Injection Spectrum Research Articles

Maximum likelihood analysis of clusters of ultrahigh energy cosmic rays

We present a numerical code designed to conduct a likelihood analysis for clusters of nucleons above ${10}^{19}$ eV originating from discrete astrophysical sources such as powerful radio galaxies, $\ensuremath{\gamma}\ensuremath{-}$ray bursts or topological defects. The code simulates the propagation of nucleons in a large-scale magnetic field and constructs the likelihood of a given observed event cluster as a function of the average time delay due to deflection in the magnetic field, the source activity time scale, the total fluence of the source, and the power-law index of the particle injection spectrum. Its dependence on coherence length and the power spectrum of the magnetic field are found to be negligible within their usually considered ranges. We apply our code to the three pairs of events above $4\ifmmode\times\else\texttimes\fi{}{10}^{19}$ eV recently reported by the Akeno Giant Air Shower Array (AGASA) experiment, assuming that these pairs were caused by nucleon primaries which originated from a common source. Although current data are too sparse to constrain fully each of the parameters considered, and/or to discriminate models of the origin of ultrahigh energy cosmic rays, several tendencies are indicated. If the clustering suggested by AGASA is real, next generation experiments with their increased exposure should detect more than $\ensuremath{\sim}10$ particles per source over a few years and our method will put strong constraints on both the large-scale magnetic field parameters and the nature of these sources.

Possible origin and spectrum of ultrahigh-energy cosmic rays

The complicated form of the cosmic-ray spectrum recorded in the energy range 1017–1020 eV by giant detector arrays is analyzed. It is shown that the spectrum in the region 1018–1019 eV is apparently identical to the injection spectrum with power-law exponent approximately equal to 3.2–3.3. The flat component in the region (3.2–5)×1019 eV is due to the braking of extragalactic protons by relict photons. The spectrum apparently has no blackbody cutoff at energies above 3.2×1019 eV.

Diode lasers locked to noisy injection

We have analyzed the behavior of a diode laser with low-amplitude optical injection. The noisy injection field has phase fluctuations only, with a linewidth larger than both the free-running slave laser linewidth and the locking range. Simulations show that the laser output spectrum can be much narrower than the injection spectrum and may have a dip at the free-running laser frequency. A model describing these features is based on linear superposition of the stationary responses to monochromatic injection. The mechanism of line narrowing is that the response to injection outside the locking range lies mainly inside.

Avalanche Breakdown Luminescence of InGaN/AlGaN/GaN Heterostructures

Luminescence spectra of InGaN/AlGaN/GaN p-n-heterostructures were studied at reverse bias sufficient for impact ionization. There is a high electric field in the active InGaN-layer, and the tunnel component of the current dominates at the low reverse bias. Avalanche breakdown begins at |Vth|> 8⋄10 V, i.e. ≈3 Eg/e. Radiation spectra have a short wavelength edge 3.40 eV, and maxima in the range 2.60⋄2.80 eV corresponding to the injection spectra. Mechanisms of the hot plasma recombination in p-n-heterojunctions are discussed.

The 1990 May 24 solar cosmic-ray event

This paper presents an integrated analysis of GOES 6, 7 and neutron monitor observations of solar cosmic-ray event following the 1990 May 24 solar flare. We have used a model which includes particle injection at the Sun and at the interplanetary shock front and particle propagation through the interplanetary medium. The model does not attempt to simulate the physical processes of coronal transport and shock acceleration, therefore the injections at the Sun and at the shock are represented by source functions in the particle transport equation. By fitting anisotropy and angle-average intensity profiles of high-energy (>30 MeV) protons as derived from the model to the ones observed by neutron monitors and at GOES 6 and 7, we have determined the parameters of particle transport, the injection rate and spectrum at the source. We have made a direct fit of uncorrected GOES data with both primary and secondary proton channels taken into account.

The Inversion of Electron Time-of-Flight Distances from Hard X-Ray Time Delay Measurements

