Ultrahigh energy photons,electrons, and neutrinos,the microwave background,and the universal cosmic-ray hypothesis

The production of ultrahigh energy photons, electrons and neutrinos as the decay products of pions produced in photomeson interactions between cosmic-ray nucleons and the blackbody microwave background is discussed in terms of the resultant energy spectra of these particles. Simple asymptotic formulas are given for calculating the ultrahigh energy photon spectrum predicted for the universal cosmic-ray hypothesis and the resulting spectra are compared with those obtained previously by numerical means using a different propagation equation for the photons. Approximate analytic solutions for the photon spectra are given in terms of simple power-law energy functions and slowly varying logarithmic functions. These can be used to estimate ultrahigh energy photon fluxes for various astrophysical parameters. The generic relation between the various secondary components is then discussed in terms of their astrophysical implications which are summarized in the conclusion.     

Generation of gamma-rays in electron-photon cascades

We have studied an electron-photon cascade in an isotropic photon field as one of the possible gamma-ray generation mechanisms in compact sources.A cascade in a monoenergetic photon field and in a field of the power-law spectrum is considered. Two types of interaction of cascade particles with the photon field are taken into account: the inverse Compton scattering of electrons and the photoproduction of electron-positron pairs by gamma-quanta. The cascade characteristics have been obtained by numerical solution of the kinetic equations. A quantitative and qualitative analysis is made of the main regularities of the cascade. We have established simple relations between the spectra of cascade particles and the parameters of the photon field and primary radiation. The magnetic field effect on the cascade characteristics is estimated. The results obtained are compared with the results of calculation of other investigators.In the first part of the paper we outline the method of solution and the results relating to the monoenergetic photon field. The theory of cascades in a photon field of the power-law spectrum and its application to the problem of gamma-rays in compact sources are discussed in the second part of the present paper.     

Modification of gamma-ray spectrum in a photon field

The changes in the high-energy gamma-ray spectra due to electron-photon cascading in the photon field (e.g., microwave background radiation) are investigated.The propagation of gamma-rays with an initial power-law spectrum through an isotropic monoenergetic photon field is considered. Two processes of the cascade particle-photon field interaction are taken into account, namely, the photoproduction of electron-positron pairs and the inverse Compton effect. The effect of the synchrotron energy loss by cascade electrons in a magnetic field on the cascade gamma-quantum spectrum is studied. The results may be used to estimate the absorption and the variations in the shape of the spectrum of radiation from compact gamma-ray sources in the metagalaxy.The cascade characteristics have been obtained by numerically solving the cascade equations by the moment method.     

Role of the solar wind parameters in changing orbital motion of the Earth’s satellites

The investigation of the solar wind and geomagnetic activity parameters' effect on variations of the orbital motion periods of artificial satellites has been continued. The periods of orbital motion of uncontrolled satellites from the database of the Ukrainian network of optical stations (UNOS) for 2012–2014 was used. The data have been compared with the values of geomagnetic planetary index K and the energy spectra of protons and electrons obtained by the GEOS satellites in events during which the orbital periods have changed. It is shown that, in the energy spectra of the proton and electron fluxes, there is no effect of softening the spectrum with time at the time of the flare appearance. This indicates the possibility of particle accumulation above the active region (AR), which entails further continuous energy emission of the solar flare from AR. Dependences have been obtained between the geomagnetic activity and the solar wind speed at a given interplanetary magnetic field strength during the periods under study for the changes in the orbital motion periods of satellites. The corresponding correlation coefficients are 0.93–0.96.     

强磁场中的逆Compton散射与γ射线爆能谱

本文认为强磁场中的逆Compton散射可能是γ射线爆的主要辐射机制.其能谱是由源区质子产生的低频光子经强磁场中非热电子的Compton散射形成的.我们利用非相对论情形(B/B_(cr)≤1,hv_i/m_ec~2≤1)下强磁场中的Compton散射微分截面,导出了上述Compton散射的辐射谱公式,由此很好地拟合了典型γ射线爆GB811016的观测能谱.     

Photon Spectra of Electron–Electron Bremsstrahlung

A formula is given for the cross section of electron–electron bremsstrahlung in the rest system of the target electron. It is in particular appropriate for the calculation of photon spectra in astrophysical applications, e.g., if the primary electrons have energy distributions in the form of a power law. For the long-wavelength limit of the spectrum the cross section is specified in closed form.     

