Shock Acceleration Process Research Articles

Verification of the diffusive shock acceleration in Mrk 501

The present work considers a plane shock front propagating along a cylindrical jet. Electrons experience the 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 IC 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 implications of the model results. It suggests that the process of diffusive shock acceleration operates in the outflow of Mrk 501.

Probing maximum energy of cosmic rays in SNR through gamma rays and neutrinos from the molecular clouds around SNR W28

The galactic cosmic rays are generally believed to be originated in supernova remnants (SNRs), produced in diffusive shock acceleration (DSA) process in supernova blast waves driven by expanding SNRs. One of the key unsettled issue in SNR origin of cosmic ray model is the maximum attainable energy by a cosmic ray particle in the supernova shock. Recently it has been suggested that an amplification of effective magnetic field strength at the shock may take place in young SNRs due to growth of magnetic waves induced by accelerated cosmic rays and as a result the maximum energy achieved by cosmic rays in SNR may reach the knee energy instead of ∼ 200 TeV as predicted earlier under normal magnetic field situation. In the present work we investigate the implication of such maximum energy scenarios on TeV gamma rays and neutrino fluxes from the molecular clouds interacting with the SNR W28. The authors compute the gamma-ray and neutrino flux assuming two different values for the maximum energy reached by cosmic rays in the SNR, from CR interaction in nearby molecular clouds. Both protons and nuclei are considered as accelerated particles and as target material. Our findings suggest that the issue of the maximum energy of cosmic rays in SNRs can be observationally settled by the upcoming gamma-ray experiment the Large High Altitude Air Shower Observatory (LHAASO). The estimated neutrino fluxes from the molecular clouds are , however, out of reach of the present/near future generation of neutrino telescopes.

Anomalous cosmic ray fluxes in diffusive shock acceleration processes in the heliosphere and in planetary and WR–nebulae

Based on the analogy between interacting stellar winds of planetary nebulae and WR–nebulae, on the one hand, and the heliosphere and the expanding envelopes of supernovae, on the other, an attempt is made to calculate the differential intensity of the energetic protons accelerated to energies of 100 MeV by the shock wave. The proposed one–parameter formula for estimating the intensity at 1–100 MeV, when applied to the heliosphere, shows good agreement with the Voyager–1 data, to within a factor of less than 2. The same estimate for planetary (and WR–) nebulae yield a value 7–8 (3–4) orders of magnitude higher than the mean galactic intensity value. The obtained estimate of the intensity of energetic protons in mentioned kinds of nebulae was used to estimate the doses of irradiation of certain substances, in order to show that such accelerated particles play an important role in radiation–chemical transformations in such nebulae.

Why is solar cycle 24 an inefficient producer of high-energy particle events?

The aim of the study is to investigate the reason for the low productivity of high-energy SEPs in the present solar cycle. We employ scaling laws derived from diffusive shock acceleration theory and simulation studies including proton-generated upstream Alfv\'en waves to find out how the changes observed in the long-term average properties of the erupting and ambient coronal and/or solar wind plasma would affect the ability of shocks to accelerate particles to the highest energies. Provided that self-generated turbulence dominates particle transport around coronal shocks, it is found that the most crucial factors controlling the diffusive shock acceleration process are the number density of seed particles and the plasma density of the ambient medium. Assuming that suprathermal populations provide a fraction of the particles injected to shock acceleration in the corona, we show that the lack of most energetic particle events as well as the lack of low charge-to-mass ratio ion species in the present cycle can be understood as a result of the reduction of average coronal plasma and suprathermal densities in the present cycle over the previous one.

Gamma-Ray Solar Flares and In Situ Particle Acceleration

AbstractAt present two concurrent paradigms of solar energetic particle (SEP) origin exist: acceleration directly in the flare site or by the shock wave of coronal mass ejection (CME). Active discussions on a relative role of flares and coronal mass ejections for SEP acceleration and propagation are continuous until now. In my opinion only future observations of solar high energy γ–emission with better spectral, spatial and temporal resolution may clarify this issue. In my report I discuss possible signatures of the flare and shock acceleration processes. What is a picture provided by the current instruments? What can we expect to observe with a perfect instrument in high energy gamma rays in one or another case on a time scale of impulsive and long decay flare phases?

