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A numerical simulation of a fully relativistic jet in slab geometry is presented. The simulation uses a covariant divergence formulation of the equations of hydrodynamics. A Mach disk familiar from nonrelativistic simulations is observed. We also find relativistically narrow streaks in the pressure distribution near the aperture.
The effect of using a finite nucleus model in quantum-chemical calculations is examined. Relativistic corrections from the first order Foldy-Wouthuysen terms are affected indirectly by the change in wavefunction, but also directly as a result of revised expressions for the Darwin and spin-orbit terms due to the change in nuclear potential. A calculation for the Rn atom indicates that the mass-velocity and Darwin corrections are much more sensitive to the finite nucleus than the non-relativistic total energy, but that the total contribution for these two terms is quite stable provided the revised form of the Darwin term is used. The spin-orbit interaction is not greatly affected by the choice of nuclear model.
We explore the generalized Grad-Shafranov (GS) equation (Lovelace et al. 1986), which describes the cross-field balance of the magnetic flux surfaces in a stationary, axisymmetric, cold relativistic MHD wind. We construct a family of self-consistent, jet-type, non-self-similar solutions in which flux surfaces thread the equatorial plane vertically and are eventually collimated into nested cylinders. These solutions conserve the total energy and angular momentum along each flux surface and satisfy the relativistic GS equation in the cross-field direction. We find that the total specific energy in the flow depends primarily on a dimensionless combination of the poloidal magnetic flux, the rotation, and the mass loading rate, which reduces to Michel's (1969) magnetization parameter for radial winds. The final width of the flow and its ratio of kinetic energy flux to Poynting flux depend sensitively on the pressure distribution of the ambient medium, which is required to contain the jet at its outer edge when no jet-confirming external toroidal magnetic field is present. Furthermore, we show that the magnetic pressure in the flow can be much higher near the axis than close to the edge, reflecting the 'pinching' effect of the toroidal magnetic field.
Possible ozone changes at 1 mb associated with the time variation and precipitation of relativistic electrons are investigated by examining the NIMBUS 7 SBUV ozone data set and corresponding temperatures derived from NMC data. No ozone depletion was observed in high-latitude summer when temperature fluctuations are small. In winter more variation in ozone occurs, but large temperature changes make it difficult to identify specific ozone decreases as being the result of relativistic electron precipitation.
Highly relativistic electron precipitation events (HRE's) can provide a major source of energy affecting mesospheric constituents and ionization. Based on satellite data, these events are most pronounced near the minimum of the solar sunspot cycle, increasing in intensity, spectral hardness, and frequency of occurrence as the solar cycle declines. Since such events can be sustained up to several days, their integrated effect in the mesosphere can dominate over those of other energy sources such as relativistic electron precipitation events (REP's) and auroral precipitation. The energy deposition data to be discussed and analyzed were obtained by rocket at Poker Flat, Alaska, in May 1990 during a modest HRE observed at midday near the peak of the sunspot cycle. Using a NASA two dimensional model, significant enhancement of OH and depletion of O3 at 75 +/- 10 km altitude from the measured radiation are found. Estimates of enhanced effects were made for more intense HRE events, as might be expected during solar minimum. By causing O3 depletion, the electron precipitation can also regulate the penetration of solar UV radiation, which could affect the thermal properties of the mesosphere.
A well known prediction of Einstein's general theory of relativity states that two ideal clocks that move with a relative velocity, and are submitted to different gravitational fields will, in general, be observed to run at different rates. Similarly the rate of a clock with respect to the coordinate time of some spacetime reference system is dependent on the velocity of the clock in that reference system and on the gravitational fields it is submitted to. For the syntonization of clocks and the realization of coordinate times (like TAI) this rate shift has to be taken into account at an accuracy level which should be below the frequency stability of the clocks in question, i.e. all terms that are larger than the instability of the clocks should be corrected for. We present a theory for the calculation of the relativistic rate shift for clocks in the vicinity of the Earth, including all terms larger than one part in 10(exp 18). This, together with previous work on clock synchronization (Petit & Wolf 1993, 1994), amounts to a complete relativistic theory for the realization of coordinate time scales at picosecond synchronization and 10(exp -18) syntonization accuracy, which should be sufficient to accommodate future developments in time transfer and clock technology.
We examine constraints on the energetics and radiative efficiencies of highly relativistic, synchrotron-emitting jets. If the observed intraday radio variability of compact radio sources is intrinsic and results from incoherent synchrotron radiation, then the associated jets must have bulk Lorentz factors in the range Gamma varies approximately 30 to 100, several times larger than the largest values inferred from superluminal expansion, and larger even than the values required to avoid the synchrotron self-Compton catastrophe. We show that such highly relativistic jets produce synchrotron radiation with extremely low radiative efficiency. As a result they must carry enormous kinetic energy fluxes, L(sub j) approximately greater than 10(exp 47)(Delta Omega/0.1 sr), where Delta Omega is the solid angle subtended by the jet, in order to produce 'apparent' synchrotron brightness temperatures approximately greater than 10(exp 16) K. Energy losses by such jets should be strongly dominated by Compton scattering of diffuse ambient radiation, and they should produce large X-ray and gamma-ray fluxes.