A semianalytical method for calculating the parameters of the electromagnetic halos around extragalactic gamma-ray sources

The ultrahigh-energy (>20 TeV ) gamma rays emitted by active galactic nuclei can be absorbed in intergalactic space through the production of electron-positron pairs during their interaction with extragalactic background photon fields. The electrons and positrons produced by this interaction form an electromagnetic halo. We have studied the halo formation and calculated the halo radiation spectrum. The magnetic field in the halo formation region is assumed to be strong enough for the electron velocities to be isotropized. For such fields, the halo formation process can be described by the method of generations. We calculated the synchrotron and Compton backscattering radiation spectra for the total halo luminosity. We obtained the spatial distribution of the radiation for a point gamma-ray source.     

Intergalactic shock acceleration and the cosmic gamma-ray background

We investigate numerically the contribution to the cosmic gamma-ray background from cosmic-ray ions and electrons accelerated at intergalactic shocks associated with cosmological structure formation. We show that the kinetic energy of accretion flows in the low-redshift intergalactic medium is thermalized primarily through moderately strong shocks, which allow for an efficient conversion of shock ram pressure into cosmic-ray pressure. Cosmic rays accelerated at these shocks produce a diffuse gamma-ray flux which is dominated by inverse Compton emission from electrons scattering off cosmic microwave background photons. Decay of neutral π mesons generated in p–p inelastic collisions of the ionic cosmic-ray component with the thermal gas contribute about 30 per cent of the computed emission. Based on experimental upper limits on the photon flux above 100 MeV from nearby clusters we constrain the efficiency of conversion of shock ram pressure into relativistic CR electrons to  ≲1 per cent  . Thus, we find that cosmic rays of cosmological origin can generate an overall significant fraction of order 20 per cent and no more than 30 per cent of the measured gamma-ray background.     

Non-thermal emission from Vela X and PWN G0.9＋0.1

We study the multi-waveband non-thermal emission from the pulsar wind neb- ulae (PWNe) Vela X and G0.9 + 0.1 in the frame of a time-dependent model describing non-thermal radiation from the PWNe. In such a model, the relativistic wind of parti- cles driven by a central pulsar blows into the ambient medium and creates a termination shock that accelerates the particles to very high energy in a PWN. The non-thermal pho-tons in the PWN are produced both by synchrotron radiation and the inverse Compton process, with electrons coming directly from the pulsar magnetosphere and electrons be- ing accelerated at the termination shock. We apply this model to reproduce the observed multi-waveband photon spectra of Vela X and the G0.9+0.1, both of which have been detected emitting very high energy photons. Our results indicate that TeV photons are produced by the inverse Compton scattering of the high-energy electrons in the infrared photon field in both Vela X and PWN G0.9+0.1. The TeV photons from these two PWNe may have leptonic origins.     

Rocket observations of the interaction of auroral electrons with the atmosphere

Electron spectra obtained during the flight of Black Brant VB-31 on August 17, 1970 through a stable aurora to a height of 268 km have been analyzed in detail to obtain the pitch angle distributions from 25 to 155° and the electron energy distributions over an energy range of 18 keV to 20 eV through the region of atmospheric interaction down to 97 km. Backscatter ratios for 140° pitch angle range from 0.065 for 18 keV electrons to 0.22 for 1 keV electrons. Backscatter of lower energy electrons decreases with atmospheric depth below 200 km. The effect of the interactions between auroral electrons and the atmosphere is such as to give a peak in electron flux which moves progressively to higher energies with penetration depth. The secondary electron flux increases monotonically with height up to 200 km. The secondary electron spectrum can be approximated by an energy power over small energy ranges but its form is somewhat dependent on height and on the primary electron spectrum.     

A Study of the Low Energy Cutoff of Nonthermal Electrons in RHESSI Flares

The flattening at the low energy end of the hard X-ray (HXR) photon spectrum of solar flares was generally thought to be due to a cutoff of nonthermal electrons in flares. However, some authors have suggested that inverse Compton scattering (i.e., the albedo effect) or certain other reaction of flare photons with the lower atmosphere can also lead to the flattening. This paper adopts the method of deriving the cutoff proposed by Gan et al. ^[12–14], and makes a statistical analysis on 100 flares observed by the satellite Ramaty High Energy Solar Spectroscopy Imager (RHESSI) in 2002–2005. We found that after the albedo correction, the HXR photon spectra of 18 flares can be fitted with single powerlaw spectra, and those of 80 flares, with double power-law spectra. Besides, 21 flares can be directly interpreted with a single power-law electron spectrum plus a low energy cutoff. The range of the low energy cutoff is 20–50 keV and the mean value is approximately 30 keV. Some other possible interpretations are also investigated.     

