A momentum distribution of high energy particles around Crab pulsar

We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (10³10⁹ eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f() ^–5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping), _M 8×10⁶, corresponds to the upper cut-off energy of the -ray spectrum, 10⁹ eV. The lower limit to the momentum, _m 1.8×10⁵, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation.     

Absorption of gamma-rays by X-ray photons around an accretion binary source

Simulation calculations have been made to examine the modification effect of a hot X-ray photon field on a-ray spectrum by the photon-photon pair production and inverse Compton scattering processes. The Cyg X-3 system was used as a paradigm. It is shown that a-ray spectrum can change significantly when passing through the ambient keV X-ray photon field of an accretion binary source. For Cyg X-3, a significant amount of r-rays originated near the central source in the range of 10²-10⁴ MeV could be absorbed by the extended X-ray photons from accretion disk corona in a high X-ray luminosity state and, on the other hand, the inverse Compton effect of secondary electrons could cause a considerable increase in intensity of-rays between ~ 10 MeV and ~ 50 MeV. The relevance of the absorption effect for observations is discussed.     

On the spectrum of relativistic electrons accelerated in cosmic-ray sources

The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE ^–0, with 01.5–2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN _n (E)=K _n E ^– _n, _n = + 2, =w cr/(w–w cr), wherew cr is the cosmic-ray energy density in the source, andw=w cr+w n+w _turb, the total energy density. We obtain =2.5 in agreement with observations on the natural assumption that =0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with _{0 n} = + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.     

The Radio-Silent Start of an Intense Solar Gamma-Ray Flare

Radio-silent -ray flares are solar flares that lack any significant emission in the (non-thermal) radio wave band during their impulsive hard X-ray and -ray emission phases. Flares with extremely suppressed long-wavelength spectra have previously been reported by White et al. (1992) and have been discussed in different context by Hudson and Ryan (1995). A striking example of a radio-silent flare was observed by SMM during the onset of the 6 March 1989 energetic -ray flare. We argue that the absence of radio emission at wavelengths longer than microwave wavelengths is an indication of the compactness of the flare rather than that the flare did not exhibit non-thermal properties. Probably the flare site was restricted to altitudes above the photosphere in a newly emerging loop configuration lower than the equivalent altitude corresponding to an emission frequency of 1.4 GHz. This implies the presence of a dense and highly magnetized closed field configuration confining the electron component which causes the impulsive -ray continuum. Reconnection in such a configuration did not lead to open magnetic fields and streamer formation. Acceleration of particles in the and hard X-ray bursts was restricted to closed field lines. Thermal expansion of the loop system may subsequently lead to the generation of radially propagating blast waves in the solar corona which are accompanied by type II solar radio bursts and decimetre emissions. The emission during the onset of the flare was dominated by a continuum originating from electron bremsstrahlung at X-ray and -ray energies with only little evidence for the presence of energetic ions. It is, therefore, concluded that energetic electrons have been primary and not secondary products of the particle acceleration process.     

Time variation of the spectrum of Gyro-synchrotron emission from the Sun

The emission spectra and their time variations of gyro-synchrotron emission from an ensemble of energetic electrons are computed for some initial power-law distributions of the electron energies N()d= ^– with =2 or 4. The spectra and decay curves of the emission are compared with solar microwave bursts in order to separately estimate the magnetic field H and . From a limited number of observations, we have 3 and H 10³ gauss for the microwave impulsive bursts, and 2 and H (500–1000) gauss for the microwave type-IV bursts.     

On the formation of energy spectra in synchrotron sources

The observed energy spectra in synchrotron sources are power laws,N (E)=KE ^–, with the distribution in peaked around 2.5. These are consistent with initially injected spectra with between 1 and 2, subsequently steepened by synchrotron losses. Contrary to the results of Kardashev (1962), it is shown that statistical acceleration when coupled with synchrotron losses lead naturally to the formation of flat stationary spectra with 1. These stationary spectra have bends near the energy at which synchrotron losses balance the energy gains by acceleration. Above this bend the spectrum tends to =2. The time evolution of an initial spectrum towards the stationary spectrum is investigated. It is suggested that the initially flat spectra with 1 to 1.5 observed in some variable sources result from an incomplete approach to the stationary spectrum, and that in sources with constant acceleration spectra with 2 are to be expected.     

