Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane

We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations

Several New Active Galactic Nuclei Among X-ray Sources Detected by INTEGRAL and SWIFT Observatories

We present the results of the optical identifications of a set of X-ray sources from the all-sky surveys of INTEGRAL and SWIFT observatories. Optical data were obtained with Russian-Turkish 1.5-m Telescope (RTT150). Nine X-ray sources were identified as active galactic nuclei (AGNs). Two of them are hosted by nearby, nearly exactly edge-on, spiral galaxies MCG -01-05-047 and NGC 973. One source, IGR J16562-3301, is most probably BL Lac object (blazar). Other AGNs are observed as stellar-like nuclei of spiral galaxies, with broad emission lines in their spectra. For the majority of our hard X-ray selected AGNs, their hard X-ray luminosities are well-correlated with the luminosities in [OIII],5007 optical emission line. However, the luminosities of some AGNs deviate from this correlation. The fraction of these objects can be as high as 20%. In particular, the flux in [OIII] line turns to be lower in two nearby edge-on spiral galaxies, which can be explained by the extinction in their galactic disks.Comment: 9 pages, 3 figures, accepted for publication in Astronomy Letters, the original text in Russian can be found at http://hea.iki.rssi.ru/~rodion/poptid.pd

Magnetic structure in the spin liquid Tb2_{2}Ti2_{2}O7_{7} induced by a [111] magnetic field: Search for a magnetization plateau

We have studied the field-induced magnetic structures of Tb2Ti2O7 pyrochlore by single-crystal neutron diffraction under a field applied along the [111] axis, up to H=12 T and down to T=40 mK. We refined the magnetic structures with k=0 propagation vector by performing a symmetry analysis in the space group R3¯m, reducing the number of free parameters to three only. The Tb moments gradually reorient towards the field direction, keeping close to a “3-in, 1-out / 1-in, 3-out” spin structure (magnetic space group R3¯m′) in the whole measured field range 0.05–12 T. Our results rule out the “all-in/all-out” structure previously proposed and do not support the existence of a magnetization plateau. We perform a quantitative comparison with mean-field calculations and we propose the presence of a low-temperature dynamic symmetry breaking of the local trigonal symmetry, akin to a dynamic Jahn-Teller effect, i.e., preserving the overall cubic symmetry. We discuss the possible origin of this off-diagonal mixing term in the crystal field Hamiltonian in terms of quadrupole-quadrupole interaction or magnetoelastic effects

The profile of a narrow line after single scattering by Maxwellian electrons: relativistic corrections to the kernel of the integral kinetic equation

The frequency distribution of photons in frequency that results from single Compton scattering of monochromatic radiation on thermal electrons is derived in the mildly relativistic limit. Algebraic expressions are given for (1) the photon redistribution function, K(nu,Omega -> nu',Omega'), and (2) the spectrum produced in the case of isotropic incident radiation, P(nu -> nu'). The former is a good approximation for electron temperatures kT_e < 25 keV and photon energies hnu < 50 keV, and the latter is applicable when hnu(hnu/m_ec^2) < kT_e < 25 keV, hnu < 50 keV. Both formulae can be used for describing the profiles of X-ray and low-frequency lines upon scattering in hot, optically thin plasmas, such as present in clusters of galaxies, in the coronae of accretion disks in X-ray binaries and AGNs, during supernova explosions, etc. Both formulae can also be employed as the kernels of the corresponding integral kinetic equations (direction-dependent and isotropic) in the general problem of Comptonization on thermal electrons. The K(nu,Omega -> nu',Omega') kernel, in particular, is applicable to the problem of induced Compton interaction of anisotropic low-frequency radiation of high brightness temperature with free electrons in the vicinity of powerful radiosources and masers. Fokker-Planck-type expansion (up to fourth order) of the integral kinetic equation with the P(nu -> nu') kernel derived here leads to a generalization of the Kompaneets equation. We further present (1) a simpler kernel that is necessary and sufficient to derive the Kompaneets equation and (2) an expression for the angular function for Compton scattering in a hot plasma, which includes temperature and photon energy corrections to the Rayleigh angular function.Comment: 29 pages, 17 figures, accepted for publication in ApJ, uses emulateapj.sty, corrects misprints in previous astro-ph versio

Heating of gas inside radio sources to mildly relativistic temperatures via induced Compton scattering

Measured values of the brightness temperature of low-frequency synchrotron radiation emitted by powerful extragalactic sources reach 10^11--10^12 K. If some amount of nonrelativistic ionized gas is present within such sources, it should be heated as a result of induced Compton scattering of the radiation. If this heating is counteracted by cooling due to inverse Compton scattering of the same radio radiation, then the plasma can be heated up to mildly relativistic temperatures kT~10--100 keV. The stationary electron velocity distribution can be either relativistic Maxwellian or quasi-Maxwellian (with the high-velocity tail suppressed), depending on the efficiency of Coulomb collisions and other relaxation processes. We derive several easy-to-use approximate expressions for the induced Compton heating rate of mildly relativistic electrons in an isotropic radiation field, as well as for the stationary distribution function and temperature of electrons. We also give analytic expressions for the kernel of the integral kinetic equation (one as a function of the scattering angle and another for the case of an isotropic radiation field), which describes the redistribution of photons in frequency caused by induced Compton scattering in thermal plasma. These expressions can be used in the parameter range hnu<< kT<~ 0.1mc^2 (the formulae earlier published in Sazonov, Sunyaev, 2000 are less accurate).Comment: 22 pages, 7 figures, submitted to Astronomy Letter