Observational limits on inverse Compton processes in gamma-ray bursts

Inverse Compton (IC) scattering is one of two viable mechanisms that can produce prompt non-thermal soft gamma-ray emission in gamma-ray bursts. IC requires low-energy seed photons and a population of relativistic electrons that upscatter them. The same electrons will upscatter the gamma-ray photons to even higher energies in the TeV range. Using the current upper limits on the prompt optical emission, we show that under general conservative assumption the IC mechanism suffers from an 'energy crisis'. Namely, IC will overproduce a very high energy component that would carry much more energy than the observed prompt gamma-rays, or alternatively it will require a low-energy seed that is more energetic than the prompt gamma-rays. Our analysis is general, and it makes no assumptions on the specific mechanism that produces the relativistic electron population.     

Calibration of the Cherenkov telescope array using cosmic ray electrons

Cosmic ray electrons represent a background for gamma-ray observations with Cherenkov telescopes, initiating air-showers which are difficult to distinguish from photon-initiated showers. This similarity, however, and the presence of cosmic ray electrons in every field observed, makes them potentially very useful for calibration purposes. Here we study the precision with which the relative energy scale and collection area/efficiency for photons can be established using electrons for a major next generation instrument such as CTA. We find that variations in collection efficiency on hour timescales can be corrected to better than 1%. Furthermore, the break in the electron spectrum at ∼ 0.9 TeV can be used to calibrate the energy scale at the 3% level on the same timescale. For observations on the order of hours, statistical errors become negligible below a few TeV and allow for an energy scale cross-check with instruments such as CALET and AMS. Cosmic ray electrons therefore provide a powerful calibration tool, either as an alternative to intensive atmospheric monitoring and modelling efforts, or for independent verification of such procedures.     

Non-thermal emission from old supernova remnants

We study the non-thermal emission from old shell-type supernova remnants (SNRs) on the frame of a time-dependent model. In this model, the time-dependent non-thermal spectra of both primary electrons and protons as well as secondary electron/positron (e^±) pairs can be calculated numerically by taking into account the evolution of the secondary e^± pairs produced from proton–proton (p–p) interactions as accelerated protons collide with the ambient matter in an SNR. The multiwavelength photon spectrum for a given SNR can be produced through leptonic processes such as electron/positron synchrotron radiation, bremsstrahlung and inverse Compton scattering as well as hadronic interaction. Our results indicate that the non-thermal emission of the secondary e^± pairs is becoming more and more prominent when the SNR ages in the radiative phase because the source of the primary electrons has been cut off and the electron synchrotron energy loss is significant for a radiative SNR, whereas the secondary e^± pairs can be produced continuously for a long time in the phase due to the large energy-loss time for the p–p interaction. We apply the model to two old SNRs, G8.7−0.1 and G23.3−0.3, and the predicted results can explain the observed multiwavelength photon spectra for the two sources.     

Diffuse extragalactic gamma-radiation above ‘black-body cutoff’

The possible contribution of gamma-rays predicted within the universal cosmic-ray (CR) hypothesis to the energy range of CR spectrum above black-body cutoff is calculated. These gamma-rays arise from the relativistic electromagnetic cascade generated in the field of microwave background radiation (MBR). The ultra-high energy photons and electrons that initiate the cascade are produced at the decay of -mesons created in interactions of photons with the MBR. Simple analytic expression for cascade gamma-ray spectrum is obtained from the solution of kinetic equations for electrons and photons as well as for protons propagating in the MBR field. It is shown that at certain values of magnetic field and radio-wave density in the intergalactic space te flux of cascade gamma-rays may at least partly mask the black-body cutoff in the CR spectrum.Deceased, August 13, 1989.     

Electrons in a closed galaxy model of cosmic rays

We consider the consistency of positrons and electrons with a propagation model in which the cosmic rays are stopped by nuclear collisions or energy losses before they can escape from the Galaxy (the closed-galaxy model). The fact that we find no inconsistency between the predictions and the data implies that the protons which produce the positrons by nuclear reactions could have their origin in a large number of distant sources, as opposed to the heavier nuclei which in this model come from a more limited set of sources. The closed-galaxy model predicts steep electron and positron spectra at high energies. None of these are inconsistent with present measurements; but future measurements of the spectrum of high-energy positrons could provide a definite test for the model. The closed-galaxy model also predicts that the interstellar electron intensity below a few GeV is larger than that implied by other models. The consequence of this result is that electron brems-strahlung is responsible for about 50% of the galactic gamma-ray emission at photon energies greater than 100 MeV.     

Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey

The Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) X-ray data base (February 2002 – May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularized inversion technique, we determine the mean electron flux distribution from count spectra for a selection of events with flat photon spectra in the 15 – 20 keV energy range. Such spectral behavior is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range (e.g., a low-energy cutoff in the mean electron spectra of nonthemal particles). We have found 18 cases that exhibit a statistically significant local minimum (a dip) in the range of 13 – 19 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction is applied, all low-energy cutoffs in the mean electron spectrum are removed, and hence the low-energy cutoffs in the mean electron spectrum of solar flares above ∼ 12 keV cannot be viewed as real features. If low-energy cutoffs exist in the mean electron spectra, their energies should be less than ∼ 12 keV.     

Joint Effects of Compton Backscattering and Low-Energy Cutoff on the Flattening of Solar Hard X-Ray Spectra at Lower Energies

Theoretical calculation has shown that the spectrum of the Compton backscattering component in solar hard X-ray flares has a peak around 30 keV for a primary power-law source. Thus the superposition of the Compton backscattering component could cause a photon spectrum received at the Earth to be flattened below the peak energy and steeper above the peak energy. On the other hand, because a thick-target bremsstrahlung photon with a given energy E only could be produced by a nonthermal electron with an energy larger than E, thus if a power-law electron spectrum is cutoff below an energy E _c, then the produced photon spectrum will become flattened below E _c. In this work we present a calculation of the joint effects of the Compton backscattering and the low-energy cutoff on the spectral characteristics of the received solar hard X-ray in the energy range 10–100 keV. The results show that the flattening caused purely by the Compton backscattering could be comparable with that by the low-energy cutoff for hard spectra. So, it is obvious that the joint effects of the low-energy cutoff and the Compton backscattering could result in the received photon spectra to be much more flattened at lower energies. On the other hand, compared to the primary photon spectrum, the received photon spectral index will increase about 0.15 due to the Compton backscattering at higher energy, which seems independent of the primary spectral index.     

Energy spectra of particles accelerated in a reconnecting current sheet with the guiding magnetic field

Electron and proton acceleration by a super-Dreicer electric field is investigated in the non-neutral reconnecting current sheet (RCS) with a non-zero longitudinal component of the magnetic field ('guiding field'). The guiding field is assumed parallel to the direction of electric field and constant within an RCS. The other two magnetic field components, transverse and tangential, are considered to vary with distances from the X null point of an RCS. The proton and electron energy spectra are calculated numerically from a motion equation using the test particle approach for model RCSs with constant and variable densities. In the presence of a strong or moderate guiding field, protons were found fully or partially separated from electrons at ejection from an RCS into the opposite, 'electron' and 'proton', semiplanes. In the case of a weak guiding field, both protons and electrons are ejected symmetrically in equal proportions as neutral beams. The particles ejected from an RCS with a very weak or very strong guiding field have power-law energy spectra with spectral indices of about 1.5 for protons and 2.0 for electrons. For a moderate guiding field, the energy spectra of electrons ejected into the opposite semiplanes are mixed, i.e. in the 'electron-dominated' semiplane power-law energy spectra for electrons and thermal-like for protons, while in the 'proton' semiplane they are symmetrically mirrored.     

Acceleration of Electrons and Protons in Reconnecting Current Sheets Including Single or Multiple X-points

Kinematic characteristics of electrons and protons in the magnetic reconnecting current sheet in the presence of a guide field are investigated. Particle trajectories are calculated for different values of the guide field by a test-particle calculation. The relationship between the final energy and the initial position has also been studied. We found that the addition of a guide field not only allows particles to get more energy and not only results in the separation of electrons and protons, but also causes the reconnecting electric field to selectively accelerate electrons and protons for different initial positions. The energy spectrum eventually obtained is the common power-law spectrum, and as the guide field increases, the index for the spectrum of electrons decreases rapidly. However, for a weak background magnetic field, proton spectra are not very sensitive to the guide field; but for a strong background field, the dependence of the spectrum index is similar to the electron spectrum. Meanwhile, kinematic characteristics of the accelerated particles in the current sheet including multiple X-points and O-points were also investigated. The result indicates that the existence of the multiple X- and O-points helps particles trapped in the accelerating region to gain more energy, and yields the double or multiple power-law feature.