Book

Abstract

This volume presents the lecture notes of the 24th Advanced Course of the Swiss Society for Astrophysics and Astronomy in March 1994 at Les Diablerets. In three lectures on magnetohydrodynamics, on kinetic plasma physics and on particle acceleration leading experts describe the physical basis of their subjects and extend the discussion to several applications in modern problems of astrophysics. In style and presentation the texts are well-suited for graduate work in plasma astrophysics, one of the very important tools of modern astronomy. The themes developed in this book will be helpful in understanding many processes in the universe from the solar corona to active galaxies.

Chapters (3)

Many fundamental processes in the universe are determined by the magnetic field. The object in which we can study such processes in greatest detail is the Sun, and so it will be natural in this course of lectures to focus on the Sun. In the first lecture I aim to introduce you to it and then in the second to set up the basic theory for magnetic field behaviour. In later lectures this theory is applied to many mysterious processes on the Sun that are only just beginning to be understood. Chapters 3, 4 and 6 develop the theory for the fundamental processes of magnetohydrodynamic force balance, waves and reconnection. Chapter 5 describes the solar wind, bearing in mind that winds occur in many other stars and galaxies. Chapter 7 discusses mechanisms for heating the solar corona, which are likely to be relevant to the coronae of other stars and of accretion discs. Chapter 8 describes prominences, which are evidence of the basic astrophysical process of radiative instability and which occur on other stars. Finally, the flare-like behaviour modelled in Chapter 9 is not restricted to the Sun alone. Thus many of the key processes occur elsewhere in the cosmos, so it is very important to develop a good understanding of what the Sun is telling us about them.
In the kinetic theory of plasmas, particles are described by distribution functions whose evolution is determined by kinetic equations. The spectrum of fluctuations in the plasma includes distributions of weakly damped waves. The kinetic equation for the particles may be averaged over these fluctuations to find averaged kinetic equations, sometimes called the quasilinear equations. These kinetic equations describe the slow evolution of the waves, which may be damped or may grow, and of the particles, which diffuse in momentum space. In this lecture course, a general derivation of the quasilinear equations is given in the first two lectures, and these equations are used to treat resonant scattering and related processes is the next three lectures. The last four lectures are concerned with radiation processes in various astrophysical sources. Radiation processes may also be treated using the theory outlined in the first two lectures.
... The Sun, its atmosphere, and associated flow dynamics have been an active area of present-day research for many years because of their richness in various collective degrees of freedom exhibited through diverse waves, fluctuations, and oscillations [1][2][3][4][5][6]. Because of many such gravito-electromagnetic wave-related phenomena, the outer solar atmosphere is so hot that even its gravity cannot prevent it from continuously expanding in association with thermal pressure into surrounding cold interplanetary space [3][4][5][6][7][8]. ...
... The problem of multiscale outflow formation dynamics, dynamical stability, and the mechanism of the solar wind acceleration from the slow to fast components are yet to be well understood in detail [7][8][9][10][11][12][13]. Many authors in the past have made bold efforts to see the solar wind flow dynamics and stability from different perspectives, like the hydrodynamic model [1,4,8,9], magnetohydrodynamic (MHD) model [1,3,4,6,7], kinetic model [11,12], and so forth. ...
... The problem of multiscale outflow formation dynamics, dynamical stability, and the mechanism of the solar wind acceleration from the slow to fast components are yet to be well understood in detail [7][8][9][10][11][12][13]. Many authors in the past have made bold efforts to see the solar wind flow dynamics and stability from different perspectives, like the hydrodynamic model [1,4,8,9], magnetohydrodynamic (MHD) model [1,3,4,6,7], kinetic model [11,12], and so forth. ...
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A linear stability analysis of a simple polytropic model for the solar wind dynamics within the framework of a magnetohydrodynamic (MHD) equilibrium configuration is theoretically proposed. The simplistic analysis is based on the model developed basing on the data available from the Advanced Composition Explorer (ACE) spacecraft mission. A unique form of dispersion relation is derived by coupling the adiabatic and polytropic processes in the limit of ideal gas approximation for the solar wind gas in accordance with the standard Fourier technique. Applying usual variable-separation methodology on the dispersion relation, we obtain the linear growth rate of the fluctuations. It is seen that the growth rate is an explicitly nonlinear function of the variable polytropic index (α) and radial position (r) with respect to the considered center of the Sun. Numerical analyses are carried out to understand the physical insight of the growth profiles of the fluctuations. It is shown that the growth is maximum near the solar corona, where α ~ 1, relative to that observed elsewhere in the entire solar plasma system. The source for this growth may be attributed to the free flow of energy coming from the dynamic equilibrium of the solar plasma itself. As compared with existing model predictions, our results are qualitatively capable to reproduce the average behavior of the solar wind fluctuation and stability behaviors on the astrophysical scales of space and time.
... Jos jokin mekanismi, esimerkiksi sironta, muuttaa varausten nousukulmaa magneettikentän ollessa kokoonpuristettuna, saa osa hiukkasista lisäyksen pitkittäiseen energiaan, joka ei katoa laajentumisen aikana. Jatkamalla tätä usean pumppauksen ajan saa pieni osa hiukkaspopulaatiosta jatkuvaa lisäystä energiaan [11]. ...
... Yhtälöt (3.15) voidaan ratkaista ilmaisemalla suureet alavirran puolella kaukaa ylävirrasta mitattujen arvojen avulla. Ratkaisuja on kolme: nopea ja hidas shokki sekä rotationaalinen epäjatkuvuus -tässä ollaan kiinnostuneita vain nopean shokin tapauksesta [11]. Merkitään puristussuhdetta eli tiheyden hyppyä X:llä, jolloin jatkuvuusyhtälöstä saadaan ...
... positiivisena ratkaisuna [11]. ...
