Radio mini-halos and AGN heating in cool core clusters of galaxies

The brightest cluster galaxy (BCG) in the majority of relaxed, cool core galaxy clusters is radio loud, showing non-thermal radio jets and lobes ejected by the central active galactic nucleus (AGN). Such relativistic plasma has been unambiguously shown to interact with the surrounding thermal intra-cluster medium (ICM) thanks to spectacular images where the lobe radio emission is observed to fill the cavities in the X-ray-emitting gas. This `radio-mode AGN feedback' phenomenon, which is thought to quench cooling flows, is widespread and is critical to understand the physics of the inner regions of galaxy clusters and the properties of the central BCG. At the same time, mechanically-powerful AGN are likely to drive turbulence in the central ICM which may contribute to gas heating and also play a role for the origin of non-thermal emission on cluster-scales. Diffuse non-thermal emission has been observed in a number of cool core clusters in the form of a radio mini-halo surrounding the radio-loud BCG on scales comparable to that of the cooling region. This contribution outlines the main points covered by the talk on these topics. In particular, after summarizing the cooling flow regulation by AGN heating and the non-thermal emission from cool core clusters, we present a recent study of the largest collection of known mini-halo clusters (~ 20 objects) which investigated the scenario of a common origin of radio mini-halos and gas heating. We further discuss the prospects offered by future radio surveys with the Square Kilometre Array (SKA) for building large (>> 100 objects), unbiased mini-halo samples while probing at the same time the presence of radio-AGN feedback in the host clusters.Comment: 8 pages, 3 figures. Conference proceeding of "The many facets of extragalactic radio surveys: towards new scientific challenges", 20-23 October 2015, Bologna, Ital

Limit cycles for a class of quintic Z6−\mathbb{Z}_6-equivariant systems without infinite critical points

We analyze the dynamics of a 4-parameter family of planar ordinary differential equations, given by a polynomial of degree 5 that is equivariant under a symmetry of order 6. We obtain the number of limit cycles as a function of the parameters, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points. The method used is the reduction of the problem to an Abel equation

His Name Was Don Francisco Muro: Reconstructing an Image of American Imperialism

Visual culture played a significant role in the debates surrounding American colonialism in the Philippines in the early twentieth century. One of the most important photographers working the Philippines at that time was Dean Conant Worcester, who also served as a colonial administrator. Worcester\u27s three-part sequence of photographs supposedly showing an Igorot man becoming civilized through his contact with Americans is one of the more iconic sets of images from that time period. In recent years, many historians have reprinted the Igorot sequence to illustrate American imperial ideologies. However, neither the identity of the subject, nor the circumstances surrounding the creating of the sequence has been published, and different historians have traced the sequence to different points of origin. Understanding the history of the sequence provides a way to better understand both the history of American colonialism in the Philippines and the challenges of using photographs as historical evidence

Tomographic three-dimensional seismic velocity structure of the SW Ibero-Maghrebian region

The present tomographic study focuses on SW Ibero-Maghrebian region. To locate the seismic events and find the local velocity structure of epicentral area, the P and S arrivals at 42 stations located at north of Morocco, south of Portugal and Spain are used. The arrival times data used, in this study, were obtained by the “Instituto de Meteorologia” (IM, Lisbon, Portugal), the National Institute of Geophysics (CNRST, Rabat, Morocco) and the “Instituto Geografico Nacional” (IGN, Madrid, Spain) (between 12/1988 and 30/2008). The preliminary estimate of origin times and hypocentral coordinates are determined by the hypocenter 3.2 program. In this study we use a linearized inversion procedure comprising two steps: 1) finding the minimal 1-D model and simultaneous reloca- tion of hypocenters and 2) determination of local velocity structure assuming a continuous velocity field. The earth structure is represented in three dimensions by velocity at discrete points, and velocity at any intervening point is determined by linear interpolation among the surrounding eight grid points. The resolutions tests results indicate that the calculated images give near true structure for the studied region at 15, 30, 45 and 60 km depth. At 5km depth it gives near true structure in the continental region of Portugal, Spain, and Morocco. This study shows that the total crustal thickness varies from 30 to 35 km and contains low-velocity anomalies. A prominent low velocity anomaly that shows a maximum decrease in P-wave velocity of approximately 6 per cent in the Gibraltar region is observed extending down to a depth of approximately 30 km. This low velocity demarcates a small bloc located between Iberia and Nubia plates. The resulting tomographic image has a prominent high velocity anomaly that shows a maximum increase in P-wave velocity of approximately 6 per cent between 45 to 60 km depth beneath South of Portugal and the Golf of Cadiz. High-velocity anomalies could be associated with the location of deep active faults in the uplift and upper crust of South of Portugal. In the Golf of Cadiz, these anomalies could be associated with the seismogenic zone and probably more at the south with the Iberia-Nubia plate boundary

