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NASA NTRS1990

Electromagnetic fire-hose instability in a fully relativistic bi-Maxwellian plasma

Detailed properties of the classical hydromagnetic Alfven wave and the fire-hose instability, driven by an excess in the parallel energy are well understood in the nonrelativistic regime. In this brief communication, the analysis is extended to the fully relativistic regime. The analysis is carried out for fully relativistic bi-Maxwellian distributions of electrons and ions (or positrons). It is shown that the relativistic effect has a nonnegligible effect on the wave and stability properties of the low-frequency modes under certain conditions.

Yoon, Peter H.↗

NASA NTRS1990

Spectropolarimetric test of the relativistic disk model for the broad emission lines of active galactic nuclei

Previously, it was claimed that the broad emission lines of the radio galaxy Arp 102B can be fitted by the line profile from a simple relativistic Keplerian thin disk. It was argued that the lines originating from the relativistic accretion disk could be polarized due to electron scattering, which is likely to be the dominant opacity in the line-emitting region of Arp 102B. In the present work, the expected polarization properties of these broad emission lines are calculated. The percentage of polarization depends strongly on the inclination angle. For some angles, the red peak of the polarized, double-peaked line profile can be higher than the blue peak. This is in contrast to the total line profile, in which the blue peak is always higher than the red one. Spectropolarimetric observations could, therefore, provide an independent test of the relativistic disk model for the broad emission lines of Arp 102B and other active galactic nuclei.

Chen, Kaiyou↗

NASA NTRS1990

The behavior of beams of relativistic nonthermal electrons under the influence of collisions and synchrotron losses

For many astrophysical situations, such as in solar flares or cosmic gamma-ray bursts, continuum gamma rays with energies up to hundreds of MeV were observed, and can be interpreted to be due to bremsstrahlung radiation by relativistic electrons. The region of acceleration for these particles is not necessarily the same as the region in which the radiation is produced, and the effects of the transport of the electrons must be included in the general problem. Hence it is necessary to solve the kinetic equation for relativistic electrons, including all the interactions and loss mechanisms relevant at such energies. The resulting kinetic equation for non-thermal electrons, including the effects of Coulomb collisions and losses due to synchrotron emission, was solved analytically in some simple limiting cases, and numerically for the general cases including constant and varying background plasma density and magnetic field. New approximate analytic solutions are presented for collision dominated cases, for small pitch angles and all energies, synchrotron dominated cases, both steady-state and time dependent, for all pitch angles and energies, and for cases when both synchrotron and collisional energy losses are important, but for relativistic electrons. These analytic solutions are compared to the full numerical results in the proper limits. These results will be useful for calculation of spectra and angular distribution of the radiation (X rays, gamma-rays, and microwaves) emitted via synchrotron or bremsstrahlung processes by the electrons. These properties and their relevance to observations will be observed in subsequent papers.

Mctiernan, James M.↗

NASA NTRS1991

Unsaturated Comptonization of isotropic photon spectra by relativistic electrons

The multiple scattering approach for evaluating the transformation of an arbitrary soft photon spectrum as a result of unsaturated Compton scatterings in a medium of relativistic electrons is explored. The medium is assumed to be infinite and spatially homogeneous but may be time-dependent, and the photons are isotropic. It is shown that the distortion of a radiation spectrum can be described analytically in a compact form using the Fourier transform of the single-scattering probability. In the nonrelativistic case, the validity of the known analytical results derived from the Kompaneets (1957) equation is extended to arbitrary electron distribution functions and photon spectra. For relativistic electrons, simple expressions are obtained for the total energy that is transferred from the electrons to the photons and for the distortion in the Rayleigh-Jeans regime of a blackbody spectrum. It is demonstrated that the treatment applies to Comptonization in a relativistic jet and that Comptonization of very soft trapped photons by semirelativistic electrons in an expanding medium leads naturally to a log Gaussian spectrum, of the form observed in blazars.

Loeb, Abraham↗

NASA NTRS1992

Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

Maung, Khin Maung↗

NASA NTRS1993

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

Zylka, Christian↗

NASA NTRS1992

Energetic particle transport in relativistic flows

A discussion is given of pitch angle dependent and diffusive transport equations for cosmic rays applicable for both special relativistic and general relativistic flows, derived from the relativistic Boltzmann equation. As an example of particle transport in a curved spacetime we give a pitch angle dependent transport equation appropriate for radial accretion onto a Schwarzschild black hole. The roles of fluid shear, acceleration and compression on the energy changes of particles in the diffusive transport equations are emphasized. Also discussed are special flows (e.g. rigidly rotating flows) associated with a Killing vector for which a constant of the motion of the particles can be identified, and for which simplified transport equations can be constructed.