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Planeettainvälisessä avaruudessa havaitaan runsaasti Auringosta peräisin olevia korkeaenergiaisia hiukkasia. Havainnot voidaan jakaa karkeasti lyhyt- ja pitkäkestoisiin. Yleisin selitys jälkimmäisille on diffusiivinen shokkikiihdytys koronan massapurkausten edellään työntämissä shokkiaalloissa. Hiukkaset siroavat shokin turbulentista sähkömagneettisesta kentästä ja saavat lisää energiaa ylittäessään shokkirintaman monta kertaa. Kiihdytys alkaa koronassa ja jatkuu useiden päivien ajan massapurkauksen liikkuessa poispäin Auringosta. Havaintojen mukaan koronassa tapahtuva kiihdytys, jossa protonit voivat saavuttaa jopa 1 GeV suuruusluokkaa olevan energian, tapahtuu minuuttien aikaskaaloissa. Korkeaenergiaisten hiukkasten energiaspektri on tyypillisesti potenssilaki dN/dE ~ E^{-sigma}, missä sigma on lähellä ykköstä oleva vakio. Opinnäytteessä esitellään diffusiivisen shokkikiihdytyksen teoria ja tutkitaan kiihdytystä testihiukkassimulaatiolla. Koronan aktiivista aluetta mallinnetaan yksinkertaistetulla magneettikentällä. Simulaatiossa lasketaan tasomaisen shokin eteen injektoitujen protonien ratoja siihen asti, kun ne joko osuvat Auringon pintaan tai karkaavat planeettainväliseen avaruuteen. Lopputuloksista lasketuista statistiikoista etsitään kiihdytykseen vaikuttavia tekijöitä. Saatujen tuloksien perusteella koronan magneettikentän geometrialla on suuri merkitys saavutettavaan energiaan. Tehokkainta kiihdytys on geometrioissa, joissa shokki on lähes poikittainen. Erityisesti sironnan ei tarvitse olla voimakasta suurten energioiden saavuttamiseksi. Sen vaikutus näyttäisi olevan enneminkin jakaumafunktion isotropisointi, jolloin energiaspektristä tulee potenssilakimuotoinen.
... In general there are two classes of generation mechanisms of SRBT III: (i) nonlinear wave-wave coupling processes [190] the coalescence of two Langmuir waves, first proposed by [184] and (ii) the highly nonlinear process proposed by Yoon [191,192] and direct emission mode conversion due to density inhomogeneity [109,193,194]. A standard homogeneous quasi-linear theory argues that the back-reaction to wave growth should plateau the beam, remove its free energy, and cease the production of Langmuir-like waves and radiation within much less than 100 km of the source of the beam [195]. ...
... 35 are highly localized [202,203]. One fundamental theory, it is believed is that Landau resonance with the unstable electron beam is responsible generates Langmuir waves, which are thought to undergo nonlinear wave-wave interactions that produce electromagnetic emissions at the local electron plasma frequency (f pe ) and its second harmonic (2f pe ) [190,194,[204][205][206][207]. The second question concerning the origin of type III burst is how the generated Langmuir waves can convert to electromagnetic waves either the fundamental or the second harmonic of the electron plasma frequency associated with the observed bursts. ...
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The solar flare and Coronal Mass Ejections (CMEs) are well known as one of the most massive eruptions which potentially create major disturbances in the interplanetary medium and initiate severe magnetic storms when they collide with the Earth's magnetosphere. However, how far the solar flare can contribute to the formation of the CMEs is still not easy to be understood. These phenomena are associated with II and III burst it also divided by sub-type of burst depending on the physical characteristics and different mechanisms. In this work, we used a Compound Astronomical Low-cost Low-frequency Instrument for Spectroscopy in Transportable Observatories (CALLISTO) system. The aim of the present study is to reveal dynamical properties of solar burst type II and III due to several mechanisms. Most of the cases of both solar radio bursts can be found in the range less that 400 MHz. Based on solar flare monitoring within 24 hours, the CMEs that has the potential to explode will dominantly be a class of M1 solar flare. Overall, the tendencies of SRBT III burst form the solar radio burst type III at 187 MHz to 449 MHz. Based on solar observations, it is evident that the explosive, short timescale energy release during flares and the long term, gradual energy release expressed by CMEs can be reasonably understood only if both processes are taken as common and probably not independent signatures of a destabilization of pre-existing coronal magnetic field structures. The configurations of several active regions can be sourced regions of CMEs formation. The study of the formation, acceleration and propagation of CMEs requires advanced and powerful observational tools in different spectral ranges as many 'stages' as possible between the photosphere of the Sun and magnetosphere of the Sun and magnetosphere of the Earth. In conclusion, this range is a current regime of solar radio bursts during CMEs events.
... Both ideas grew from the fact that, in the solar corona, there are corrugated density structures (e.g. see Benz [21]) that imply the existence of under-dense and over-dense flux tubes. According to Duncan [19], the emission may occur inside an under-dense flux tube, where the density is at least four times lower than the exterior density, such that F and H waves with the same frequency would leave the duct at the same altitude, whereas Robinson [20] argued that over-dense density fibers could result in scattering that tends to shift the apparent source heights of both F and H waves. ...
... Motivated by the two critical issues discussed in the preceding section, a totally different scenario was proposed by Wu et al. [23,24] and Yoon et al. [25], in which the cyclotron maser mechanism [26,21] is advocated. The basic idea developed from observations that F/H waves with identical frequencies have overlapping source regions, as discussed previously in Section 2. In this more recent theory, we extend Duncan's notion by considering that, in the corona, there are density-depleted flux tubes in which the plasma density is much lower than the density of the exterior plasma (A model theory was proposed by Wu et al. [27] to explain the origin of such density depletion). ...
Article
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In solar radiophysics, many theories for type III bursts have been proposed during the past 60 years. Almost all these theories are based on the plasma hypothesis, which assumes that (i) the radiation is mainly generated by Langmuir waves via nonlinear processes and (ii) the radiation has frequencies close to the local plasma frequency and/or its second harmonic in the source region. We feel strongly that it is time to advocate an alternative approach without recourse to the plasma hypothesis. This brief discussion explains why.
... Particle acceleration processes provide an alternative way to accelerate particles in the absence of a global electric field. The existing literature (Blandford 1994;Kirk et al. 1994;Melrose 1996) suggests three main approaches to accelerate charged particles in an astrophysical plasma environment: shock acceleration (DSA), coherent electric field acceleration, and stochastic acceleration (STA). ...