We propose a model of a optical 'wisps' of the Crab Nebula, features observed in the nebular synchrotron surface brightness near the central pulsar, as manifestations of the internal structure of the shock terminating the pulsar wind. We assume that this wind is composed of ions and a much denser plasma of electrons and positrons, frozen together to a toroidal magnetic field and flowing relativistically. We construct a form of solitary wave model of the shock structure in which we self-consistently solve for the ion orbits and the dynamics of the relativistically hot, magnetized e(+/-) background flow. We ignore dispersion in the ion energies, and we treat the pairs as an adiabatic fluid. The synchrotron emission enhancements, observed as the wisps, are then explained as the regions where reflection of the ions in the self-consistent magnetic field causes compressions of the e(+/-).
Model calculation of inhomogenuous magnetized neutron star atmospheres are used to analyze the phase-dependent spectra of 4U 1538-52 and Vela X-1 taking into account general relativistic effects. A chi (exp 2) fitting procedure is used on the Ginga data for these objects to determine the geometry and the magnetic structure of the polar caps, as well as their size and location on the surface of the stars. Other parameters determined by the fit are the masses and radii of neutron stars, the accretion rates, and the rotation and magnetic inclination angles including an azimuthal offset to reproduce the asymmetry of the pulse shapes. We find that general relativistic effects play a significant role in determining the derived cap sizes, the fluxes, and the observational appearance of the pulses. There is evidence that the polar caps are unequal and nonantipodal, suggesting either an off-center or bent magnetic axis, or a strong nondipole component. The magnetic field structure is approximated by a two-component model. The rotation axes are inferred to be moderately close to the mean magnetic axes and seen at large inclinations with respect to the line of sight.
The role of high-speed solar wind streams in driving relativistic electron acceleration within the earth's magnetosphere is discussed based on International Solar-Terrestrial Physics (ISTP) Observatory and related spacecraft observations. A 'recirculation' mechanism for electron acceleration and redistribution was invoked. Recently, an increase in the number of coronal mass ejections (CMEs) and related 'magnetic clouds' was seen at 1 AU. As these CME/cloud systems interact with the earth's magnetosphere, they are able to produce rapid enhancements in the magnetospheric electron population. The relativistic electron signatures observed by the POLAR, SAMPEX, and other spacecraft during recent magnetic cloud events, especially January 1997 and May 1997, were compared and contrasted. In these cases, there were large solar wind and IMF changes during the cloud passages and very rapid energetic electron acceleration was observed. The relative geoeffectiveness of these events is examined and 'space weather' predicatability is assessed.
Relativistic shock models of gamma-ray bursts may be tested by comparing their predicted low-energy asymptotic spectral indices s to observations. Synchrotron radiation theory predicts that the instantaneous spectrum has s = 1/3, and the spectrum integrated over the radiative decay of the electrons' energies has s = 1/2 with other cases lying between these limits. We examine the spectra of 11 bursts obtained by the Large Area Detectors on BATSE. One agrees with the predicted instantaneous spectrum, as does the initial portion of a second, and three are close to the predicted integrated spectrum. All of the observed asymptotic spectral slopes lie in the predicted range. This evidence for relativistic shocks is independent of detailed models of bursts and of assumptions about their distances. Radiation observed with the predicted instantaneous spectrum has a comparatively smooth time dependence, consistent with the necessarily long radiation time, while radiation observed with the predicted integrated spectrum has a spiky time dependence, consistent with the necessarily short radiation time.
The High Energy Particle Spectrometer (HEPS) instrument on the Upper Atmosphere Research Satellite (UARS) provides a database of electron intensities well resolved in energy and pitch-angle. Because of its 57 deg. orbital inclination, UARS encounters with magnetic shells L greater than 2 occur quite far off-equator (B/B (sub 0) greater than 9), corresponding to equatorial pitch angle alpha (sub 0) greater than 20 deg. Data acquired by HEPS (October 1991 through September 1994) span the declining phase of Solar Cycle 22. To reveal the storm-associated time dependence of relativistic electron intensities over the wide range of energies (50 keV to 5 MeV) covered by HEPS, we divide the daily average of the measured spectrum at a given L value (bin width = 0.25) by the corresponding 500-day average and plot the results with a color scale that spans only 2.5 decades. The data show that our off-equatorial electron intensities typically increase with time after the end of recovery phase (not during main phase or recovery phase) of each geomagnetic storm. The delay in off-equatorial energetic electron response and the subsequent lifetime of the corresponding electron flux enhancement seem to increase with particle energy above 300 keV. The trend below 300 keV seems to be opposite, such that the delay varies inversely with electron energy. Our working hypothesis for interpretation is that stormtime radial transport tends to increase the phase-space densities of trapped relativistic electrons but typically leads to a flux increases at specified energies only as the current (as indicated by Dst) decays. Flux enhancements in early recovery phase are greatest for equatorially mirroring electrons, and to pitch-angle anisotropies are initially large. Subsequent pitch-angle diffusion broadens the flux enhancement to particles that mirror off equator, thus gradually increasing low-altitude electron intensities (as detected by HEPS/UARS) on time scales equal to about 20% of corresponding lifetimes against diffusion into the loss cone. Alternative interpretations will also be examined.