Webb, G. M.↗

NASA NTRS1992

Monte Carlo simulation of electron acceleration in modified relativistic shocks

We give a brief review of Monte Carlo simulations of nonlinear Fermi shock acceleration and then give new results on electron acceleration in SNRs and in relativistic parallel shocks. The acceleration of low energy electrons in shocks is poorly understood, but even when energetic electrons are considered, where electron and proton scattering should be qualitatively similar, dramatic differences result between electron and proton acceleration in relativistic shocks. If the shocked plasma is a mixture of electrons and protons, the electrons are accelerated much less efficiently than protons. We predict that only e(-)-e(+) pair dominated plasmas can produce significant radio emission in relativistic flows if the standard Fermi mechanism operates in parallel shocks.

Ellison, Donald C.↗

NASA NTRS1993

Relativistic effects on the bonding and properties of the hydrides of platinum

The ground state of PtH2 and several low-lying states of PtH(+) and PtH have been studied at the all-electron self-consistent-field level of theory to examine the importance of relativistic effects. The results of calculations based on Dirac-Hartree-Fock theory, nonrelativistic theory, and the spin-free no-pair relativistic approximation of Hess are compared to separate the effects of the spin-free terms and the spin-orbit terms of the Hamiltonian on the relativistic corrections to the molecular properties. Comparison is also made between first-order perturbation theory including the one-electron spin-free terms and the method of Hess to determine the size of effects beyond first order. It is found that the spin-orbit interaction significantly affects the properties and energetics of these molecules because of the participation of the Pt 5d orbitals in the bonding, and that effects beyond first order in perturbation theory are large. Any treatment of Pt compounds will have to include both the spin-free and spin-orbit interactions for an accurate description.

Dyall, Kenneth G.↗

NASA NTRS1993

Relativistic proton-nucleus scattering and one-boson-exchange models

Relativistic p-(Ca-40) elastic scattering observables are calculated using four sets of relativistic NN amplitudes obtained from different one-boson-exchange (OBE) models. The first two sets are based upon a relativistic equation in which one particle is on mass shell and the other two sets are obtained from a quasipotential reduction of the Bethe-Salpeter equation. Results at 200, 300, and 500 MeV are presented for these amplitudes. Differences between the predictions of these models provide a study of the uncertainty in constructing Dirac optical potentials from OBE-based NN amplitudes.

Maung, Khin Maung↗

NASA NTRS1994

Relativistic induced Compton scattering in synchrotron self-absorbed sources

We present a model of the radio emission from synchrotron self-absorbed sources, including the effects of induced Compton scattering by the relativistic electrons in the source. Order of magnitude estimates show that stimulated scattering becomes the dominant absorption process when (kT(sub B)/m(sub e) c(exp 2))Tau(sub T) greater than or approximately 1.0. Numerical simulations demonstrate that relativistic induced Compton scattering limits the brightness temperature of a self-absorbed synchroton sources to T(sub B) less than or approximately 2 x 10(exp 11) nu(exp -1/p + 3) (sub zero, 9) gamma(exp p + 2/p + 5) (sub min) K, where gamma(sub min) is the low-energy cutoff to the relativistic electron distribution with a power-law index of p. It can also significantly flatten the radio spectrum. The radio spectrum of the core of 3C 279 is well matched by a model in which stimulated scattering is important, and the additional constraint T(sub B) less than 2 x 10(exp 11)K may be important to the interpretation of the broadband spectra in variable extragalactic compact radio sources. Stimulated scattering reduces the amplitude of the radio frequency variability relative to the X-ray variability, an effect which can be detected by multiwavelength variability studies. Data for a sample of resolved compact radio cores indicate that it is inconsistent to neglect induced Compton scattering when inferring the physical parameters of the sources. The necessary generalizations to the standard synchrotron self-Compton theory are p resented.

Sincell, Mark W.↗

NASA NTRS1994

Relativistic particle acceleration in plerions

We discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized -- the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put approximately 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) varies as E(exp -2), where N(E)dE is the number of particles with energy between E and E+dE. The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be gamma(sub +/-)m(sub +/-)c squared = m(sub i)c squared gamma(sub 1)/Z(sub i), where gamma(sub 1) is the Lorentz factor of the upstream flow and Z(sub i) is the atomic number of the ions. The shock's spatial structure is shown to contain a series of 'overshoots' in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value. This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the 'wisps,' surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar's wind in the Crab Nebula is spatially resolved, and allows one to measure gamma(sub 1) and a number of other properties of the pulsar's wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.

