i.e.; the dark matter halos appear consistent with the Kormendy relation defined by luminous elliptical galaxies. These objects are also seen to define the new, and equally important, relation log(ρe) = 0.5 - 2.5 log(Re), in which ρe is the internal density at r = Re. Simulated (1014.5 M⊙) cluster-sized dark matter halos and the gas component of real galaxy clusters follow the relation log(ρe) = 2.5[1 - log(Re)]. Given the shapes of the various density profiles, we are able to conclude that while dwarf elliptical galaxies and galaxy clusters can have dark matter halos with effective radii of comparable size to the effective radii of their baryonic component, luminous elliptical galaxies cannot. For increasingly large elliptical galaxies, with increasingly large profile shapes n, to be dark-matter-dominated at large radii requires dark matter halos with increasingly large effective radii compared to the effective radii of their stellar components.

Density–potential pairs for spherical stellar systems with Sérsic light profiles and (optional) power-law cores

Popular models for describing the luminosity-density profiles of dynamically hot stellar systems (e.g. Jaffe, Hemquist, Dehnen) were constructed with the desire to match the deprojected form of an R 1/4 light profile. Real galaxies, however, are now known to have a range of different light-profile shapes that scale with mass. Consequently, although highly useful, the above models have implicit limitations, and this is illustrated here through their application to a number of real galaxy density profiles. On the other hand, the analytical density profile given by Prugniel & Simien closely matches the deprojected form of Sersic R 1/n light profiles - including deprojected exponential light profiles. It is thus applicable for describing bulges in spiral galaxies, dwarf elliptical galaxies, and both ordinary and giant elliptical galaxies. Moreover, the observed Sersic quantities define the parameters of the density model. Here we provide simple equations, in terms of elementary and special functions, for the gravitational potential and force associated with this density profile. Furthermore, to match galaxies with partially depleted cores, and better explore the supermassive black hole/galaxy connection, we have added a power-law core to this density profile and derived similar expressions for the potential and force of this hybrid profile. Expressions for the mass and velocity dispersion, assuming isotropy, are also given. These spherical models may also prove appropriate for describing the dark matter distribution in haloes formed from ACDM cosmological simulations.

Supermassive Black Hole Binaries as Galactic Blenders

This paper focuses on the dynamical implications of close supermassive black hole binaries both as an example of resonant phase mixing and as a potential explanation of inversions and other anomalous features observed in the luminosity profiles of some elliptical galaxies. The presence of a binary comprised of black holes executing nearly periodic orbits leads to the possibility of a broad resonant coupling between the black holes and various stars in the galaxy. This can result in efficient chaotic phase mixing and, in many cases, systematic increases in the energies of stars and their consequent transport toward larger radii. Allowing for a supermassive black hole binary with plausible parameter values near the center of a spherical, or nearly spherical, galaxy characterized initially by a Nuker density profile enables one to reproduce in considerable detail the central surface brightness distributions of such galaxies as NGC 3706.

Orbital structure in oscillating galactic potentials

Subjecting a galactic potential to (possibly damped) nearly periodic, time-dependent variations can lead to large numbers of chaotic orbits experiencing systematic changes in energy, and the resulting chaotic phase mixing could play an important role in explaining such phenomena as violent relaxation. This paper focuses on the simplest case of spherically symmetric potentials subjected to strictly periodic driving with the aim of understanding precisely why orbits become chaotic and under what circumstances they will exhibit systematic changes in energy. Four unperturbed potentials V 0(r) were considered, each subjected to a time dependence of the form V(r, t) = V 0(r)(1 + m0 sin ωt). In each case, the orbits divide clearly into regular and chaotic, distinctions which appear absolute. In particular, transitions from regularity to chaos are seemingly impossible. Over finite time intervals, chaotic orbits subdivide into what can be termed ‘sticky’ chaotic orbits, which exhibit no large-scale secular changes in energy and remain trapped in the phase-space region where they started; and ‘wildly’ chaotic orbits, which do exhibit systematic drifts in energy as the orbits diffuse to different phase-space regions. This latter distinction is not absolute, transitions corresponding apparently to orbits penetrating a ‘leaky’ phase-space barrier. The three different orbit types can be identified simply in terms of the frequencies for which their Fourier spectra have the most power. An examination of the statistical properties of orbit ensembles as a function of driving frequency ω allows us to identify the specific resonances that determine orbital structure. Attention focuses also on how, for fixed amplitude m0, such quantities as the mean energy shift, the relative measure of chaotic orbits and the mean value of the largest Lyapunov exponent vary with driving frequency ω; and how, for fixed ω, the same quantities depend on m0.