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Particle acceleration is an ubiquitous phenomenon in astrophysical and space plasma. Diffusive shock acceleration (DSA) and stochastic turbulent acceleration are known to be the possible mechanisms for producing very high energetic particles, particularly in weakly magnetized regions. An interplay of different acceleration processes along with various radiation losses is typically observed in astrophysical sources. While DSA is a systematic acceleration process that energizes particles in the vicinity of shocks, stochastic turbulent acceleration (STA) is a random energizing process, where the interaction between cosmic ray particles and electromagnetic fluctuations results in particle acceleration. This process is usually interpreted as a biased random walk in energy space, modelled through a Fokker-Planck equation. In the present work, we describe a novel Eulerian algorithm, adopted to incorporate turbulent acceleration in the presence of DSA and radiative processes like synchrotron and Inverse-Compton emission. The developed framework extends the hybrid Eulerian-Lagrangian module in a full-fledged relativistic Magneto-hydrodynamic (RMHD) code PLUTO. From our validation tests and case studies, we showcase the competing and complementary nature of both acceleration processes. Axisymmetric simulations of an RMHD jet with this extended hybrid framework clearly demonstrate that emission due to shocks is localized while that due to turbulent acceleration originates in the backflow and is more diffuse, particularly in the high energy X-ray band.
... The solar space weather events like Coronal Mass Ejections and solar flares are usually accompanied by solar radio bursts, which can be used for a low-cost real-time space weather monitoring [2]. There are many reviews of the history of these phenomena, specifically, by Kundu [3] and McLean and Labrum [4] for observational reviews, Zheleznyakov [5], Melrose [6] and Benz [7] for the theory of radio emission in these bursts, and Pick [8] and Schwenn [9] for the relationship with space weather. Over periods of increased solar activity, several Coronal Mass Ejections (CMEs) can be launched by the same or nearby active regions [10]. ...
Article
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Solar space weather events like Coronal Mass Ejections and solar flares are usually accompanied by solar radio bursts, which can be used for a low-cost real-time space weather monitoring. In order to make a standard system, a CALLISTO (Compound Astronomical Low-cost Low-frequency Instrument for Spectroscopy in Transportable Observatory) spectrometers, designed and built by electronics engineer Christian Monstein of the Institute for Astronomy of the Swiss Federal Institute of Technology Zurich (ETH Zurich) have been already developed all over the world since 2005 to monitor the solar activities such as solar flare and Coronal Mass Ejections (CMEs). Up to date, there are 25 sites that used the same system in order to monitor the Sun within 24 hours. This outstanding project also is a part of the United Nations together with NASA initiated the International Heliophysical Year IHY2007 to support developing countries participating in ‘Western Science’. Beginning February 2012, Malaysia has also participated in this project. The goals of this work is to highlight how does the signal processing of solar radio burst data transfer from a site of National Space Centre Banting Selangor directly to the Institute of Astrophysics Switzerland. Solar activities in the low region, focusing from 150 MHz to 400 MHz is observed daily beginning from 00.30UT 12.30 UT. Here, we highlighted how does the signal processing work in order to make sure that the operation is in the best condition. Although the solar activities have experienced rapid growth recently, high-level management of CALLISTO system has remained successfully manage the storage of data. It is also not easy to maintain the future data seems the number of sites are also growing from time to time. In this work, we highlighted the potential role of Malaysia as one of the candidate site that possible gives a good data and focusing on a few aspects such as optimization, and performance evaluation data and visualization.
... The intensity of radiation of frequency o produced per unit path length (z) per uniqut frequency interval by a single electron of velocity pci travelling in a medium of dielectric constant &(U) is given by [13] The spontaneous Cerenkov radiation, being proportional to the number of electrons, is a weak process. It can be strengthened if the prebunched electron beam of bunch size smaller than the wavelength of the radiation is sent through the medium. ...
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The universe is made up of plasmas and fluids. The plasma phenomena exhibits itself through electromagnetic processes and the fluid through configurational processes. I shall try to illustrate both these aspects by taking examples from the observable universe.
... Surprisingly, SC has written in Section 3.2 of his paper that he has applied the approximation << V A 2 based on the values given in We calculate the values of damping length scales (D) at a few locations from the data presented by SC in his Fig. 1(a). Since it is not clear from the SC's paper for which period he has produced Fig (ii) The group velocity of damped Alfvén waves cannot be equal to the local Alfvénic velocity in the solar plasma in which the collisional dissipating properties (viscosity, magnetic diffusivity etc.) are effectively presented [1,6]. This is the case for the ideal plasma in which no dissipation mechanism works, i.e., angular frequency ( ) is linearly proportional to the wave number (k) [7]. ...
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We comment on the recently published paper by Chandra (Open Astronomy Journal, 2009, 2, 16-18), and show that his results are erroneous in the context of the propagation and dissipation of Alfvén waves in polar coronal holes under individual effects of magnetic diffusivity and viscosity.
... The low frequency part of the gyrosynchrotron spectrum after 09:57 UT ($300 MHz) is therefore likely dominated by self-absorption. Following Melrose (1978), the maximum flux density F from a self-absorbed source at a frequency m is such that: ...
Article
The GOES X3.9 flare on 03 November 2003 at ∼09:45 UT was observed from metric to millimetric wavelengths by the Nançay Radioheliograph (NRH), the Radio Solar Telescope Network (RSTN) and by radio instruments operated by the Institute of Applied Physics (University of Bern). This flare was simultaneously observed and imaged up to several 100 keV by the RHESSI experiment. The time profile of the X-ray emission above 100 keV and of the radio emissions shows two main parts, impulsive emission lasting about 3 min and long duration emission (partially observed by RHESSI) separated in time by 4 min. We shall focus here on the modulations of the broad-band radio continua and of the X-ray emissions observed in the second part of the flare. The observations suggest that gyrosynchrotron emission is the prevailing emission mechanism even at decimetric wavelengths for the broad-band radio emission. Following this interpretation, we deduce the density and the magnetic field of the decimetric sources and briefly comment on possible interpretations of the modulations.
Article
We examine the effect of a jet transversal structure from magnetohydrodynamic semi-analytical modelling on the total intensity profiles of relativistic jets from active galactic nuclei. In order to determine the conditions for forming double- and triple-peaked transverse intensity profiles, we calculate the radiative transfer for synchrotron emission with self-absorption from the jets described by the models with a constant angular velocity and with a total electric current closed inside a jet. We show that double-peaked profiles appear either in the models with high maximal Lorentz factors or in optically thick conditions. We show that triple-peaked profiles in radio galaxies constrain the fraction of the emitting particles in a jet. We introduce the possible conditions for triple-peaked profiles under the assumptions that nonthermal electrons are preferably located at the jet edges or are distributed according to Ohmic heating.
