A Redshift Survey of Nearby Galaxy Groups: the Shape of the Mass Density Profile

We constrain the mass profile and orbital structure of nearby groups and clusters of galaxies. Our method yields the joint probability distribution of the density slope n, the velocity anisotropy beta, and the turnover radius r0 for these systems. The measurement technique does not use results from N-body simulations as priors. We incorporate 2419 new redshifts in the fields of 41 systems of galaxies with z < 0.04. The new groups have median velocity dispersion sigma=360 km/s. We also use 851 archived redshifts in the fields of 8 nearly relaxed clusters with z < 0.1. Within R < 2 r200, the data are consistent with a single power law matter density distribution with slope n = 1.8-2.2 for systems with sigma < 470 km/s, and n = 1.6-2.0 for those with sigma > 470 km/s (95% confidence). We show that a simple, scale-free phase space distribution function f(E,L^2) ~ (-E)^(alpha-1/2) L^(-2 \beta) is consistent with the data as long as the matter density has a cusp. Using this DF, matter density profiles with constant density cores (n=0) are ruled out with better than 99.7% confidence.Comment: 22 pages; accepted for publication in the Astrophysical Journa

Distribution function of the dark matter

There is good evidence from N-body simulations that the velocity distribution in the outer parts of halos is radially anisotropic, with the kinetic energy in the radial direction roughly equal to the sum of that in the two tangential directions. We provide a simple algorithm to generate such cosmologically important distribution functions. Introducing r_E(E), the radius of the largest orbit of a particle with energy E, we show how to write down almost trivially a distribution function of the form f(E,L)=g(r_E)/L for any spherical model -- including the NFW profile. We in addition give the generic form of the distribution function for any model with a local density power-law index and anisotropy parameter, and provide limiting forms appropriate for the central parts and envelopes of dark matter halos. From those, we argue that, regardless of the anisotropy, the density fall-off at large radii must evolve to 1/r^4 or steeper ultimately.Comment: to appear in PRD, including 3 figures, typo correcte

Preventing Running Injuries Using a Pre-Running Exercise Program (PREP): A Pilot Study

Hypothesis: An 8 week supervised PREP implemented prior to a 5k running program will reduce the incidence of RRI\u27s among novice runners training for a 5k below the previously published incidence rates

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case $\mu\propto r^{-2}$ for the energy density which arises in many astrophysical applications. In the second class the singularity at the center of the star is not present in the energy density. The models presented in this paper allow for increasing and decreasing profiles in the behavior of the energy density.Comment: 9 pages, to appear in Pramana - J. Phy

The velocity and mass distribution of clusters of galaxies from the CNOC1 cluster redshift survey

In the context of the CNOC1 cluster survey, redshifts were obtained for galaxies in 16 clusters. The resulting sample is ideally suited for an analysis of the internal velocity and mass distribution of clusters. Previous analyses of this dataset used the Jeans equation to model the projected velocity dispersion profile. However, the results of such an analysis always yield a strong degeneracy between the mass density profile and the velocity dispersion anisotropy profile. Here we analyze the full (R,v) dataset of galaxy positions and velocities in an attempt to break this degeneracy. We build an `ensemble cluster' from the individual clusters under the assumption that they form a homologous sequence. To interpret the data we study a one-parameter family of spherical models with different constant velocity dispersion anisotropy. The best-fit model is sought using a variety of statistics, including the overall likelihood of the dataset. Although the results of our analysis depend slightly on which statistic is used to judge the models, all statistics agree that the best-fit model is close to isotropic. This result derives primarily from the fact that the observed grand-total velocity histogram is close to Gaussian, which is not expected to be the case for a strongly anisotropic model. The best-fitting models have a mass-to-number-density ratio that is approximately independent of radius over the range constrained by the data. They also have a mass-density profile that is consistent with the dark matter halo profile advocated by Navarro, Frenk & White, in terms of both the profile shape and the characteristic scale length. This adds important new weight to the evidence that clusters do indeed follow this proposed universal mass density profile. [Abridged]Comment: 37 pages, LaTeX, with 11 PostScript figures. Accepted by the Astronomical Journal, to appear in the May 2000 issue. This replacement version contains an additional Appendix and one additional Figure with respect to the version submitted to astro-ph originall