Mechanisms of optical,X-ray andγ-radiation from Crab pulsar

The synchrotron mechanism of radiation from the Crab pulsar has been investigated on the assumption that the mechanism acts in a source moving with relativistic velocity round a neutron star. A detailed matching has been made of the theoretical spectra of synchrotron radiation from relativistic electrons with the results of measurements of the radiation flux from the Crab pulsar in the infrared, optical and X-ray ranges. The parameters of the radiating region (intensity of the magnetic field, source dimensions, density and lifetime of radiating electrons) have been found. They are expressed through the ratio of the energy density of the magnetic field in the source to that of radiating electrons. The level of Compton-radiation in this region is estimated. Possible values of at which the level will correspond to the available results of measurements of the-radiation flux from the Crab pulsar are given. An estimate is presented for the surface magnetic field of the neutron star which does not contradict those obtained from considerations of the magnetic flux conservation when compressing the object up to the neutron star dimensions.     

Gamma-ray astrophysics: parsecs to megaparsecs

A rapidly spinning, slowly accreting magnetic white dwarf (or X-ray pulsar) in hibernation is expected to result in rapid spindown as a result of the stretching and reconnection of magnetic field lines, leading to particle acceleration at the magnetospheric radiusoutside the corotation radius, and the propeller type ejection of magnetized synchrotron-emitting clouds. This may explain the non-thermal (radio and-rays) emission seen from the unique nearby AE Aquarii. Moving to Galactic distances we show how TeV-ray observations of pulsar-driven supernova remnants (with well-measured synchrotron X-ray spectra) allow us to obtain a direct measurement of the average magnetic field strength in the nebula. Finally, GeV to TeV observations of-ray blazars out to redshifts of 2 allow us to probe the intergalactic infrared radiation field, the Hubble constant and possibly the parameter of the Universe.     

On a new class of impulsive flares with no nuclear γ-ray line emission

The new class of -ray spectra from impulsive flares without nuclear -ray lines is compared with bremsstrahlung spectra of energetic electrons undergoing stochastic acceleration, Coulomb and synchrotron losses. The remarkable agreement of both the produced -spectra from the precipitated electrons and the electron spectra measured in the interplanetary space leads to the conclusion that seed population and acceleration process are identical for both classes of electrons. A new estimate of the electron bremsstrahlung contribution in -spectra of impulsive solar flares seems to be necessary.     

Simulation for electron acceleration by DC electric field in the presence of ion sound waves and associated hard X-ray emission

Time-dependent Fokker-Planck equation was numerically solved to demonstrate the dynamics of electrons in a uniform coronal loop with an applied axial DC electric field in the presence of ion-sound waves. This electric field is attributed to an anomalous resistivity due to the ion-sound turbulence caused by an initially given critical current density.The electron momentum distribution becomes a steady state in the whole turbulent region in a short time for which some electrons can be accelerated to the maximum electric potential K _c. The steady energy distribution of electrons flowing out the end of the turbulent region has a very hard power-law-like spectrum with an index of about 0.75. The associated hard X-rays from a thick target also show a hard spectrum with a photon spectral index of 1.3. In order for to be much greater as observed in impulsive X-ray bursts, it is required that the source is a sum of many elementary loops with a power-law-like distribution in K _c with an index = – + 2.5.     

Radio-emitting electrons and cosmic ray confinement

The propagation of cosmic ray electrons in the framework of the Disk-Halo diffusion model in which the diffusion coefficientD z E (wherez is the distance from the galactic plane andE is the energy), and the magnetic fieldHz ^– has been examined by making use of the recently available radio data up to 8 GHz toward the Anticenter (A) and Halo Minimum (M). The following inferences are then made. From the difference in the frequency at which steepening occurs in the radio spectra towardA andH, it is found that the observations are consistent with the magnetic field decreasing withz such that =0.24–0.37. An electron injection spectrum with a single power law down to energies well below 1 GeV cannot explain satisfactorily the observed radio spectra. All observations, however, can be understood in a self consistent way if the observed steepening of the radio spectra, and hence the interstellar electron spectrum, is due partly to the deviation in the power law electron injection spectrum below a few GeV and partly to the first break arising from electron energy losses occurring in the same energy region. In this case, using the value of obtained above and a value of =0.3–0.6, it is found that the spectral index ₀ of the injected electrons above a few GeV has a value between 1.9 and 2.3 and the index a value between 0.5 and 1. Further, if the electrons and protons have the same spectral shape at injection, then ₀=2.1–2.3.NASA-NRC, Senior Research Associate on leave from Tata Institute of Fundamental Research, Bombay, India.     

