Stimulated Raman scattering of water maser lines in astrophysical plasmas

Radiative transfer equations are derived and solved for the stimulated Raman scattering of water maser lines in the astrophysical plasmas with electron density of about 10^6 - 10^7 cm-3. In stimulated Raman scattering, the energy of water maser line is transferred to the side band modes: Stokes mode and anti-Stokes mode. The Stokes mode is easily produced by backward Raman scattering while the anti-Stokes mode is created by the interacting intersecting masers in the plasma. The intensity of the Stokes mode is higher than that of the anti-Stokes mode. These side band modes are proposed as explanation for the extreme velocity features observed in the galaxy NGC 4258. The threshold value of the brightness temperature for the Raman scattering is about 10^16 - 10^19 K, and it is satisfied in the case of NGC 4258.Comment: 12 pages, 4 Postscript figures. Accepted for Physics of Plasma

Fredholm conditions for invariant operators: finite abelian groups and boundary value problems

We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth, compact, manifold $M$ without boundary and let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical, pseudodifferential operator acting between sections of two $\Gamma$-equivariant vector bundles $E_0$ and $E_1$. Let $\alpha$ be an irreducible representation of the group $\Gamma$. Then $P$ induces by restriction a map $\pi_\alpha(P) : H^s(M; E_0)_\alpha \to H^{s-m}(M; E_1)_\alpha$ between the $\alpha$-isotypical components of the corresponding Sobolev spaces of sections. We study in this paper conditions on the map $\pi_\alpha(P)$ to be Fredholm. It turns out that the discrete and non-discrete cases are quite different. Additionally, the discrete abelian case, which provides some of the most interesting applications, presents some special features and is much easier than the general case. We thus concentrate in this paper on the case when $\Gamma$ is finite abelian. We prove then that the restriction $\pi_\alpha(P)$ is Fredholm if, and only if, $P$ is "$\alpha$-elliptic", a condition defined in terms of the principal symbol of $P$. If $P$ is elliptic, then $P$ is also $\alpha$-elliptic, but the converse is not true in general. However, if $\Gamma$ acts freely on a dense open subset of $M$, then $P$ is $\alpha$-elliptic for the given fixed $\alpha$ if, and only if, it is elliptic. The proofs are based on the study of the structure of the algebra $\psi^{m}(M; E)^\Gamma$ of classical, $\Gamma$-invariant pseudodifferential operators acting on sections of the vector bundle $E \to M$ and of the structure of its restrictions to the isotypical components of $\Gamma$. These structures are described in terms of the isotropy groups of the action of the group $\Gamma$ on $E \to M$

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

Influence of the Lower Hybrid Drift Instability on the onset of Magnetic Reconnection

Two-dimensional and three-dimensional kinetic simulation results reveal the importance of the Lower-Hybrid Drift Instability LHDI to the onset of magnetic reconnection. Both explicit and implicit kinetic simulations show that the LHDI heats electrons anisotropically and increases the peak current density. Linear theory predicts these modifications can increase the growth rate of the tearing instability by almost two orders of magnitude and shift the fastest growing modes to significantly shorter wavelengths. These predictions are confirmed by nonlinear kinetic simulations in which the growth and coalescence of small scale magnetic islands leads to a rapid onset of large scale reconnection

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

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

Random Dirac operators with time-reversal symmetry

Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and Goldsheid-Margulis to the analysis of random products of matrices in the group SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of singular spectrum can be shown by adapting an argument of Jaksic-Last if the potential contains random Dirac peaks with absolutely continuous distribution.Comment: parts of introduction made more precise, corrections as follow-up on referee report

ROSAT Evidence for Intrinsic Oxygen Absorption in Cooling Flow Galaxies and Groups

Using spatially resolved, deprojected ROSAT PSPC spectra of 10 of the brightest cooling flow galaxies and groups with low Galactic column densities we have detected intrinsic absorption over energies ~0.4-0.8 keV in half of the sample. Since no intrinsic absorption is indicated for energies below ~0.4 keV, the most reasonable model for the absorber is collisionally ionized gas at temperatures T=10^{5-6} K with most of the absorption arising from ionized states of oxygen but with a significant contribution from carbon and nitrogen. The soft X-ray emission of this warm gas can explain the sub-Galactic column densities of cold gas inferred within the central regions of most of the systems. Attributing the absorption to ionized gas reconciles the large columns of cold H and He inferred from EINSTEIN and ASCA with the lack of such columns inferred from ROSAT. Within the central ~10-20 kpc, where the constraints are most secure, the estimated mass of the ionized absorber is consistent with most (perhaps all) of the matter deposited by a cooling flow over the lifetime of the flow. Since the warm absorber produces no significant H or He absorption the large absorber masses are consistent with the negligible atomic and molecular H inferred from HI and CO observations of cooling flows. It is also found that if T > ~2x10^5 K then the optical and UV emission implied by the warm gas does not violate published constraints. Finally, we discuss how the prediction of warm ionized gas as the product of mass drop-out in these and other cooling flows can be verified with new CHANDRA and XMM observations. (Abridged)Comment: 17 pages (5 figures), Accepted for publication in ApJ, expanded discussion of multiphase spectral models, theoretical implications of warm gas in cooling flows, and the statistical significance of the oxygen absorptio