Compact anisotropic spheres with prescribed energy density

New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav., Vol 21, 899-905, 1989) and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav., Vol 26, 75-84, 1994) as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.Comment: 22 pages, 3 figures, to appear in Gen. Rel. Gra

Anisotropic distribution functions for spherical galaxies

A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral distribution functions for axisymmetric galaxies.Comment: 5 figure

Radial stability of a family of anisotropic Hernquist models with and without a supermassive black hole

We present a method to investigate the radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative supermassive black holes. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the supermassive black hole has a significant effect on the overall stability of the system, i.e. an SBH with a mass of a few percent of the total mass of the galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its mass not only determines the strength of the instability reduction, but also the time in which this occurs. These effects are most significant for models with strong radial anisotropies. Furthermore, our analysis shows that unstable systems with similar SBH but with different anisotropy radii evolve differently: highly radial systems become oblate, while more isotropic models tend to form into prolate structures. In addition to this study, we also present a Monte-Carlo algorithm to generate particles in spherical anisotropic systems.Comment: 16 pages, 12 figures, accepted for publication in MNRAS (some figures have a lowered resolution

Galaxy Models with Tangentially Anisotropic Velocity Distributions

This paper provides two families of flexible and simple galaxy models. Representatives of many of the families possess the important cosmological cusps, with the density behaving like 1/r or 1/r^1.33 or 1/r^1.5 at small radii. The density falls off between 1/r^3 and 1/r^5 at large radii. We provide analytic and anisotropic distribution functions for all the models. Unlike many existing methods, our algorithm can yield tangentially anisotropic velocity dispersions in the outer parts, and so is useful for modeling populations of satellite galaxies and substructure in host galaxy halos. As an application, we demonstrate the degeneracy between mass and anisotropy for the satellite galaxy population of the Milky Way. This can introduce a factor of ~3 uncertainty in the mass of the Milky Way as inferred from the kinematics of the satellite population.Comment: to appear in AJ, extended appendix, typo corrected from the 2nd version (completely rewritten from the 1st version, see also astro-ph/0508419 for some materials split from the 1st version

Dietary experience modifies horses' feeding behavior and selection patterns of three macronutrient rich diets

Choice feeding is often used to investigate an animal’s nutritional requirements and dietary preferences. A problem with this approach is that animals with long gut transit times, such as the horse, may find it difficult to associate a chosen food with its nutritional consequence when alternative foods are presented simultaneously. One solution is to present foods singly for a period of time before a simultaneous choice session to allow the development of learned associations. This method was used to determine if horse’s voluntary intake and feeding behavior was influenced by the macronutrient composition of the diet. Seven stabled horses, maintained on a low intensity exercise regimen, were allowed, on an ad libitum basis, haylage and 3 isocaloric forage based diets that were rich in 1 of 3 macronutrients (protein, lipid, and hydrolyzable carbohydrate). Initially, diets were presented as a 3-way choice for 5 d (self-selection a [SSa]), then singly (monadic phase) with exposure to each diet for 2 separate periods of 3 d each, and finally again as a choice for 5 d (self-selection b [SSb]). The total amount of trial diet offered differed with trial phase, with 2 to 2.5% of BW during SSa and the monadic phase, increasing to ad libitum access during SSb. To control differences in the total amount of trial diet offered, 2 measurements of voluntary intake were taken at 4 and 22 h postpresentation. Daily macronutrient and energy intakes were estimated from proximate analysis of the trial diets and batches of haylage fed. Feeding behavior was observed over a single 4-h period during both self-selection phases. Horses showed no initial preference after 4 h for any 1 diet during SSa. Following the monadic phase, horses demonstrated a preference for the protein and hydrolyzable carbohydrate rich diets over the lipid rich diet (P < 0.001). Dietary experience modified foraging behavior as the total number of visits to the diets decreased during SSb (P < 0.005). Analysis of 24 -h macronutrient consumption showed that protein and hydrolyzable carbohydrate intake increased during SSb, whereas lipid intake remained constant over both self-selection phases (P < 0.001). These data indicate for perhaps the first time that horses can respond to dietary macronutrient content and that single presentations during choice studies facilitates expression of dietary preferences