Sharp edges in solar microwave spectra: Neutral current sheets or cyclotron lines?

We have mapped two solar active regions using the VLA at three closely spaced frequencies (4496, 4716, and 4996 MHz) in an attempt to determine the origin of the steep spectra (index –5 to –8) sometimes observed with large single telescopes. One of the regions observed indeed shows an anomalously large slope ( –6) compared to the usual ( –2 to –2.5). The other region shows a similar slope ( –5) but with a larger range of statistical error. Two possible explanations for such steep edges in solar spectra are (1) transmission effects of neutral current sheets, and (2) the appearance of cyclotron lines. The internal evidence of the microwave maps and simultaneous optical observations favor an explanation in terms of cyclotron lines.On leave from Indian Institute of Astrophysics, Bangalore, India.     

Dynamic spectral characteristics of thermal models for solar hard X-ray bursts

The dynamic spectral characteristics of the thermal model for solar hard X-ray bursts recently proposed by Brown et al. (1979) (BMS) are investigated. It is pointed out that this model, in which a single source is heated impulsively and cooled by anomalous conduction across an ion-acoustic turbulent thermal front, predicts that the total source emission measure should rise as the temperature falls. This prediction, which is common to all conductively cooled single-source models, is contrary to observations of many simple spike bursts. It is proposed, therefore, that the hard X-ray source may consist of a distribution of many small impulsively-heated kernels, each cooled by anomalous conduction, with lifetimes shorter than current burst data temporal resolution. In this case the dynamic spectra of bursts are governed by the dynamic evolution of the kernel production process, such as magnetic-field dissipation in the tearing mode. An integral equation is formulated, the solution of which yields information on this kernel production process, from dynamic burst spectra, for any kernel model.With a BMS-type kernel model in one-dimensional form, the derived instantaneous spectra are limited in hardness to spectral indices 4 for any kernel production process, due to the nature of the conductive cooling. Ion-acoustic conductive cooling in three dimensions, however, increases the limiting spectral hardness to 3. Other forms of anomalous conduction yield similar results but could permit bursts as hard as 2, consistent with the hardest observed.The contribution to the X-ray spectrum from the escaping tail of high-energy kernel electrons in the BMS model is calculated in various limits. If this tail dissipates purely collisionally, for example, its thick-target bremsstrahlung can significantly modify the kernel spectrum at the high-energy end. The energetics of this dynamic dissipation model for thermal hard X-ray bursts also are briefly discussed.Now at: Department of Mathematics, University of Waikato, Hamilton, New Zealand.     

Constraints on the high-energy properties of active galactic nuclei

Number-flux relations at -ray energies for active galactic nuclei have been computed, starting from their X-ray luminosity function and making different assumptions on the spectral shape and cosmological evolution of these sources.The radiation resulting from their integrated emission has been computed and compared to the observed intensity and spectrum of the extragalactic -ray diffuse background (0.3–20 MeV), in order to derive quantitative constraints on the evolution and spectral properties of active galactic nuclei at -ray energies.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

A coronal loop model for the production of X-ray and radio flares in the RS CVn binary HR 1099

The RS CVn binary stellar system HR 1099 is a source of both X-ray and radio flares. We present here a model of the system in which the two types of flare are produced by the same population of mildly-relativistic ( 10) electrons, injected into a coronal loop. After reviewing possible radiation mechanisms we conclude that, given the probable conditions in the flaring region, the radio emission is gyrosynchrotron radiation and the X-ray emission is thermal bremsstrahlung. The thermal X-ray source must lie in the stellar chromosphere, but the apparent absence of plasma absorption at radio frequencies indicates that the radio source is located high in the coronal loop. Using the relationships given by Dulk and Marsh (1982) for the radio emission from a power-law electron energy spectrum,N() ( - 1)^–, we conclude that 3 7, with 30% of the electron population trapped in the radio source. Some implications of these results for one particular version of the model are discussed.     