Narrow-band emission in Thomson sources operating in the high-field regime.

We present a novel and quite general analysis of the interaction of a high-field chirped laser pulse and a relativistic electron, in which exquisite control of the spectral brilliance of the up-shifted Thomson-scattered photon is shown to be possible. Normally, when Thomson scattering occurs at high field strengths, there is ponderomotive line broadening in the scattered radiation. This effect makes the bandwidth too large for some applications and reduces the spectral brilliance. We show that such broadening can be corrected and eliminated by suitable frequency modulation of the incident laser pulse. Furthermore, we suggest a practical realization of this compensation idea in terms of a chirped-beam-driven free electron laser oscillator configuration and show that significant compensation can occur, even with the imperfect matching to be expected in these conditions.

An Efficient Deterministic Parallel Algorithm for Adaptive Multidimensional Numerical Integration on GPUs

Recent development in Graphics Processing Units (GPUs) has enabled a new possibility for highly efficient parallel computing in science and engineering. Their massively parallel architecture makes GPUs very effective for algorithms where processing of large blocks of data can be executed in parallel. Multidimensional integration has important applications in areas like computational physics, plasma physics, computational fluid dynamics, quantum chemistry, molecular dynamics and signal processing. The computationally intensive nature of multidimensional integration requires a high-performance implementation. In this study, we present an efficient deterministic parallel algorithm for adaptive multidimensional numerical integration on GPUs. Various optimization techniques are applied to maximize the utilization of the GPU. GPU-based implementation outperforms the best known sequential methods and achieves a speed-up of up to 100. It also shows good scalability with the increase in dimensionality.

Semi-analytic estimates of Lyapunov exponents in lower-dimensional systems

Abstract Statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable estimates of Lyapunov exponents χ in lower-dimensional Hamiltonian systems. This Letter explores the assumptions incorporated into these arguments. The predicted χ s are insensitive to most details, but do depend sensitively on the nongeneric form of the auto-correlation function characterising the time-dependence of an orbit. This dependence on dynamics implies a fundamental limitation to the application of thermodynamic arguments to lower-dimensional systems.

A memory efficient algorithm for adaptive multidimensional integration with multiple GPUs

We present a memory-efficient algorithm and its implementation for solving multidimensional numerical integration on a cluster of compute nodes with multiple GPU devices per node. The effective use of shared memory is important for improving the performance on GPUs, because of the bandwidth limitation of the global memory. The best known sequential algorithm for multidimensional numerical integration CUHRE uses a large dynamic heap data structure which is accessed frequently. Devising a GPU algorithm that caches a part of this data structure in the shared memory so as to minimizes global memory access is a challenging task. The algorithm presented here addresses this problem. Furthermore we propose a technique to scale this algorithm to multiple GPU devices. The algorithm was implemented on a cluster of Intel® Xeon® CPU X5650 compute nodes with 4 Tesla M2090 GPU devices per node. We observed a speedup of up to 240 on a single GPU device as compared to a speedup of 70 when memory optimization was not used. On a cluster of 6 nodes (24 GPU devices) we were able to obtain a speedup of up to 3250. All speedups here are with reference to the sequential implementation running on the compute node.