Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models

New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics behaviour are presented as an example. The special attention is paid for the singular case $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur

Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde

Polarization of Thermal X-rays from Isolated Neutron Stars

Since the opacity of a magnetized plasma depends on polarization of radiation, the radiation emergent from atmospheres of neutron stars with strong magnetic fields is expected to be strongly polarized. The degree of linear polarization, typically ~10-30%, depends on photon energy, effective temperature and magnetic field. The spectrum of polarization is more sensitive to the magnetic field than the spectrum of intensity. Both the degree of polarization and the position angle vary with the neutron star rotation period so that the shape of polarization pulse profiles depends on the orientation of the rotational and magnetic axes. Moreover, as the polarization is substantially modified by the general relativistic effects, observations of polarization of X-ray radiation from isolated neutron stars provide a new method for evaluating the mass-to-radius ratio of these objects, which is particularly important for elucidating the properties of the superdense matter in the neutron star interiors.Comment: 7 figures, to be published in Ap

Discrete Lie Advection of Differential Forms

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan's homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC

The X-ray Spectrum of the Vela Pulsar Resolved with Chandra

We report the results of the spectral analysis of two observations of the Vela pulsar with the Chandra X-ray observatory. The spectrum of the pulsar does not show statistically significant spectral lines in the observed 0.25-8.0 keV band. Similar to middle-aged pulsars with detected thermal emission, the spectrum consists of two distinct components. The softer component can be modeled as a magnetic hydrogen atmosphere spectrum - for the pulsar magnetic field $B=3\times 10^{12}$ G and neutron star mass $M=1.4 M_\odot$ and radius $R^\infty =13$ km, we obtain \tef^\infty =0.68\pm 0.03 MK, $L_{\rm bol}^\infty = (2.6\pm 0.2)\times 10^{32}$ erg s$^{-1}$, $d=210\pm 20$ pc (the effective temperature, bolometric luminosity, and radius are as measured by a distant observer). The effective temperature is lower than that predicted by standard neutron star cooling models. A standard blackbody fit gives $T^\infty =1.49\pm 0.04$ MK, $L_{\rm bol}^\infty=(1.5\pm 0.4)\times 10^{32} d_{250}^2$ erg s$^{-1}$ ($d_{250}$ is the distance in units of 250 pc); the blackbody temperature corresponds to a radius, $R^\infty =(2.1\pm 0.2) d_{250}$ km, much smaller than realistic neutron star radii. The harder component can be modeled as a power-law spectrum, with parameters depending on the model adopted for the soft component - $\gamma=1.5\pm 0.3$, $L_x=(1.5\pm 0.4)\times 10^{31} d_{250}^2$ erg s$^{-1}$ and $\gamma=2.7\pm 0.4$, $L_x=(4.2\pm 0.6)\times 10^{31} d_{250}^2$ erg s$^{-1}$ for the hydrogen atmosphere and blackbody soft component, respectively ($\gamma$ is the photon index, $L_x$ is the luminosity in the 0.2--8 keV band). The extrapolation of the power-law component of the former fit towards lower energies matches the optical flux at $\gamma\simeq 1.35$--1.45.Comment: Submitted to ApJ, three figures; color figure 1 can be found at http://www.xray.mpe.mpg.de/~zavlin/pub_list.htm

Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field

We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a created pair of the quasi-particles, corresponding to a diagonal form of the instantaneous Hamiltonian. The case of an adiabatic change of the metric of homogeneous isotropic space is analyzed. We show that the created pairs of quasi-particles in de Sitter space should be interpreted as pairs of virtual particles.Comment: 7 pages, 3 figure

X-ray emission from PSR B1800-21, its wind nebula, and similar systems

We detected X-ray emission from PSR B1800-21 and its synchrotron nebula with the Chandra X-ray Observatory. The pulsar's observed flux is (1.4+/-0.2) 10^{-14} ergs cm^{-2} s^{-1} in the 1-6 keV band. The spectrum can be described by a two-component PL+BB model, suggesting a mixture of thermal and magnetospheric emission. For a plausible hydrogen column density n_{H}=1.4 10^{22} cm^{-2}, the PL component has a slope Gamma=1.4+/-0.6 and a luminosity L_{psr}^{nonth}=4 10^{31}(d/4 kpc)^2 ergs s^{-1}. The properties of the thermal component (kT=0.1-0.3 keV, L^{bol}=10^{31}-10^{33} ergs s^{-1}) are very poorly constrained because of the strong interstellar absorption. The compact, 7''\times4'', inner pulsar-wind nebula (PWN), elongated perpendicular to the pulsar's proper motion, is immersed in a fainter asymmetric emission. The observed flux of the PWN is (5.5+/-0.6) 10^{-14} ergs cm^{-2} s^{-1} in the 1-8 keV band. The PWN spectrum fits by a PL model with Gamma=1.6+/-0.3, L=1.6 10^{32} (d/4 kpc})^2 ergs s^{-1}. The shape of the inner PWN suggests that the pulsar moves subsonically and X-ray emission emerges from a torus associated with the termination shock in the equatorial pulsar wind. The inferred PWN-pulsar properties (e.g., the PWN X-ray efficiency, L_{pwn}/\dot{E}~10^{-4}; the luminosity ratio, L_{pwn}/L_{psr}^{nonth}=4; the pulsar wind pressure at the termination shock, p_s=10^{-9} ergs cm^{-3}) are very similar to those of other subsonically moving Vela-like objects detected with Chandra (L_{pwn}/\dot{E}=10^{-4.5}-10^{-3.5}, L_{pwn}/L_{psr}^{nonth}~5, p_s=10^{-10}-10^{-8} ergs cm^{-1}).Comment: 11 pages, 10 figures, 2 tables; submitted to ApJ. Version with the high-resolution figures is available at http://www.astro.psu.edu/users/green/B1800/B1800_ApJ.pd

Classification of integrable hydrodynamic chains and generating functions of conservation laws

New approach to classification of integrable hydrodynamic chains is established. Generating functions of conservation laws are classified by the method of hydrodynamic reductions. N parametric family of explicit hydrodynamic reductions allows to reconstruct corresponding hydrodynamic chains. Plenty new hydrodynamic chains are found