Implications of supernova remnant origin model of galactic cosmic rays on gamma rays from young supernova remnants

It is widely believe that galactic cosmic rays are originated in supernova remnants (SNRs) where they are accelerated by diffusive shock acceleration process at supernova blast waves driven by expanding SNRs. In recent theoretical developments of the diffusive shock acceleration theory in SNRs, protons are expected to accelerate in SNRs at least up to the knee energy. If SNRs are true generator of cosmic rays, they should accelerate not only protons but also heavier nuclei with right proportion and the maximum energy of heavier nuclei should be atomic mass (Z) times that of protons. In this work we investigate the implications of acceleration of heavier nuclei in SNRs on energetic gamma rays those are produced in hadronic interaction of cosmic rays with ambient matter. Our findings suggest that the energy conversion efficiency has to be nearly double for the mixed cosmic ray composition instead of pure protons to explain the observation and secondly the gamma ray flux above few tens of TeV would be significantly higher if cosmic rays particles can attain energies Z times of the knee energy in lieu of 200 TeV, as suggested earlier for non-amplified magnetic fields. The two stated maximum energy paradigm will be discriminated in future by the upcoming gamma ray experiments like Cherenkov Telescope array (CTA).

Shocks in collisionless plasmas

The Earth’s bow shock is the best-known collisionless shock in space. Although much is known about the bow shock, the mechanisms of heating and thermalization processes still remain poorly understood. Collisionless shocks are different from ordinary fluid shocks, because a fraction of the incident solar wind is reflected from the bow shock and the transmitted particles are not immediately thermalized. The reflected particles interact with the incident solar wind producing waves and instabilities that can heat and accelerate particles to high energies. Some of the waves can grow to large amplitudes such as Short Large Amplitude Magnetic Structures. Other upstream nonlinear structures include hot flow anomalies and density holes. The upstream nonlinear structures subsequently convect Earthward with the SW and could impact the structure and dynamics of the bow shock. These observations have clearly indicated that the upstream dynamics are an integral part of the bow shock system. Although much has been learned about the behavior of Earth’s bow shock dynamics from the existing data, many fundamental questions remain not answered. This article will review observations of ion dynamics of Earth’s bow shock system, what we have learned from recent and past observations. We provide new perspectives from multi-spacecraft Cluster observations about the spatial and temporal variations including the fundamental shock heating, acceleration, and entropy generation processes.

Efficient shock drift acceleration in the collision of two asymmetric pair plasma shells

The shock drift acceleration (SDA) process in the collision between two asymmetric relativistic pair plasma shells was investigated. It is found that the density ratio (nL/nR) of the two different plasma shells plays a crucial role in the SDA process and determines the efficiency of the SDA process. By increasing this parameter, the plasma bulk velocity and so as to the convection electric field in the downstream region can be much enhanced compared with the symmetric case, in which the densities in the two plasma shells are the same. As a result, the particles are efficiently accelerated by the large convection electric field and the efficiency of the SDA process is much increased as the density ratio is increased. Our particle-in-cell simulations demonstrate that the SDA efficiency can be improved by three to four times in the asymmetric case. In this way, more high energy particles could enter into the phase of the diffusive shock acceleration process.

Joint Ne/O and Fe/O Analysis to Diagnose Large Solar Energetic Particle Events during Solar Cycle 23

Abstract We have examined 29 large solar energetic particle (SEP) events with the peak proton intensity J pp(>60 MeV) > 1 pfu during solar cycle 23. The emphasis of our examination is put on a joint analysis of Ne/O and Fe/O data in the energy range (3–40 MeV nucleon−1) covered by Wind/Low-Energy Matrix Telescope and ACE/Solar Isotope Spectrometer sensors in order to differentiate between the Fe-poor and Fe-rich events that emerged from the coronal mass ejection driven shock acceleration process. An improved ion ratio calculation is carried out by rebinning ion intensity data into the form of equal bin widths in the logarithmic energy scale. Through the analysis we find that the variability of Ne/O and Fe/O ratios can be used to investigate the accelerating shock properties. In particular, the high-energy Ne/O ratio is well correlated with the source plasma temperature of SEPs.