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Solar energetic particles (SEPs) accelerated from shocks driven by coronal mass ejections (CMEs) are one of the major causes of geomagnetic storms on Earth. Therefore, it is necessary to predict the occurrence and intensity of such disturbances. For this purpose we analyzed in detail 38 non-interacting halo and partial halo CMEs, as seen by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph, generating SEPs (in > 10 MeV, > 50 MeV, and > 100 MeV energy channels) during the quadrature configuration of the Solar TErrestrial RElations Observatory (STEREO) twin spacecrafts with respect to the Earth, which marks the ascending phase of solar cycle 24 (i.e., 2009–2013). The main criteria for this selection period is to obtain height–time measurements of the CMEs without significant projection effects and in a very large field of view. Using the data from STEREO/Sun Earth Connection Coronal and Heliospheric Investigation (STEREO/SECCHI) images we determined several kinematic parameters and instantaneous speeds of the CMEs. First, we compare instantaneous CME speed and Mach number versus SEP fluxes for events originating at the western and eastern limb; we observe high correlation for the western events and anticorrelation for the eastern events. Of the two parameters, the Mach number offers higher correlation. Next we investigated instantaneous CME kinematic parameters such as maximum speed, maximum Mach number, and the CME speed and Mach number at SEP peak flux versus SEP peak fluxes. Highly positive correlation is observed for Mach number at SEP peak flux for all events. The obtained instantaneous Mach number parameters from the emperical models was verified with the start and end time of type II radio bursts, which are signatures of CME-driven shock in the interplanetary medium. Furthermore, we conducted estimates of delay in time and distance between CME, SEP, and shock parameters. We observe an increase in the delay in time and distance when SEPs reach peak flux with respect to CME onset as we move from the western to the eastern limb. Western limb events (longitude 60°) have the best connectivity and this decreases as we move towards the eastern limb. This variation is due to the magnetic connectivity from the Sun to the Earth, called the Parker spiral interplanetary magnetic field. Comparative studies of the considered energy channels of the SEPs also throw light on the reacceleration of suprathermal seed ions by CME-driven shocks that are pre-accelerated in the magnetic reconnection.
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Electrons are accelerated at the shock wave diffuse and advect outward, and subsequently drift away into the emitting region of the jet that is located in the downstream flow from the plane shock. The current work considers the acceleration of the electrons in the shock front. Assuming a proper boundary condition at the interface between the shock and the downstream zones, a novel particle distribution in the downstream flow is proposed in this work to reproduce the broadband spectral energy distribution of BL Lac objects. We find that (1) we can obtain the particle distribution downstream of the shock wave in four cases; (2) electrons with higher energy (γ>γ0) dominate the emission spectrum; (3) the distinctly important physical parameters assumed in our model can reasonably reproduce the multi-wavelength spectrum of the high-synchrotron-peaked BL Lac object Markarian 421 (Mrk 421).
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Context. Radio observations at metre-centimetre wavelengths shed light on the nature of the emission of H II regions. Usually this category of objects is dominated by thermal radiation produced by ionised hydrogen, namely protons and electrons. However, a number of observational studies have revealed the existence of H II regions with a mixture of thermal and non-thermal radiation. The latter represents a clue as to the presence of relativistic electrons. However, neither the interstellar cosmic-ray electron flux nor the flux of secondary electrons, produced by primary cosmic rays through ionisation processes, is high enough to explain the observed flux densities. Aims. We investigate the possibility of accelerating local thermal electrons up to relativistic energies in H II region shocks. Methods. We assumed that relativistic electrons can be accelerated through the first-order Fermi acceleration mechanism and we estimated the emerging electron fluxes, the corresponding flux densities, and the spectral indexes. Results. We find flux densities of the same order of magnitude of those observed. In particular, we applied our model to the “deep south” (DS) region of Sagittarius B2 and we succeeded in reproducing the observed flux densities with an accuracy of less than 20% as well as the spectral indexes. The model also gives constraints on magnetic field strength (0.3–4 mG), density (1–9 × 10 ⁴ cm ⁻³ ), and flow velocity in the shock reference frame (33–50 km s ⁻¹ ) expected in DS. Conclusions. We suggest a mechanism able to accelerate thermal electrons inside H II regions through the first-order Fermi acceleration. The existence of a local source of relativistic electrons can explain the origin of both the observed non-thermal emission and the corresponding spectral indexes.
Article
We present astrochemical photodissociation region models in which cosmic-ray (CR) attenuation has been fully coupled to the chemical evolution of the gas. We model the astrochemical impact of CRs, including those accelerated by protostellar accretion shocks, on molecular clouds hosting protoclusters. Our models with embedded protostars reproduce observed ionization rates. We study the imprint of CR attenuation on ions for models with different surface CR spectra and different star formation efficiencies. We find that abundances, particularly ions, are sensitive to the treatment of CRs. We show the column densities of ions are underpredicted by the “classic” treatment of CRs by an order of magnitude. We also test two common chemistry approximations used to infer ionization rates. We conclude that the approximation based on the abundance underpredicts the ionization rate, except in regions where the CRs dominate the chemistry. Our models suggest the chemistry in dense gas will be significantly impacted by the increased ionization rates, leading to a reduction in molecules such as NH 3 and causing H 2 -rich gas to become [C ii ] bright.
Article
The present work considers a plane shock front propagating along a cylindrical jet. Electrons experience diffusive shock acceleration around the shock front, and subsequently drift away into the downstream flow, in which they emit most of their energy. Assuming a proper boundary condition at the interface between the shock zone and the downstream zone, we solve the transport equation for the electrons in the downstream flow zone, where the combined effects of escape, synchrotron and inverse Compton cooling in the Thomson regime are taken into account. Using the electron spectrum obtained in this manner we calculate the multi-wavelength spectral energy distribution of Mrk 501 in the synchrotron self-Compton scenario. We check numerically if the Klein-Nishina cross-section could be approximated to the Thomsom regime. We consider whether the model results yield physically reasonable parameters, and further discuss some of the implications of the model results. They suggest that the process of diffusive shock acceleration operates in the outflow of Mrk 501.
Chapter
We consider the acceleration of a charged test particle due to the centrifugal force in a rotating magnetosphere. We analyse the forces acting on a particle while moving along a rotating radial field line and give an analytic expression for its centrifugal acceleration. Near the light cylinder the approximation of the motion of a particle as a bead-on-the-wire along a magnetic field line breaks down. Bearing on the breakdown of this approximation, we estimate the maximum Lorentz factor attainable via centrifugal acceleration.
