68 research outputs found
Generation of potential/surface density pairs in flat disks Power law distributions
We report a simple method to generate potential/surface density pairs in flat
axially symmetric finite size disks. Potential/surface density pairs consist of
a ``homogeneous'' pair (a closed form expression) corresponding to a uniform
disk, and a ``residual'' pair. This residual component is converted into an
infinite series of integrals over the radial extent of the disk. For a certain
class of surface density distributions (like power laws of the radius), this
series is fully analytical. The extraction of the homogeneous pair is
equivalent to a convergence acceleration technique, in a matematical sense. In
the case of power law distributions, the convergence rate of the residual
series is shown to be cubic inside the source. As a consequence, very accurate
potential values are obtained by low order truncation of the series. At zero
order, relative errors on potential values do not exceed a few percent
typically, and scale with the order N of truncation as 1/N**3. This method is
superior to the classical multipole expansion whose very slow convergence is
often critical for most practical applications.Comment: Accepted for publication in Astronomy & Astrophysics 7 pages, 8
figures, F90-code available at
http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2applawd.htm
Changes in Achilles Tendon Thickness Following a 10 – Week Heavy Load Eccentric Exercise Program
Achilles tendinopathy (AT) is a common overuse injury in running or jumping activities where the tendon is unable to properly respond to the load. AT increases tendon thickness while decreasing stiffness and function (1).
Studies have shown that tendon properties can be positively influenced by load (5,6). Therefore, AT has typically been treated conservatively through physical therapy, with eccentric calf strengthening exercises as the focus of the treatment (2)
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
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 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
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
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
Galactic kinematics with modified Newtonian dynamics
We look for observational signatures that could discriminate between
Newtonian and modified Newtonian (MOND) dynamics in the Milky Way, in view of
the advent of large astrometric and spectroscopic surveys. Indeed, a typical
signature of MOND is an apparent disk of "phantom" dark matter, which is
uniquely correlated with the visible disk-density distribution. Due to this
phantom dark disk, Newtonian models with a spherical halo have different
signatures from MOND models close to the Galactic plane. The models can thus be
differentiated by measuring dynamically (within Newtonian dynamics) the disk
surface density at the solar radius, the radial mass gradient within the disk,
or the velocity ellipsoid tilt angle above the Galactic plane. Using the most
realistic possible baryonic mass model for the Milky Way, we predict that, if
MOND applies, the local surface density measured by a Newtonist will be
approximately 78 Msun/pc2 within 1.1 kpc of the Galactic plane, the dynamically
measured disk scale-length will be enhanced by a factor of 1.25 with respect to
the visible disk scale-length, and the local vertical tilt of the velocity
ellipsoid at 1 kpc above the plane will be approximately 6 degrees. None of
these tests can be conclusive for the present-day accuracy of Milky Way data,
but they will be of prime interest with the advent of large surveys such as
GAIA.Comment: 5 page
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
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
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