view Abstract Citations (24) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Inversion of Electron Time-of-Flight Distances from Hard X-Ray Time Delay Measurements Aschwanden, Markus J. ; Schwartz, Richard A. Abstract The electron time-of-flight distance 1 between the acceleration site and the chromosphere can be measured during solar flares from energy-dependent hard X-ray (HXR) time delays τ(ɛ), based on the applicability of the thick-target model. The determination of the path length l represents an inversion problem because the time-dependent electron injection spectrum at the acceleration site, N(E, t, x = 0), is retarded by the propagation time tprop(E)=l/v(E) at the thick-target site, i.e., N(E, t, x = l) = N[E, t - tprop(E), x - 0], and has to be convolved with the bremsstrahlung cross section σ(ɛ, E) and the instrumental detector response function Ri(ɛ) to reproduce the observed HXR time profiles I(Ei, t) (in different detector channels i), from which the time delay differences τ(ɛi) - τ(ɛi) can be measured. In this study, we solve this inversion problem by numerical forward integration of time-dependent electron injection spectra N(E, t) with Gaussian pulse shapes to obtain the convolved time-dependent HXR spectra I(ɛ, t), using specific detector response functions from the Burst and Transient Source Experiment/Compton Gamma Ray Observatory and the Hard X-Ray Burst Spectrometer/Solar Maximum Mission. We find that the timing of HXR pulses can be accurately represented with the (monoenergetic) photon energy ɛi that corresponds to the median of the channel count spectra Ci(ɛ) = I(ɛ)Ri(ɛ). We compute numerical conversion factors qE(ɛ, y, E0) that permit the conversion of the timing of photon energies ɛi(t) (for a power-law spectrum with slope γ and upper cutoff energy E0) into electron energies Ei(t) = qEɛi(t), from which kinematic parameters can be fitted to determine the electron time-of-flight path length l. We test the inversion procedure with numeric simulations and demonstrate that the inversion is accurate within σl/l ≤ 1% for noise-free data. This inversion procedure is applied to the Masuda flare (in this volume) to localize the electron acceleration region. Publication: The Astrophysical Journal Pub Date: June 1996 DOI: 10.1086/177385 Bibcode: 1996ApJ...464..974A Keywords: RADIATION MECHANISMS: NONTHERMAL; RADIATIVE TRANSFER; SUN: FLARES; SUN: X-RAYS; GAMMA RAYS full text sources ADS |

On the Injection Energy Distribution of Ultra--High-Energy Cosmic Rays

We investigate the injection spectrum of ultra-high-energy (>10^{15} eV) cosmic rays under the hypotheses that (1) these cosmic rays are protons and (2) the sources of these cosmic rays are extra-galactic and are homogeneously distributed in space. The most puzzling aspect of the observed ultra-high-energy cosmic ray spectrum is the apparent nonexistence of a ``Greisen cut-off'' at about 10^{19.8} eV. We show that this fact could be naturally explained if most (or all) of the cosmic rays presently observed above about 10^{19.6} eV were initially injected with energy above the Greisen cut-off. However, we find that the injection of cosmic rays above the Greisen cut-off cannot account for the observed flux below about 10^{19.6} eV unless the injection rate of these particles was enormously higher in the past, as would be the case if the injection resulted from the decay of an ultra-massive particle with lifetime of order 10^{9} yr. Even with such a rapid source evolution, the observed cosmic ray spectrum below about 10^{18.5} eV cannot be explained in this manner. However, we show that a 1/E^3 injection spectrum can account for the observed spectrum below 10^{18.5} eV}, with the steepening observed by the Fly's Eye group between 10^{17.6} eV and 10^{18.5} eV being very naturally explained by e+ - e- production effects. This latter fact lends support to the hypothesis that the cosmic rays in this energy regime are protons. However, due to e+ - e- production effects, a 1/E^3 injection spectrum cannot account for the observed flux above about 10^{18.5} eV.

Propagation of ultra high energy protons and gamma rays over cosmological distances and implications for topological defect models

We describe the results of a hybrid matrix-Monte Carlo calculation of cascading of UHE cosmic rays and γ-rays through the cosmic background radiation fields over cosmological distances. We calculate the γ-ray and neutrino emission that results from the cascade, as well as the effect of cascading on the primary spectrum. We discuss the results for various cosmic ray injection spectra and primary species. Certain models for the production of the highest energy cosmic rays are ruled out.

Helium photodisintegration and nucleosynthesis: Implications for topological defects, high energy cosmic rays, and massive black holes.

We consider the production of $^{3}\mathrm{He}$ and $^{2}\mathrm{H}$ by $^{4}\mathrm{He}$ photodisintegration initiated by nonthermal energy releases during early cosmic epochs. We find that this process cannot be the predominant source of primordial $^{2}\mathrm{H}$ since it would result in anomalously high $^{3}\mathrm{He}$/D ratios in conflict with standard chemical evolution assumptions. We apply this fact to constrain topological defect models of highest energy cosmic ray (HECR) production. Such models have been proposed as possible sources of ultrahigh energy particles and \ensuremath{\gamma} rays with energies above ${10}^{20}$ eV. The constraints on these models derived from $^{4}\mathrm{He}$ photodisintegration are compared to corresponding limits from spectral distortions of the cosmic microwave background radiation and from the observed diffuse \ensuremath{\gamma}-ray background. It is shown that for reasonable primary particle injection spectra superconducting cosmic strings, unlike ordinary strings or annihilating monopoles, cannot produce the HECR flux at the present epoch without violating at least the $^{4}\mathrm{photodisintegration}$ bound. The constraint from the diffuse \ensuremath{\gamma}-ray background rules out the dominant production of HECR by the decay of grand unification particles in models with cosmological evolution assuming standard fragmentation functions. Constraints on massive black hole induced photodisintegration are also discussed. \textcopyright{} 1995 The American Physical Society.

