Extended Hodge Theory for Fibred Cusp Manifolds

For a particular class of pseudo manifolds, we show that the intersection cohomology groups for any perversity may be naturally represented by extended weighted $L^2$ harmonic forms for a complete metric on the regular stratum with respect to some weight determined by the perversity. Extended weighted $L^2$ harmonic forms are harmonic forms that are almost in the given weighted $L^2$ space for the metric in question, but not quite. This result is akin to the representation of absolute and relative cohomology groups for a manifold with boundary by extended harmonic forms on the associated manifold with cylindrical ends. As in that setting, in the unweighted $L^2$ case, the boundary values of the extended harmonic forms define a Lagrangian splitting of the boundary space in the long exact sequence relating upper and lower middle perversity intersection cohomology groups.Comment: 26 page

Self-Generated Magnetic Fields in Galactic Cooling Flows

Interstellar magnetic fields in elliptical galaxies are assumed to have their origin in stellar fields that accompany normal mass loss from an evolving population of old stars. The seed fields are amplified by interstellar turbulence driven by stellar mass loss and supernova events. These disordered fields are further amplified by time-dependent compression in the inward moving galactic cooling flow and are expected to dominate near the galactic core. Under favorable circumstances, fields similar in strength to those observed $B \sim 1-10~(r/10~kpc)^{-1.2}\mu$G can be generated solely from these natural galactic processes. In general the interstellar field throughout elliptical galaxies is determined by the outermost regions in the interstellar gas where the turbulent dynamo process can occur. Because of the long hydrodynamic flow times in galactic cooling flows, currently observed magnetic fields may result from periods of intense turbulent field amplification that occurred in the outer galaxy in the distant past. Particularly strong fields in ellipticals may result from ancient galactic mergers or shear turbulence introduced at the boundary between the interstellar gas and ambient cluster gas.Comment: 21 pages in AASTEX LaTeX with 2 figures; accepted by Astrophysical Journa

Shear-Flow Driven Current Filamentation: Two-Dimensional Magnetohydrodynamic Simulations

The process of current filamentation in permanently externally driven, initially globally ideal plasmas is investigated by means of two-dimensional Magnetohydrodynamic (MHD)-simulations. This situation is typical for astrophysical systems like jets, the interstellar and intergalactic medium where the dynamics is dominated by external forces. Two different cases are studied. In one case, the system is ideal permanently and dissipative processes are excluded. In the second case, a system with a current density dependent resistivity is considered. This resistivity is switched on self-consistently in current filaments and allows for local dissipation due to magnetic reconnection. Thus one finds tearing of current filaments and, besides, merging of filaments due to coalescence instabilities. Energy input and dissipation finally balance each other and the system reaches a state of constant magnetic energy in time.Comment: 32 Pages, 13 Figures. accepted, to appear in Physics of Plasmas (049012

A Radio Polarimetric Study of the Galactic Center Threads

Multi-frequency, polarimetric VLA observations of the non-thermal filaments (NTF's), G0.08+0.15, and G359.96+0.09, also known as the Northern and Southern Threads are presented at 20, 6, 3.6 and 2 cm, with high enough spatial resolution to be resolved for the first time at 6 and 3.6 cm. The 20 cm image reveals a wealth of new detail in the radio sources lying within the inner 60 pc of the Galaxy. The Southern Thread has a prominent split along its length, similar to splitting at the ends of previously studied NTF's. With resolutions as fine as 2'', the 3.6 and 6 cm images reveal a high degree of continuity and little substructure internal to the filament. The spectral index of the Northern Thread has been determined over a broad range of frequencies. Its flux density falls with frequency, alpha=-0.5 between 90 and 6 cm, and becomes much steeper (alpha=-2.0) between 6 and 2 cm. The spectral index does not vary significantly along the length of the Northern Thread, which implies either that the diffusion timescale for the emitting electrons is less than their synchrotron lifetime, or that the emitting electrons are reaccelerated continuously at multiple positions along the filament. Because of the lack of spectral index variation, we have not located the source of relativistic electrons. Polarization observations at 6 and 3.6 cm confirm the non-thermal nature of the emission from the Northern Thread. The fractional polarization in the Northern Thread reaches 70% in some regions, although the polarized emission is patchy. Large rotation measures (RM > 2000 rad/m2) have been observed with irregular variations across the filament.The intrinsic magnetic field in the Northern Thread is predominantly aligned along its long axis.Comment: 19 pages, incl. 24 figs; to appear in the Astrophysical Journa

Particle Acceleration in three dimensional Reconnection Regions: A New Test Particle Approach

Magnetic Reconnection is an efficient and fast acceleration mechanism by means of direct electric field acceleration parallel to the magnetic field. Thus, acceleration of particles in reconnection regions is a very important topic in plasma astrophysics. This paper shows that the conventional analytical models and numerical test particle investigations can be misleading concerning the energy distribution of the accelerated particles, since they oversimplify the electric field structure by the assumption that the field is homogeneous. These investigations of the acceleration of charged test particles are extended by considering three-dimensional field configurations characterized by localized field-aligned electric fields. Moreover, effects of radiative losses are discussed. The comparison between homogeneous and inhomogeneous electric field acceleration in reconnection regions shows dramatic differences concerning both, the maximum particle energy and the form of the energy distribution.Comment: 11 pages, 21 figure

Shuffle relations for regularised integrals of symbols

We prove shuffle relations which relate a product of regularised integrals of classical symbols to regularised nested (Chen) iterated integrals, which hold if all the symbols involved have non-vanishing residue. This is true in particular for non-integer order symbols. In general the shuffle relations hold up to finite parts of corrective terms arising from renormalisation on tensor products of classical symbols, a procedure adapted from renormalisation procedures on Feynman diagrams familiar to physicists. We relate the shuffle relations for regularised integrals of symbols with shuffle relations for multizeta functions adapting the above constructions to the case of symbols on the unit circle.Comment: 40 pages,latex. Changes concern sections 4 and 5 : an error in section 4 has been corrected, and the link between section 5 and the previous ones has been precise

Inflation-Produced Magnetic Fields in Nonlinear Electrodynamics

We study the generation of primeval magnetic fields during inflation era in nonlinear theories of electrodynamics. Although the intensity of the produced fields strongly depends on characteristics of inflation and on the form of electromagnetic Lagrangian, our results do not exclude the possibility that these fields could be astrophysically interesting.Comment: 6 page

Non-thermal Processes in Black-Hole-Jet Magnetospheres

The environs of supermassive black holes are among the universe's most extreme phenomena. Understanding the physical processes occurring in the vicinity of black holes may provide the key to answer a number of fundamental astrophysical questions including the detectability of strong gravity effects, the formation and propagation of relativistic jets, the origin of the highest energy gamma-rays and cosmic-rays, and the nature and evolution of the central engine in Active Galactic Nuclei (AGN). As a step towards this direction, this paper reviews some of the progress achieved in the field based on observations in the very high energy domain. It particularly focuses on non-thermal particle acceleration and emission processes that may occur in the rotating magnetospheres originating from accreting, supermassive black hole systems. Topics covered include direct electric field acceleration in the black hole's magnetosphere, ultra-high energy cosmic ray production, Blandford-Znajek mechanism, centrifugal acceleration and magnetic reconnection, along with the relevant efficiency constraints imposed by interactions with matter, radiation and fields. By way of application, a detailed discussion of well-known sources (Sgr A*; Cen A; M87; NGC1399) is presented.Comment: invited review for International Journal of Modern Physics D, 49 pages, 15 figures; minor typos corrected to match published versio