Stimulated comption effect in very compact radio sources

Expressions for the stimulated Compton effect are derived that are complete to order /ge/, where is the photon energy in the laboratory system, and =m ₀ C ² is the electron energy. Explicit formulas are given for the energy flow between a relativistic electron and a radiation field that obeys a power law so that the number of photons is proportional to ^–m–1. The amount of energy gained by an electron per second is then numerically calculated for conditions suggested by very compact radio sources as a function of the width of the spectrum, the spectral index, and the electron energy.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A theory for gamma ray and X-ray burst sources

A common mechanism for both X-ray and-ray bursters is proposed on the basis that a window can be created transiently in the polar cap of a degenerate star, a white dwarf for X-ray bursts and a neutron star for-ray bursts. The window exposes transiently a hot degenerate sub-layer of the star at shallow depth, from which escapes blackbody flux for a source at temperature 3 kev with window radius 10 km in the case of X-ray bursts and for a source at temperature 300 kev with window radius 0.5 km in the case of-ray bursts.     

Plasma acceleration by radiation in X-ray pulsars

Charged particle acceleration is considered by a radiation flux from a star or hot spot in X-ray pulsars. It is shown that for any distance from the star there exists the upper velocity limit up to which a particle can be accelerated by radiation. This critical velocity does not depend on the luminosity of the spot. Near the hot spot surface the critical velocityv0.65c. These results are applied to plasma acceleration inX-ray pulsars. The mechanism is advanced, of -ray generation in the course of plasma accretion, onto a neutron star. It is shown that in the presence of a large magnetic field and high luminosity of the spot the relativistic electron-position avalanche may appear. The optical depth of the electron-positron cloud achieves the value of order one. The X-ray quanta emitted by the spot are scattered by relativistic (2.6) electron-positron pairs and are transformed into -radiation. Hard quanta with energy 1 MeV leave the generation region in the narrow cone 0.25.     

Equilibrium spectra of secondary cosmic-ray positrons in the galaxy and the spectrum of cosmic gamma-rays resulting from their annihilation

A general formula is derived for calculating the -ray spectrum resulting from the annihilation of cosmic-ray positrons. This formula is used to calculate annihilation--ray spectra from various equilibrium spectra of secondary galactic positrons. These spectra are then compared with the -ray spectra produced by other astrophysical processes.Particular attention is paid to the form of the -ray spectrum resulting from the annihilation of positrons having kinetic energies below 5 keV. It is found that for mean leakage times out of the galaxy of less than 400 million years, most of the positrons annihilating near rest come from the -decay of unstable nuclei produced in cosmic-ray p-C¹², p-N¹⁴, and p-O¹⁶ interactions, rather than from pi-meson decay. It is further found that the large majority of these positrons will annihilate from an S state of positronium and that 3/4 of these will produce a three-photon annihilation continuum rather than the two-photon line spectrum at 0.51 MeV. The results of numerical calculations of the -ray fluxes from these processes are given. It is concluded that annihilation -rays from the galactic halo may remain forever masked by a metagalactic continuum. However, an 0.51 MeV line from the disk may well be detectable. It is most reasonable to assume that this line is formed predominantly by the annihilation of the CNO -decay positrons. Under this assumption, the intensity of the line becomes a sensitive measure of the galactic cosmic-ray flux below 1000 MeV/nucleon.     

Estimates of proton energies in extragalactic radio sources

It is shown that inelastic proton collisions in extragalactic radio sources can account for their radio and -ray emissions. The proton Lorentz-factor _p responsible for -ray emission is estimated to lie between 1.4 and 86. But for the radio emission (with _e ~ 10³-10⁴) the estimated _p values lie between 7 to 300. The estimates of total particle and magnetic energy for a typical radio source is in agreement with equipartition theory.