Electrons and positrons in the galactic cosmic rays.

The detection of primary cosmic ray electrons with energies above 1 TeV implies the existence of a nearby, r\ensuremath{\le}100 pc, and relatively young, t\ensuremath{\le}${10}^{5}$ yr, source(s) of accelerated electrons. Therefore a correct treatment of the formation of the spectra of electrons during their propagation in the interstellar medium requires a separate consideration of the contribution of one (or a few) nearby source(s) from the contribution of distant (R\ensuremath{\ge}1 kpc) sources. To implement this approach, the problem of energy-dependent diffusive propagation of relativistic particles from a single source is considered, and the analytical solution to the diffusion equation in the general case of arbitrary energy losses and injection spectrum of primary particles is found. We show that in the framework of the proposed two-component approach, i.e., separating the contribution of the local (discrete) source(s) from the contribution of distant sources, it is possible to explain all the locally observed features of the energy spectrum of cosmic ray electrons from sub-GeV to TeV energies. In addition, assuming that the local source produces electrons and positrons in equal amounts, the model allows us to explain also the reported increase of the positron content in the flux above 10 GeV.

Relativistic solar proton events

Energetic solar flare particles contain rich information concerning mechanisms of particle acceleration on the Sun and subsequent transport through turbulent interplanetary space. Even the most energetic particles, in particular protons with kinetic energy above ∼500 MeV, may undergo coronal and interplanetary propagation effects, disturbing their accelerated injection spectrum after release from the solar flare. Relativistic solar proton events are recorded by neutron monitors at ground level. A detailed knowledge of the response of these ground-based detectors to the impact by a beam of protons on the top of the atmosphere is required to analyze these observations. The spectral index of arriving protons can be obtained from the response of the world-wide network of neutron monitors provided their directional anisotropy is known. The spectral index may also by determined from the relative enhancements in count rates of two similar detectors at different altitudes but similar asymptotic cones of acceptances, or from the relative enhancements of two detectors with different spectral sensitivities but at the same location of high latitude. Ground level enhancements from solar flare protons have been recorded at Sanae, Antarctica, since 1971 by two neutron monitors with different sensitivities to primary protons in the rigidity range from ≲1 GV to ∼5 GV. Spectral indexes of about 20 of these more energetic solar flare proton events have been determined from the two detector enhancements recorded at Sanae. These indexes do not show any increase (softening of the relativistic proton spectra) with increasing heliolongitude away from the preferred IMF connection region as was obtained for 20–80 MeV protons. Furthermore, most of the enhanced count rates show fluctuations larger than statistical, indicative of propagation in a mostly turbulent interplanetary magnetic field.

Measurement of cosmic-ray proton and helium spectra during the 1987 solar minimum

The differential cosmic-ray proton and helium spectra have been measured during the 1987 solar minimum using a balloon-borne superconducting magnetic spectrometer launched from Prince Albert, Canada. The changing geomagnetic cutoff along the balloon trajectory was observed in the low-energy proton data to be about 25 percent below the nominal calculated values. The absolute particle fluxes were approximately equal to the highest fluxes observed at the previous solar minimum in 1977. Above 10 GV the observed spectra are represented by a power law in rigidity with spectral indices of 2.74 + or - 0.02 for protons and 2.68 + or - 0.03 for helium. The measurements above 200 MeV per nucleon are consistent with rigidity power-law interstellar spectra modulated with the solar modulation parameter phi = 500 MV. The energy dependence of the proton-to-helium ratio is consistent with rigidity power-law injection spectra and rigidity-dependent propagation without reacceleration.

