6,747 research outputs found
The ROSAT-ESO Flux-Limited X-Ray (REFLEX) Galaxy Cluster Survey VI: Constraints on the cosmic matter density from the KL power spectrum
The Karhunen-Lo\'{e}ve (KL) eigenvectors and eigenvalues of the sample
correlation matrix are used to analyse the spatial fluctuations of the REFLEX
clusters of galaxies. The method avoids the disturbing effects of correlated
power spectral densities which affects all previous cluster measurements on Gpc
scales. Comprehensive tests use a large set of independent REFLEX-like mock
cluster samples extracted from the Hubble Volume Simulation. It is found that
unbiased measurements on Gpc scales are possible with the REFLEX data. The
distribution of the KL eigenvalues are consistent with a Gaussian random field
on the 93.4% confidence level. Assuming spatially flat cold dark matter models,
the marginalization of the likelihood contours over different sample volumes,
fiducial cosmologies, mass/X-ray luminosity relations and baryon densities,
yields the 95.4% confidence interval for the matter density of
. The N-body simulations show that cosmic variance,
although difficult to estimate, is expected to increase the confidence
intervals by about 50%.Comment: 11 pages, 7 figures, accepted for publication in MNRA
A study of temporary captures and collisions in the Circular Restricted Three-Body Problem with normalizations of the Levi-Civita Hamiltonian
The dynamics near the Lagrange equilibria and of the Circular
Restricted Three-body Problem has gained attention in the last decades due to
its relevance in some topics such as the temporary captures of comets and
asteroids and the design of trajectories for space missions. In this paper we
investigate the temporary captures using the tube manifolds of the horizontal
Lyapunov orbits originating at and of the CR3BP at energy values
which have not been considered so far. After showing that the radius of
convergence of any Hamiltonian normalization at or computed with
the Cartesian variables is limited in amplitude by (
denoting the reduced mass of the problem), we investigate if regularizations
allow us to overcome this limit. In particular, we consider the Hamiltonian
describing the planar three-body problem in the Levi-Civita regularization and
we compute its normalization for the Sun-Jupiter reduced mass for an interval
of energy which overcomes the limit of Cartesian normalizations. As a result,
for the largest values of the energy that we consider, we notice a transition
in the structure of the tubes manifolds emanating from the Lyapunov orbit,
which can contain orbits that collide with the secondary body before performing
one full circulation around it. We discuss the relevance of this transition for
temporary captures.Comment: 17 pages, 9 figures. v1: original preprint. v2: author's accepted
manuscript. To appear in International Journal of Non-Linear Mechanic
- …