Article
It is largely accepted that Galactic cosmic rays, which pervade the interstellar medium, originate by means of shock waves in supernova remnants. Cosmic rays activate the rich chemistry that is observed in a molecular cloud and they also regulate its collapse timescale, determining the efficiency of star and planet formation, but they cannot penetrate up to the densest part of a molecular cloud, where the formation of stars is expected, because of energy loss processes and magnetic field deflections. Recently, observations towards young protostellar systems showed a surprisingly high value of the ionisation rate, the main indicator of the presence of cosmic rays in molecular cloud. Synchrotron emission, the typical feature of relativistic electrons, has also been detected towards the bow shock of a T Tauri star. Nevertheless, the origin of these signatures peculiar to accelerated particles is still puzzling. Here we show that particle acceleration can be driven by shock waves occurring in protostars through the first-order Fermi acceleration mechanism. We expect that shocks in protostellar jets can be efficient accelerators of protons, which can be boosted up to mildly relativistic energies. A strong acceleration can also take place at the protostellar surface, where shocks produced by infalling material during the phase of collapse are powerful enough to accelerate protons. Our model shows that thermal particles can experience an acceleration during the first phases of a system similar to the proto-Sun, and can also be used to explain recent observations. The presence of a local source of cosmic rays may have an unexpected impact over the process of the formation of stars and planets, as well as on the pre-biotic molecule formation.
Chapter
We have seen in the discussion of synchrotron radiation that there are high energy electrons in different environments in nature. One also knows since the beginning of the twentieth century that there is a “penetrating” radiation that comes from outer space and that is measurable on the ground.
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We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional MHD (see Porth et al. (2014b) for details) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter includes radiative and adiabatic losses, diffusion, and advection on the background flow of the simulated MHD nebula. By combining the models, the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9, the inner regions of Vela, and 3C 58, thereby allowing us to derive governing parameters: the magnetic field strength, average flow velocity and spatial diffusion coefficient. For comparison, the nebulae are also modelled with the semi-analytic Kennel & Coroniti (1984a) model but the Porth et al. (2014b) model generally yields better fits to the observational data. We find that high velocity fluctuations in the turbulent nebula (downstream of the termination shock) give rise to efficient diffusive transport of particles, with average Péclet number close to unity, indicating that both advection and diffusion play an important role in particle transport. We find that the diffusive transport coefficient of the order of $\sim 2\times 10^{27} (L_{\rm s}/0.42\rm Ly) cm^{2}s^{-1}$ (Ls is the size of the termination shock) is independent of energy up to extreme particle Lorentz factors of γp ∼ 1010.
Article
Powerful astrophysical sources produce non-thermal spectra of very-high-energy photons, with generic power-law distributions, through various radiative processes of charged particles, e.g., synchrotron radiation, inverse Compton processes, and hadronic interactions. Those charged particles have themselves been accelerated to ultra-relativistic energies in intense electromagnetic fields in the source. In many cases, the exact acceleration scheme is not known, but standard scenarios, such as Fermi mechanisms and reconnection processes are generally considered as prime suspects for the conversion of bulk kinetic or electromagnetic energy into a power law of supra-thermal particles. This paper proposes a short introduction to the various acceleration and radiative processes which shape the distributions of very-high-energy photons (εγ≳100 MeV) in astrophysics.
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The main signature of the interaction between cosmic rays and molecular clouds is the high ionisation degree. This decreases towards the densest parts of a cloud, where star formation is expected, because of energy losses and magnetic effects. However recent observations hint to high levels of ionisation in protostellar systems, therefore leading to an apparent contradiction that could be explained by the presence of energetic particles accelerated within young protostars. Our modelling consists of a set of conditions that has to be satisfied in order to have an efficient particle acceleration through the diffusive shock acceleration mechanism. We find that jet shocks can be strong accelerators of protons which can be boosted up to relativistic energies. Another possibly efficient acceleration site is located at protostellar surfaces, where shocks caused by impacting material during the collapse phase are strong enough to accelerate protons. Our results demonstrate the possibility of accelerating particles during the early phase of a proto-Solar-like system and can be used as an argument to support available observations. The existence of an internal source of energetic particles can have a strong and unforeseen impact on the star and planet formation process as well as on the formation of pre-biotic molecules.
Article
In the solar corona, shock waves are generated by flares and/or coronal mass ejections. They are able to accelerate electrons up to high energies and can thus be observed as type II bursts in the nonthermal solar radio radiation. In-situ measurements of shock waves in interplanetary space have shown that shock waves attached by whistler waves are preferably accompanied by the production of energetic electrons. Motivated by these observations, we study the interaction of electrons with such whistlers, which are excited by the protons accelerated by the shock. We start with a resonant whistler wave-proton interaction that accounts for the initial whistler wave generation. Then, we consider resonant whistler wave-electron interaction, treated with a relativistic approach that is responsible for the electron energization in the whistler wave field. As a result, we show that electrons can be accelerated by a resonant wave particle (i.e., whistler-electron) interaction. This mechanism acts in the case of quasi-perpendicular shock waves. After acceleration, the energetic electrons are reflected by the associated shock wave back into the upstream region. The theoretical results are compared with observations, e.g., solar type II radio bursts.
Article
The familiar correlation between the speed and angular width of coronal mass ejections (CMEs) is also found in solar cycle 24, but the regression line has a larger slope: for a given CME speed, cycle 24 CMEs are significantly wider than those in cycle 23. The slope change indicates a significant change in the physical state of the heliosphere, due to the weak solar activity. The total pressure in the heliosphere (magnetic + plasma) is reduced by ~40%, which leads to the anomalous expansion of CMEs explaining the increased slope. The excess CME expansion contributes to the diminished effectiveness of CMEs in producing magnetic storms during cycle 24, both because the magnetic content of the CMEs is diluted and also because of the weaker ambient fields. The reduced magnetic field in the heliosphere may contribute to the lack of solar energetic particles accelerated to very high energies during this cycle.