Imaging 3D seismic velocity along the seismogenic zone of Algarve region (southern Portugal)

The present seismic tomographic study is focused around Algarve region, in South of Portugal. To locate the seismic events and find the local velocity structure of epicentral area, the P and S arrival times at 38 stations are used. The data used in this study were obtained during the Algarve campaign which worked from January/2006 to July/2007. The preliminary estimate of origin times and hypocentral coordinates are determined by the Hy- poinverse program. Linearized inversion procedure was applied to comprise the following two steps: 1) finding the minimum 1D velocity model using Velest and 2) simultaneous relocation of hypocenters and determination of local velocity structure. The velocity model we have reached is a 10 layer model which gave the lowest RMS, after several runnings of eight different velocity models that we used “a priori”. The model parameterization assumes a continuous velocity field between 4.5 km/s and 7.0 km/s until 30 km depth. The earth structure is represented in 3D by velocity at discrete points, and velocity at any intervening point is determined by linear interpolation among the surrounding eight grid points. A preliminary analysis of the resolution capabilities of the dataset, based on the Derivative Weight Sum (DWS) distribution, shows that the velocity structure is better resolved in the West part of the region between the surface to15 km. The resulting tomographic image has a prominent low-velocity anomaly that shows a maximum decrease in P-wave velocity in the first 12 kms in the studied region. We also identified the occurrence of local seismic events of reduced magnitude not catalogued, in the neighbourhood of Almodôvar (low Alentejo). The spatial distribution of epicentres defines a NE-SW direction that coincides with the strike of the mapped geological faults of the region and issued from photo-interpretation. Is still expectable to refine the seismicity of the region of Almodôvar and establish more rigorously its role in the seismotectonic picture of the region. This work is expected to produce a more detailed knowledge of the structure of the crust over the region of Algarve, being able to identify seismogenic zones, potentially generators of significant seismic events and also the identification of zones of active faults

The general Li\'enard polynomial system

In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles surrounding a unique singular point for an arbitrary polynomial system. Then, by means of the same bifurcationally geometric approach, we solve the limit cycle problem for a general Li\'enard polynomial system with an arbitrary (but finite) number of singular points. This is related to the solution of Hilbert's sixteenth problem on the maximum number and relative position of limit cycles for planar polynomial dynamical systems.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:math/061114

Dynamical invariants and parameter space structures for rational maps

For parametrized families of dynamical systems, two major goals are classifying the systems up to topological conjugacy, and understanding the structure of the bifurcation locus. The family Fλ = z^n + λ/z^d gives a 1-parameter, n+d degree family of rational maps of the Riemann sphere, which arise as singular perturbations of the polynomial z^n. This work presents several results related to these goals for the family Fλ, particularly regarding a structure of "necklaces" in the λ parameter plane. This structure consists of infinitely many simple closed curves which surround the origin, and which contain postcritically finite parameters of two types: superstable parameters and escape time Sierpinski parameters. First, we derive a dynamical invariant to distinguish the conjugacy classes among the superstable parameters on a given necklace, and to count the number of conjugacy classes. Second, we prove the existence of a deeper fractal system of "subnecklaces," wherein the escape time Sierpinski parameters on the previously known necklaces are themselves surrounded by infinitely many necklaces