Arons, Jonathan↗

NASA NTRS1993

The Gravity Probe B `Niobium bird' experiment: Verifying the data reduction scheme for estimating the relativistic precession of Earth-orbiting gyroscopes

Gravity Probe B (GP-B) is a relatively gyroscope experiment begun at Stanford University in 1960 and supported by NASA since 1963. This experiment will check, for the first time, the relativistic precession of an Earth-orbiting gyroscope that was predicted by Einstein's General Theory of Relativity, to an accuracy of 1 milliarcsecond per year or better. A drag-free satellite will carry four gyroscopes in a polar orbit to observe their relativistic precession. The primary sensor for measuring the direction of gyroscope spin axis is the SQUID (superconducting quantum interference device) magnetometer. The data reduction scheme designed for the GP-B program processes the signal from the SQUID magnetometer and estimates the relativistic precession rates. We formulated the data reduction scheme and designed the Niobium bird experiment to verify the performance of the data reduction scheme experimentally with an actual SQUID magnetometer within the test loop. This paper reports the results from the first phase of the Niobium bird experiment, which used a commercially available SQUID magnetometer as its primary sensor, and adresses the issues they raised. The first phase resulted in a large, temperature-dependent bias drift in the insensitive design and a temperature regulation scheme.

Uemaatsu, Hirohiko↗

NASA NTRS1993

Relativistic Corrections to the Properties of the Alkali Fluorides

Relativistic corrections to the bond lengths, dissociation energies and harmonic frequencies of KF, RbF and CsF have been obtained at the self-consistent field level by dissociating to ions. The relativistic corrections to the bond lengths, harmonic frequencies and dissociation energies to the ions are very small, due to the ionic nature of these molecules and the similarity of the relativistic and nonrelativistic ionic radii.

Dyall, Kenneth G.↗

NASA NTRS1998

Inverse Compton Scattering in Mildly Relativistic Plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters (k(sub B)T(sub e) greater than or approximately equal to 15 keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.

Molnar, S. M.↗

NASA NTRS1997

Gamma-Ray Bursts and Relativistic MHD around Coalescing Neutron Stars

In this proposal we performed the first relativistic hydrodynamic simulations of the binary neutron stars near coalescence. Calculations were performed in three spatial dimensions and were supplemented with magnetohydrodynamic simulations of the magnetic reconnection as the neutron star fluid responds to the relativistic forces of the binary. The ultimate goal of the proposed work was to develop a theoretical model for the temporal and spectral evolution of cosmological gamma-ray bursts produced during the magnetic reconnection. This is the first time such hydrodynamic calculations were performed and some surprising results were obtained. The neutrons stars were observed to compress and heat in the simulations. They could even collapse to black holes many orbits before coalescence. The question then arose as to whether this strange phenomenon could power a gamma-ray burst. The bulk of computing effort in this proposal was therefore devoted to an analysis of the implications of this possible new gamma-ray burst paradigm. The initial focus of the work performed under this proposal was therefore to utilize (3+1) dimensional and spherical numerical general relativistic hydrodynamics to study the origin, evolution, and parametric sensitivity of the collapse instability. We derived modified conditions of hydrostatic equilibrium for stars in the curved space of quasi-static orbits. We followed the magnetic field evolution for approximately one orbit (10 msec). The magnetic field energy was observed to exponentiate with an e-folding time of about 1 msec. Thus, the field should build up very quickly to a magnitude such that reconnection and back reaction of the fluid inhibits further growth.

Mathews, Grant J.↗

NASA NTRS1997

Interfacing Relativistic and Nonrelativistic Methods: A Systematic Sequence of Approximations

A systematic sequence of approximations for the introduction of relativistic effects into nonrelativistic molecular finite-basis set calculations is described. The theoretical basis for the approximations is the normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. The key features of the normalized method are the retention of the relativistic metric and the ability to define a single matrix U relating the pseudo-large and large component coefficient matrices. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the integrals of the Breit-Pauli Hamiltonian. The first approximation fixes the ratios of the large and pseudo-large components to their atomic values, producing an expansion in atomic 4-spinors. The second approximation defines a local fine-structure constant on each atomic centre, which has the physical value for centres considered to be relativistic and zero for nonrelativistic centres. In the latter case, the 4-spinors are the positive-energy kinetic al ly-balanced solutions of the Levy-Leblond equation, and the integrals involving pseudo-large component basis functions on these centres, are set to zero. Some results are presented for test systems to illustrate the various approximations.

Dyall, Ken↗

NASA NTRS2003

Relativistic and Slowing Down: The Flow in the Hotspots of Powerful Radio Galaxies and Quasars

The 'hotspots' of powerful radio galaxies (the compact, high brightness regions, where the jet flow collides with the intergalactic medium (IGM)) have been imaged in radio, optical and recently in X-ray frequencies. We propose a scheme that unifies their, at first sight, disparate broad band (radio to X-ray) spectral properties. This scheme involves a relativistic flow upstream of the hotspot that decelerates to the sub-relativistic speed of its inferred advance through the IGM and it is viewed at different angles to its direction of motion, as suggested by two independent orientation estimators (the presence or not of broad emission lines in their optical spectra and the core-to-extended radio luminosity). This scheme, besides providing an account of the hotspot spectral properties with jet orientation, it also suggests that the large-scale jets remain relativistic all the way to the hotspots.

Kazanas, D.↗