Article
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[1] The frequency resolution of the Time Domain Samplers of the S/WAVES experiments on the STEREO spacecraft has allowed clear observations of the nature of the Langmuir-Z-mode waves observed in the solar Wind in conjunction with Type III radio bursts. These include observations of transverse polarization of what are usually identified as Langmuir waves, observations of three-wave decay, indications of the cause of the broadening of the spectrum of the observed waves, new understanding of the threshold for the three-wave-decay instability, and contributions to the understanding of conversion of these waves to electromagnetic waves. Analysis, using the decay relations, shows that decay often occurs to the Z mode, or near it. Z-mode waves cannot be produced directly by the electrons of Type III bursts. The damping of Z mode and near Z mode is very small, accounting for the common occurrence of this nonlinear process. In particular, three-wave parametric decay of a Langmuir wave to another Langmuir wave has become recognized as the dominant nonlinear process for Langmuir waves from Type III bursts. It is found, however, that decay usually leaves much of the wave energy in the daughter wave and that this wave often falls in a region where modulational instability must be considered in addition to three-wave decay. On rare occasions, further decays follow the first. In these cases, the path length of the stimulating electron beam can sometimes be determined.
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The nonlinear dispersion equation for monochromatic pump Langmuir waves is solved analytically and numerically and the results are applied to Langmuir- like waves growing in Earth's foreshock. It is shown that modulational instabilities and parametric decay instabilities occur in distinct regions of W- kAo space, confirming and extending earlier work. Here W is the ratio of electric field to thermal energy density and k is the pump wavenumber. In particular, for W  10 -a and Te  3Ti modulational instability occurs only for waves with kD  (me/9Mi) 1/2, where me and Mi are electron and ion masses; decay is relevant at higher wavenumbers. Beam-driven waves in the foreshock are shown to lie well outside the region of parameter space for which modulational instability can proceed. In contrast, the beam-driven waves have wavenumbers appropriate for the decay. The beam-driven waves are also shown theoretically and observationally to have bandwidths much larger than the nonlinear growth rate for modulational instability and the parametric decay. The absence of a random-phase version of modulational instability and the decrease in growth rate caused by finite bandwidth effects provide two more arguments against modulational instability occurring frequently in the foreshock. Modulational instability may, however, be possible for very rare, intense (W  10 -2) wave packets with small wavenumbers (kAD  (m/9Mi) 1/2) and small bandwidths (Aw/wp  10-3). Furthermore, the large Langmuir bandwidths predicted and observed require that the parametric decay cannot proceed, except perhaps for very intense wave packets with W > 10 -2. Instead the random-phase, weak turbulence decay is predicted to occur, consistent with some previous observations and theoretical suggestions. Nonlinear plasma theory and our current understanding of foreshock electron beams and waves thus argue strongly against modulational instability and/or parametric decay proceeding or being important for the great majority of beam-driven Langmuir wave packets in Earth's foreshock.
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When a weakly magnetized, relativistic electron beam is injected into a plasma, the beam-plasma instability excited by nonresonant wave-particle interaction can amplify directly the electromagnetic waves. Results of calculation show that, in regions far from resonance, electromagnetic waves can still be amplified over a wide frequency range, and form plateaus under each resonance peak. As the harmonic wave number increases, the peak value of the growth rate decreases and the width of the peak also diminishes. This paper analyzes how the growth rate varies with the background parameter ωpeΩe, and the direction of incidence of the energetic electrons and the direction of the radiation. Under typical solar coronal conditions, the size, bandwidth, directivity, polarization and harmonic modes of the waves so amplified can be used to explain the solar type-III radio bursts. The present study can also apply to plasma emission in other astronomical bodies.
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Bursty waves with widely varying electric fields persist over a wide range of altitudes ~2-7RE at polar cap latitudes in Earth's inner magnetosphere. These ``PF'' waves have frequencies near expected values of the electron plasma frequency (PF), well below the electron gyrofrequency, and are believed to be generated by electron beams. Here it is demonstrated that stochastic growth theory (SGT) can account well for the detailed field statistics of the archetypal PF wave event, by showing that the observed distributions P(logE) of envelope electric fields E are well fitted by the lognormal function predicted by SGT. Weak evidence exists that a nonlinear wave process coexists with stochastic growth physics at large fields >~1 mV m-1 on the basis of fits of the observed P(logE) distribution to the SGT prediction that includes a nonlinear process at high fields and on the discovery of a class of low-frequency waves that may be produced by nonlinear decay of PF waves. An analytic model is developed for why the waves evolve to an SGT state, on the basis of waves driven by an electron beam in MHD density turbulence and the development of fluctuations in the electron beam due to wave growth occurring in localized regions. The model is viable for the polar cap plasma parameters considered, predicting that the wave burstiness should be of order that observed and that the beam fluctuations should have timescales ~10 ms that are below current detection capabilities. SGT thus accounts well for the burstiness and wave statistics, as well as the persistence of the waves and driving distribution. The consistency of the PF wave statistics with SGT also implies the presence of local electron beams over much of the polar cap, whose source is currently unknown. This application brings to five the number of contexts in which SGT applies, suggesting that SGT is widely applicable in space plasmas.
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Radio continuum emission due to thermal bremsstrahlung and optical Hfi spectral line emission arise from processes involving similar atomic entities and physical conditions. The relationship between the ∞ux density of the emission from the two processes is mainly a function of the electron temperature of the emitting region, modifled by other factors such as the mode of radiation transfer in the hydrogen spectrum. On the other hand, radio continuum radiation due to non-thermal synchrotron emission is formed by species and processes not involved in thermal emission. As a consequence, difierences between the observed radio continuum emission and Hfi emission from cosmic sources can provide reliable information on a variety of important physical aspects of the sources, including the relative importance of thermal and non-thermal radio emission and the degree of optical obscuration. This paper reviews the theory of the formation of Hfi and the radio continuum in the interstellar medium (ISM), discusses some of the factors that must be considered in comparing observations made in the two frequency regimes, and summarises the properties of some classes of galactic object that emit both optical and radio radiation.
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Context. Observational dark sinuous inflows moving sunwards, along a fan of rays were previously numerically reproduced with two simulations of 1.5D for the first time. We showed that the dark tracks can be explained as hot plasma voids generated upstream of a slow magnetoacoustic shock wave that is produced by a localized deposition of energy. Aims. We aim to confirm our “dark lane” interpretation and to identify specific 2D contributions to the description of the phenomenon. Methods. To solve the ideal and non-stationary MHD equations we used a 2D Riemann solver Eulerian code specially designed to capture supersonic flow discontinuities. Results. The numerical 2D results agree with the observational behaviour, but they show a slight shift in the characteristic parameter with respect to those found previously. Conclusions. We qualitatively confirm the behaviour found in previous papers. For a given numerical domain the period of the kink-like structure is a function of the magnetic field intensity: larger periods are associated with lower magnetic field intensities. Contrary to the 1.5D result – where the sunwards dynamic is independent of the magnetic field intensity owing to its exclusive waveguide role – in the 2D simulation the sunwards speed is higher for higher values of the magnetic field. This can be interpreted as the capability of the low coronal plasma to collimate the deposition of energy into the magnetic field direction. The moving features that consist on low-density and high-temperature plasma cavities have higher inside values of the structuring parameter β than the neighbouring media. Thus, the voids seem to be the emergence structures of a whole nonlinear interacting plasma context of shocks and waves instead of voided plasma loops that are magnetically structured.
