67,475 research outputs found
The core size of the Fornax dwarf Spheroidal
We exploit the detection of three distinct stellar subpopulations in the red
giant branch of the Fornax dwarf Spheroidal to probe its density distribution.
This allows us to resolve directly the evolution with radius of the dark matter
mass profile. We find that a cored dark matter halo provides a perfect fit to
the data, being consistent with all three stellar populations well within
1-sigma, and for the first time we are able to put constraints on the core size
of such a halo. With respect to previous work, we do not strengthen the
statistical exclusion of a dark matter cusp in Fornax, but we find that
Navarro-Frenk-White haloes would be required to have unrealistically large
scale radii in order to be compatible with the data, hence low values of the
concentration parameter. We are then forced to conclude that the Fornax dwarf
Spheroidal sits within a dark matter halo having a constant density core, with
a core size of between 0.6 and 1.8 kpc.Comment: MNRAS Letters, submitte
Hamiltonians of Spherically Symmetric, Scale-Free Galaxies in Action-Angle Coordinates
We present a simple formula for the Hamiltonian in terms of the actions for
spherically symmetric, scale-free potentials. The Hamiltonian is a power-law or
logarithmic function of a linear combination of the actions. Our expression
reduces to the well-known results for the familiar cases of the harmonic
oscillator and the Kepler potential. For other power-laws, as well as for the
singular isothermal sphere, it is exact for the radial and circular orbits, and
very accurate for general orbits. Numerical tests show that the errors are
always small, with mean errors across a grid of actions always less than 1 %
and maximum errors less than 2.5 %. Simple first-order corrections can reduce
mean errors to less than 0.6 % and maximum errors to less than 1 %. We use our
new result to show that :[1] the misalignment angle between debris in a stream
and a progenitor is always very nearly zero in spherical scale-free potentials,
demonstrating that streams can be sometimes well approximated by orbits, [2]
the effects of an adiabatic change in the stellar density profile in the inner
regions of a galaxy weaken any existing 1/r density cusp, which is reduced to
. More generally, we derive the full range of adiabatic cusp
transformations and show how to relate the starting cusp index to the final
cusp index. It follows that adiabatic transformations can never erase a dark
matter cusp.Comment: 6 pages, MNRAS, in pres
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A review of the Yorkshire and Humber regional waste strategy
Managing waste has become a primary issue for regional planners. This article reports on the institutional process underpinning the region’s strategy and the stages in its production. It emphasises that there has been a watering down of the target for household waste production without appropriate explanation
Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials
There are several common ways to encode a tree as a matrix, such as the
adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of
the natural random walk), and the matrix of pairwise distances between leaves.
Such representations involve a specific labeling of the vertices or at least
the leaves, and so it is natural to attempt to identify trees by some feature
of the associated matrices that is invariant under relabeling. An obvious
candidate is the spectrum of eigenvalues (or, equivalently, the characteristic
polynomial). We show for any of these choices of matrix that the fraction of
binary trees with a unique spectrum goes to zero as the number of leaves goes
to infinity. We investigate the rate of convergence of the above fraction to
zero using numerical methods. For the adjacency and Laplacian matrices, we show
that that the {\em a priori} more informative immanantal polynomials have no
greater power to distinguish between trees
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