Circular Polarization Induced by Scintillation in a Magnetized Medium

A new theory is presented for the development of circular polarization as radio waves propagate through the turbulent, birefringent interstellar medium. The fourth order moments of the wavefield are calculated and it is shown that unpolarized incident radiation develops a nonzero variance in circular polarization. A magnetized turbulent medium causes the Stokes parameters to scintillate in a non-identical manner. A specific model for this effect is developed for the case of density fluctuations in a uniform magnetic field.Comment: 16 pages, 1 figure, Phys. Rev. E, accepte

Faraday rotation, stochastic magnetic fields and CMB maps

The high- and low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized $\Lambda$CDM paradigm (m$\Lambda$CDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the derivation of magnetized maps of the CMB temperature and polarization which are here obtained for the first time and within the minimal m$\Lambda$CDM model. The obtained results set the ground for direct experimental scrutiny of large-scale magnetism via the low and high frequency instruments of the Planck explorer satellite.Comment: 53 pages, 15 included figure

Influence of the Earth on the background and the sensitivity of the GRM and ECLAIRs instruments aboard the Chinese-French mission SVOM

SVOM (Space-based multi-band astronomical Variable Object Monitor) is a future Chinese-French satellite mission which is dedicated to Gamma-Ray Burst (GRB) studies. Its anti-solar pointing strategy makes the Earth cross the field of view of its payload every orbit. In this paper, we present the variations of the gamma-ray background of the two high energy instruments aboard SVOM, the Gamma-Ray Monitor (GRM) and ECLAIRs, as a function of the Earth position. We conclude with an estimate of the Earth influence on their sensitivity and their GRB detection capability.Comment: 24 pages, 15 figures, accepted for publication in Experimental Astronom

On the Sunyaev-Zel'dovich effect from dark matter annihilation or decay in galaxy clusters

We revisit the prospects for detecting the Sunyaev Zel'dovich (SZ) effect induced by dark matter (DM) annihilation or decay. We show that with standard (or even extreme) assumptions for DM properties, the optical depth associated with relativistic electrons injected from DM annihilation or decay is much smaller than that associated with thermal electrons, when averaged over the angular resolution of current and future experiments. For example, we find: $\tau_{\rm DM} \sim 10^{-9}-10^{-5}$ (depending on the assumptions) for \mchi = 1 GeV and a density profile $\rho\propto r^{-1}$ for a template cluster located at 50 Mpc and observed within an angular resolution of $10"$, compared to $\tau_{\rm th}\sim 10^{-3}-10^{-2}$. This, together with a full spectral analysis, enables us to demonstrate that, for a template cluster with generic properties, the SZ effect due to DM annihilation or decay is far below the sensitivity of the Planck satellite. This is at variance with previous claims regarding heavier annihilating DM particles. Should DM be made of lighter particles, the current constraints from 511 keV observations on the annihilation cross section or decay rate still prevent a detectable SZ effect. Finally, we show that spatial diffusion sets a core of a few kpc in the electron distribution, even for very cuspy DM profiles, such that improving the angular resolution of the instrument, e.g. with ALMA, does not necessarily improve the detection potential. We provide useful analytical formulae parameterized in terms of the DM mass, decay rate or annihilation cross section and DM halo features, that allow quick estimates of the SZ effect induced by any given candidate and any DM halo profile.Comment: 27 p, 6 figs, additional section on spatial diffusion effects. Accepted for publication in JCA

Relativistic ejecta from XRF 060218 and the rate of cosmic explosions

Over the last decade, long-duration gamma-ray bursts (GRBs) including the subclass of X-ray flashes (XRFs) have been revealed to be a rare variety of Type Ibc supernova (SN). While all these events result from the death of massive stars, the electromagnetic luminosities of GRBs and XRFs exceed those of ordinary Type Ibc SNe by many orders of magnitude. The essential physical process that causes a dying star to produce a GRB or XRF, and not just an SN, remains the crucial open question. Here we present radio and X-ray observations of XRF 060218 (associated with SN 2006aj), the second nearest GRB identified to-date, which allow us to measure its total energy and place it in the larger context of cosmic explosions. We show that this event is 100 times less energetic but ten times more common than cosmological GRBs. Moreover, it is distinguished from ordinary Type Ibc SNe by the presence of 10^48 erg coupled to mildly-relativistic ejecta, along with a central engine (an accretion-fed, rapidly rotating compact source) which produces X-rays for weeks after the explosion. This suggests that the production of relativistic ejecta is the key physical distinction between GRBs/XRFs and ordinary SNe, while the nature of the central engine (black hole or magnetar) may distinguish typical bursts from low-luminosity, spherical events like XRF 060218.Comment: To appear in Nature on August 31 2006 (15 pages, 3 figures, 1 table, including Supplementary Information