Related papers: Angular Projections of Fractal Sets
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and…
Gravitational microlensing has proven to be a powerful tool in the study of quasars, providing some of the strongest limits on the scales of structure in the central engine. Typically sources are considered to be smoothly varying on some…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
In this lecture we will try to address the "frequently asked questions about fractals" in the field of large scale galaxy distribution. This paper takes its origin from a very interesting discussion we had at this meeting. A lot of points…
We study an extreme scenario of the Mastrand projection theorem for which a fractal has the property that its orthogonal projection is the same as the orthogonal projection of its convex hull. We extend results in current literature and…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
A standard method to study the mass distribution in galaxy clusters is through strong lensing of background galaxies in which the positions of multiple images of the same source constrain the surface mass distribution of the cluster.…
Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
We study the projection effects on various observables of clusters of galaxies at redshift near zero, including cluster richness, velocity dispersion, X-ray luminosity, three total mass estimates (velocity-based, temperature-based and…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
This paper - the first of a short series dedicated to the long-stan ding astronomical problem of de-projecting the bi-dimensional apparent morpholog y of a three-dimensional mass of gas - focuses on the density distribution in real…
Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the mass distribution of cluster galaxies and potentially to test the extent of their dark matter halos as a function of the…
We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The…
In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal…
Weak gravitational lensing has become an important method to determine the masses of galaxy clusters. The intrinsic shapes of the galaxies are a dominant source of uncertainty, but there are other limitations to the precision that can be…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…