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In this paper we study the influence of radiation reaction (RR) forces on the dynamics of centrifugally accelerated particles. It is assumed that the particles move along magnetic field lines anchored in the rotating central object. The common 'bead-on-the-wire' approximation is used. The solutions are found and analyzed for cases when the form of the prescribed trajectory (rigidly rotating field line) is approximated by: (a) straight line, and (b) Archimedes spiral. Dynamics of neutral and charged particles are compared with the emphasis on the role of RR forces in the latter case. It is shown that for charged particles there exist locations of stable equilibrium. It is demonstrated that for particular initial conditions RR forces cause centripetal motion of the particles: their 'falling' on the central rotating object. It is found that in the case of Archimedes spiral both neutral and charged particles can reach infinity where their motion has asymptotically force-free character. The possible importance of these processes for the acceleration of relativistic, charged particles by rotating magnetospheres in the context of the generation of nonthermal, high-energy emission of AGN and pulsars is discussed.
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Low Mach number, high beta fast mode shocks can occur in the magnetic reconnection outflows of solar flares. These shocks, which occur above flare loop tops, may provide the electron energization responsible for some of the observed hard X-rays and contemporaneous radio emission. Here we present new 2D particle-in-cell simulations of low Mach number/high beta quasi-perpendicular shocks. The simulations show that electrons above a certain energy threshold experience shock-drift-acceleration. The transition energy between the thermal and non-thermal spectrum and the spectral index from the simulations are consistent with some of the X-ray spectra from RHESSI in the energy regime of $E\lesssim 40\sim 100$ keV. Plasma instabilities associated with the shock structure such as the modified-two-stream and the electron whistler instabilities are identified using numerical solutions of the kinetic dispersion relations. We also show that the results from PIC simulations with reduced ion/electron mass ratio can be scaled to those with the realistic mass ratio.
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The usual strong and sudden energy release sources that necessarily lead to mode excitation suggest the importance of shocks and nonlinear waves in the corona. We discuss the importance of nonlinear waves as an alternative capable of accurately matching the observational cases of coronal seismology usually interpreted as linear waves. We present two case studies where we explore the goodness of the shock wave interpretation in magnetic structures of the low corona.
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A theoretical model is proposed for interpreting the coherent emissionmechanism of solar radio moving type IV bursts. Energetic electrons produced in flares captured by an expanding and rising magnetic flux tube exhibit a beam-like distribution of velocities on the top of the flux tube. These excite beaming plasma instability and directly amplifies O-mode electromagnetic waves. The instability growth rate sensitively depends on the coronal plasma parameter, ƒpe/ƒce and the beam-temperature Tb. This can qualitatively explain the high brightness temperature and high degree of polarization as well as the broad spectrum observed in this type of solar radio bursts.
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Beams of energetic electrons can be generated by shock waves in the solar corona. At the Sun shock waves are produced either by flares and/or by coronal mass ejections (CMEs). They can be observed as type II bursts in the solar radio radiation. Shock accelerated electron beams appear as rapidly drifting emission stripes (so-called "herringbones") in dynamic radio spectra of type II bursts. A large sample of type II bursts showing "herringbones" was statistically analysed with respect to their properties in dynamic radio spectra. The electron beams associated with the "herringbones" are considered to be generated by shock drift acceleration. Then, the accelerated electrons establish a shifted loss-cone distribution in the upstream region of the associated shock wave. Such a distribution causes plasma instabilities leading to the emission of radio waves observed as "herringbones". Consequences of a shifted loss-cone distribution of the shock accelerated electrons are discussed in comparison with the observations of "herringbones" within solar type II radio bursts.
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The solar wind interaction with Venus creates an induced magnetosphere around the planet. It is shown that within the space bound by Venus' bow shock and ionopause, there is a rich occurrence of mirror-mode-like structures in the magnetic field data. The dayside magnetosheath and nightside magnetosheath/wake regions are investigated separately. It is shown that the probability to observe mirror mode structures is much higher at the dayside, where it is also strongly dependent on the angle between the solar wind magnetic field and the bow shock normal. In Venus' wake the chance to observe these structures is low, most likely because of the fully developed turbulence in this region, which will decrease temperature anisotropies. The results stand in contrast to the very low occurrence rate claimed from data taken by the Pioneer Venus Orbiter mission.
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Since the launch of the Fermi satellite, the number of gamma-ray pulsars increased by almost one order of magnitude. These objects show pulsed emission up to tens of GeV and the associated light-curves have frequently a double-pulse structure. We study this pulsed emission by considering the striped wind model. By numerical integration of the time-dependent inverse Compton emissivity in the current sheets, we compute the phase-dependent spectral variability of this radiation. Several light curves and spectra are presented. Our model is able to explain some of the high-energy (10 MeV-10 GeV) spectral features of several gamma-ray pulsars, like Geminga and Vela.
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It is the purpose of this series of lectures to give an overview of our understanding of (electromagnetic) particle acceleration processes in astrophysics. For each process I emphasize the basic physics and point out differences and correspondences with other mechanisms. Remaining problems are summarized with references to the recent literature. For instructive reasons I first discuss a number of fundamental aspects which are common to several acceleration processes. Thereafter I have grouped the various processes for particle accelaration into three chapters according to their underlying physical mechanism: plasma turbulence, shock waves, and direct electric fields.
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The observed properties of astrophysical jets are reviewed, and the techniques used to estimate the parameters of the underlying beams are described. This information is then used in a theoretical treatement of the Kelvin-Helmholtz instability of the flows, and the relevance of this instability to the persistence of the observed structures is emphasised.