Identification of harmonic sources by a state estimation technique

A reverse power flow procedure is described to identify the sources of harmonic signals in electric power systems. Methods have been reported elsewhere to analyze the propagation of these harmonics signals throughout the network. Here the reverse problem of how to identify the source (and potentially the type) of harmonic signals is considered. Line and bus data at several points in the network are used with a least-squares estimator to calculate the injection spectrum at buses suspected of being harmonic sources. When energy at harmonic frequencies is found to be injected into the network at a bus, that bus is identified as a harmonic source. >

Leakage lifetime of cosmic-ray electrons in the Galaxy

From data on the synchrotron emission in the Galactic magnetic field, the authors obtain the electron spectrum below a few GeV. Taking this to be the injection spectrum of electrons they develop a model for their propagation in the Galaxy. The model is based on a continuity formalism in which the confinement time for particles in the Galactic volume is energy dependent. The authors derive the expected spectrum of electrons near the sun over the range 0.1-103 GeV for different lifetime distribution functions corresponding to different classes of models for particle confinement. From comparison with observations, they deduce a mean lifetime varying as 5*107 (E/5.5 GeV)-0.3 years, for electron energies above 5.5 GeV.

Implications of the ultrahigh-energy cosmic-ray spectrum observed by the Fly's Eye detector.

We discuss the potential implications of the recent results of the Fly's Eye detector on the ultrahigh-energy cosmic-ray spectrum. The data suggest that the observed slope flattening immediately prior to the cutoff appears to be a recoil-proton pileup associated with an ${E}^{\mathrm{\ensuremath{-}}2.5\ifmmode\pm\else\textpm\fi{}.3}$ injection spectrum. We discuss the induced neutrino spectrum and its detectability in Fly's Eye and DUMAND detectors.

Bremsstrahlung spectra from thick-target electron beams with noncollisional energy losses

A generalization of the Brown's (1971) formulation of the relationship between bremsstrahlung spectrum and mean electron spectrum (electrons in the range 10-100 keV) is presented with an objective of demonstrating the information content of bremsstrahlung spectra from a thick target. It is shown that the observed photon spectrum can be inverted to yield an integral functional of the electron spectrum and the effective energy loss rate. Furthermore, if observational or theoretical electron injection spectrum is known, an effective 'phenomenological' energy loss function can be obtained.

Photon-photon absorption and the uniqueness of the spectra of active galactic nuclei

The effects of the feedback of e(+)-e(-) pair reinjection in a plasma due to photon-photon absorption of its own radiation was examined. Under the assumption of continuous electron injection with a power law spectrum E to the minus gamma power and Compton losses only, it is shown that for gamma 2 the steady state electron distribution function has a unique form independent of the primary injection spectrum. This electron distribution function can, by synchrotron emission, reproduce the general characteristics of the observed radio to optical active galactic nuclei spectra. Inverse Compton scattering of the synchrotron photons by the same electron distribution can account for their X-ray spectra, and also implies gamma ray emission from these objects. This result is invoked to account for the similarity of these spectra, and it is consistent with observations of the diffuse gamma ray background.

The energy spectra of cosmic-ray positrons and electrons

Various interstellar positron spectra have been re-estimated after taking into account the anomalous solar modulation. Of the spectra, it is found that the one derived from Rockstroh and Webber (1978) is most consistent with the description based on the usual 'leaky-box' model. Further, it is shown that an electron injection spectrum with a single power law cannot explain the primary electron spectrum satisfactorily. Finally, it is proposed that the usual 'leaky-box' model can account for the mean behaviour of interstellar positrons and electrons in a cosmic-ray containment volume whose Galactic scale height and width around us are 0.5-1 kpc and 2-3 kpc respectively.

Solar flare particle injection spectra and spectra of flux maxima at the point of observation

Numerical models of impulsive solar flare particle events usually assume the radial diffusion coefficient to be independent of energy per nucleon, T, although the observations indicate a T 0.5 dependence (constant mean free path). The assumption of a constant diffusion coefficient results in a preservation of a power law injection spectrum at all radial distances throughout the event. We investigate the effect of an energy dependent diffusion coefficient on the spectrum of flux maxima at a fixed point in interplanetary space. This spectrum is harder than that of initial differential number densities close to the sun. Furthermore, the spectrum hardens with increasing radial distance which seems to be at variance with observations.

Formation of universal and diffusion regions of non-linear spectra of relativistic electrons in spatially limited sources

It is demonstrated that in the case of hard injection of relativistic electrons accompanied by the joint action of synchrotron (Compton) losses and energy-dependent spatial diffusion, a spectrum with ‘breaks’ is formed containing universal (with index γ=2) and diffusion regions, both independent of the injection spectrum. The effect from non-linearity of the electron spectrum is considered in averaged electromagnetic spectra for various geometries of sources (sphere, disk, arm). It is shown that a universal region (with index α=0.5) can occur in the radiation spectrum.