The one-electron Douglas Kroll (DK) and perturbation theory (+R) approaches are used to compute the scalar relativistic contribution to the atomization energies of GaFn. These results are compared with the previous GaCln results. While the +R and DK results agree well for the GaCln atom nation energies, they differ for GaFn. The present work suggests that the DK approach is more accurate than the +R approach. In addition, the DK approach is less sensitive to the choice of basis set. The computed atomization energies of GaF2 and GaF3 are smaller than the somewhat uncertain experiments. It is suggested that additional calibration calculations for the scalar relativistic effects in GaF2 and GaF3 would be valuable.
Utilizing 3D relativistic hydrodynamical calculations, we have examined the evolution of an expanding relativistic blob of gas intended to be representative of a jet associated with ejecta from an extremely energetic event such as a hypernova, that produces a gamma-ray burst (Aloy et al. 2000; Tan, Matzner, & McKee 2001; MacFadyen, Woosley, & Heger 2001, Zhang, Woosley, & Heger 2003, Zhang, Woosley, & MacFadyen 2003). Since these are the first such calculations applied to the blob during the time in which the afterglow radiation is produced, we have purposely kept them simple in an effort to concentrate on the most fundamental aspects of the physics. We restrict our attention to the transition from spherical to jetlike expansion that occurs during the time that the Lorentz factor becomes less than the reciprocal of the jet spreading angle. We have not yet attached specific numbers to our results. From the SRHD equations, one sees that the relevant quantities are the ratios of pressure to density, and of distance to time. If we specify either one of these two sets of numbers, the other one is also determined.
We present results for r-modes of relativistic nonbarotropic stars. We show that the main differential equation, which is formally singular at lowest order in the slow-rotation expansion, can be regularized if one considers the initial value problem rather than the normal mode problem. However, a more physically motivated way to regularize the problem is to include higher order terms. This allows us to develop a practical approach for solving the problem and we provide results that support earlier conclusions obtained for uniform density stars. In particular, we show that there will exist a single r-mode for each permissible combination of 1 and m. We discuss these results and provide some caveats regarding their usefulness for estimates of gravitational-radiation reaction timescales. The close connection between the seemingly singular relativistic r-mode problem and issues arising because of the presence of co-rotation points in differentially rotating stars is also clarified.
One of the most challenging questions in astronomy today is to understand the origin, structure, and evolution of the central engines in the nuclei of quasars and active galaxies (AGNs). The favoured theory involves the activation of relativistic jets from the fueling of a supermassive black hole through an accretion disk. In some AGN an outer optically thick, dusty torus is seen orbiting the black hole system. This torus is probably related to an inner accretion disk - black hole system that forms the actual powerhouse of the AGN. In radio-loud AGN two oppositely-directed radio jets are ejected perpendicular to the torus/disk system. Although there is a wealth of observational data on AGN, some very basic questions have not been definitively answered. The Space Interferometry Mission (SIM) will address the following three key questions about AGN. 1) Does the most compact optical emission from an AGN come from an accretion disk or from a relativistic jet? 2) Does the separation of the radio core and optical photocenter of the quasars used for the reference frame tie, change on the timescales of their photometric variability, or is the separation stable at the level of a few microarcseconds? 3) Do the cores of galaxies harbor binary supermassive black holes remaining from galaxy mergers? It is not known whether such mergers are common, and whether binaries would persist for a significant time.
Relativistic jets are considered to be generated by magnetic fields in a rotating black hole with accretion disk. Consequently, resulting outflows contain magnetic fields in them and control the propagation of jets. We have performed 3D relativistic MHD simulations to investigate the stability and structure of precessed MHD jets with large Lorentz factor by using a newly developed 3D GRMHD code. We have performed simulations of supermagnetosonic jets surrounded by a fast wind. The simulation results reveal complex pressure structure inside the RMHD jet. The structure is produced by a combination of the helical surface and body modes excited by the precession as predicted theoretically. The wavelength of the body mode which occurs in an internal helical twist is much shorter than that of the helical twist surface mode. We will present some comparisons between the RMHD simulations and theoretical predictions, and potential observables and discuss the effect of wind.
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.