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Gamma-ray bursts (GRBs) have puzzled astronomers since their accidental discovery in the late 1960s. The BATSE detector on the COMPTON-GRO satellite has been detecting one burst per day for the last six years. Its findings have revolutionized our ideas about the nature of these objects. They have shown that GRBs are at cosmological distances. This idea was accepted with difficulties at first. The recent discovery of an X-ray afterglow by the Italian/Dutch satellite BeppoSAX has led to a detection of high red-shift absorption lines in the optical afterglow of GRB970508 and in several other bursts and to the identification of host galaxies to others. This has confirmed the cosmological origin. Cosmological GRBs release ∼1051–1053 erg in a few seconds making them the most (electromagnetically) luminous objects in the Universe. The simplest, most conventional, and practically inevitable, interpretation of these observations is that GRBs result from the conversion of the kinetic energy of ultra-relativistic particles or possibly the electromagnetic energy of a Poynting flux to radiation in an optically thin region. This generic “fireball” model has also been confirmed by the afterglow observations. The “inner engine” that accelerates the relativistic flow is hidden from direct observations. Consequently, it is difficult to infer its structure directly from current observations. Recent studies show, however, that this “inner engine” is responsible for the complicated temporal structure observed in GRBs. This temporal structure and energy considerations indicates that the “inner engine” is associated with the formation of a compact object – most likely a black hole.
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The simulation of laser wakefield accelerators with particle-in-cell codes in relativistic reference frames is described, with emphasis on the computational speed-ups, which may potentially exceed three orders of magnitude in comparison with laboratory frame configurations. The initialization of laboratory quantities in a relativistically moving frame is depicted, and the method for result comparison with the plasma rest frame is described. Benchmarks with laboratory frame simulations and experimental data where gains of ˜20 times were obtained are discussed, and potential numerical issues are analyzed. This method enables numerical simulations with shorter turnaround times required for parameter scanning, and for one-to-one three-dimensional experimental modeling of current and next generation laser wakefield experiments.
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Prompt gamma-ray burst (GRB) emission requires some mechanism to dissipate an ultrarelativistic jet. Internal shocks or some form of electromagnetic dissipation are candidate mechanisms. Any mechanism needs to answer basic questions, such as what is the origin of variability, what radius does dissipation occur at, and how does efficient prompt emission occur. These mechanisms also need to be consistent with how ultrarelativistic jets form and stay baryon pure despite turbulence and electromagnetic reconnection near the compact object and despite stellar entrainment within the collapsar model. We use the latest magnetohydrodynamical models of ultrarelativistic jets to explore some of these questions in the context of electromagnetic dissipation due to the slow collisional and fast collisionless reconnection mechanisms, as often associated with Sweet-Parker and Petschek reconnection, respectively. For a highly magnetized ultrarelativistic jet and typical collapsar parameters, we find that significant electromagnetic dissipation may be avoided until it proceeds catastrophically near the jet photosphere at large radii ($r\sim 10^{13}--10^{14}{\rm cm}$), by which the jet obtains a high Lorentz factor ($\gamma\sim 100--1000), has a luminosity of $L_j \sim 10^{50}--10^{51}\ergs$, has observer variability timescales of order 1s (ranging from 0.001-10s), achieves $\gamma\theta_j\sim 10--20 (for opening half-angle $\theta_j$) and so is able to produce jet breaks, and has comparable energy available for both prompt and afterglow emission. This reconnection switch mechanism allows for highly efficient conversion of electromagnetic energy into prompt emission and associates the observed prompt GRB pulse temporal structure with dissipation timescales of some number of reconnecting current sheets embedded in the jet.[abridged]
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The basic mechanism responsible for radio emission in radio-loud active galactic nuclei (AGNs) is assumed to be synchrotron radiation. We suggest here that radio emission in radio-quiet objects is also due to synchrotron radiation of particles accelerated in shocks. We consider generic shocks and study the resulting synchrotron properties. We estimate the synchrotron radio luminosity and compare it with the X-ray component produced by inverse Compton emission. We obtain that the radio to X-ray luminosity ratio is much smaller than unity, with values typical of radio-quiet sources. The predicted trends on source parameters, black hole mass and accretion rate, may account for the anticorrelation between radio-loudness and Eddington ratio observed in different AGN samples.
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(abridged) Although discovered 40 years ago, the emission mechanism responsible for the observed pulsar radiation remains unclear. However, the high-energy pulsed emission is usually explained in the framework of either the polar cap or the outer gap model. The purpose of this work is to study the pulsed component, that is the light-curves as well as the spectra of the high-energy emission, above 10 MeV, emanating from the striped wind model. Gamma rays are produced by scattering off the soft cosmic microwave background photons on the ultrarelativistic leptons flowing in the current sheets. We compute the time-dependent inverse Compton emissivity of the wind, in the Thomson regime, by performing three-dimensional numerical integration in space over the whole striped wind. The phase-dependent spectral variability is then calculated as well as the change in pulse shape when going from the lowest to the highest energies. Several light curves and spectra of inverse Compton radiation with phase resolved dependence are presented. We apply our model to the well-known gamma-ray pulsar Geminga. We are able to fit the EGRET spectra between 10 MeV and 10 GeV as well as the light curve above 100 MeV with good accuracy. Comment: Accepted by A&A
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The Galactic (nucleonic) cosmic-ray spectrum up to the knee ($E\sim 10^{15}$ eV) is attributed to acceleration processes that take place near the external shocks around supernova remnants (SNRs). Theoretical predictions based on the theory of diffusive shock acceleration give a similar estimate for the maximum particle energy that can be reached at these shocks: $E \sim 10^{14}{-}10^{15}$ eV. Electrons with energies $E \sim 10^{14}$ eV radiate X-ray photons in the ~$10{-}100 \; \mu$G magnetic fields present in many young SNRs. These electrons near the knee give rise to a non-thermal X-ray component in the spectrum of young supernova remnants. Recent observations of SN1006 and G347.3-0.5 confirm this prediction. We have combined hydrodynamical calculations of the evolution of a young remnant with an algorithm that simultaneously calculates the acceleration of electrons, their radiation losses and the synchrotron spectrum of a young supernova remnant. The electrons are treated using a test-particle approximation. We give a semi-analytical estimate of the maximum electron energy and typical synchrotron frequencies for young remnants at the end of the free-expansion stage of their evolution. We present spectra of the energy distribution of the electrons in a young supernova remnant, and construct a synchrotron map in the X-ray domain, assuming Bohm diffusion within the remnant and a shock-compressed magnetic field.
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