A two-fluid model for black-hole accretion flows: particle acceleration and disc structure

Hot, tenuous advection-dominated accretion flows around black holes are ideal sites for the Fermi acceleration of relativistic particles at standing shock waves in the accretion disc. Previous work has demonstrated that the shock-acceleration process can be efficient enough to power the observed, strong outflows in radio-loud active galaxies such as M87. However, the dynamical effect (back-reaction) on the flow, exerted by the pressure of the relativistic particles, has not been previously considered, and this effect can have a significant influence on the disc structure. We reexamine the problem by developing a new, two-fluid model for the structure of the accretion disc that includes the dynamical effect of the relativistic particle pressure, combined with the pressure of the background (thermal) gas. The new model is analogous to the two-fluid model of cosmic ray acceleration in supernova-driven shock waves. As part of the model, we also develop a new set of shock jump conditions, which are solved along with the hydrodynamic conservation equations to determine the structure of the accretion disc. The solutions include the formation of a mildly relativistic outflow (jet) at the shock radius, driven by the relativistic particles accelerated in the disc. One of our main conclusions is that in the context of the new two-fluid accretion model, global smooth (shock-free) solutions do not exist, and the disc must always contain a standing shock wave, at least in the inviscid case considered here.

Magnetic field generation, Weibel-mediated collisionless shocks, and magnetic reconnection in colliding laser-produced plasmas

AbstractColliding plasmas are ubiquitous in astrophysical environments and allow conversion of kinetic energy into heat and, most importantly, the acceleration of particles to extremely high energies to form the cosmic ray spectrum. In collisionless astrophysical plasmas, kinetic plasma processes govern the interaction and particle acceleration processes, including shock formation, self-generation of magnetic fields by kinetic plasma instabilities, and magnetic field compression and reconnection. How each of these contribute to the observed spectra of cosmic rays is not fully understood, in particular both shock acceleration processes and magnetic reconnection have been proposed. We will review recent results of laboratory astrophysics experiments conducted at high-power, inertial-fusion-class laser facilities, which have uncovered significant results relevant to these processes. Recent experiments have now observed the long-sought Weibel instability between two interpenetrating high temperature plasma plumes, which has been proposed to generate the magnetic field necessary for shock formation in unmagnetized regimes. Secondly, magnetic reconnection has been studied in systems of colliding plasmas using either self-generated magnetic fields or externally applied magnetic fields, and show extremely fast reconnection rates, indicating fast destruction of magnetic energy and further possibilities to accelerate particles. Finally, we highlight kinetic plasma simulations, which have proven to be essential tools in the design and interpretation of these experiments.

Interplanetary magnetic field dependence of the suprathermal energetic neutral atoms originated in subsolar magnetopause

AbstractUsing energetic neutral atom (ENA) emission observations of the subsolar magnetopause measured by the Interstellar Boundary Explorer (IBEX), we study the correlation between the upstream interplanetary magnetic field (IMF) conditions and the spectral index of the source ion population. Our ENA data set includes hour‐averaged ENA measurements at energies between ∼0.5 and ∼6 keV obtained by the IBEX High Energy ENA imager from January 2009 to May 2011. Under the condition of quiet geomagnetic activity (SYM‐H index >−20 nT), we find that the shallower spectra in the suprathermal tail of the ion population of the subsolar magnetopause is weakly correlated (correlation coefficient of −0.30) with the shock angle of the Earth's bow shock, but not correlated with parameters related to magnetic reconnection (i.e., elevation and clock angle of the interplanetary magnetic field orientation). The observed correlation suggests suprathermal ion energization from diffusive shock acceleration and thus that the suprathermal ions in the subsolar magnetopause are of shocked solar wind origin. We also argue that the roles of magnetospheric ion leakage or ion acceleration by magnetic reconnection are reduced in the magnetopause emissions compared to shock acceleration processes.

Cosmic Ray Origin: Lessons from Ultra-High-Energy Cosmic Rays and the Galactic/Extragalactic Transition

We examine the question of the origin of the Galactic cosmic-rays (GCRs) in the light of the data available at the highest energy end of the spectrum. We argue that the data of the Pierre Auger Observatory and of the KASCADE-Grande experiment suggest that the transition between the Galactic and the extragalactic components takes place at the energy of the ankle in the all-particle cosmic-ray spectrum, and at an energy of the order of 1017 eV for protons. Such a high energy for Galactic protons appears difficult to reconcile with the general view that GCRs are accelerated by the standard diffusive shock acceleration process at the forward shock of individual supernova remnants (SNRs). We also review various difficulties of the standard SNR-GCR connection, related to the evolution of the light element abundances and to significant isotopic anomalies. We point out that most of the power injected by the supernovæ in the Galaxy is actually released inside superbubbles, which may thus play an important role in the origin of cosmic-rays, and could solve some persistent problems of the standard SNR-GCR scenario in a rather natural way.

Simulated morphologies of non-thermal emission from the supernova remnant RX J0852.0−4622 in a turbulent medium

The morphologies of the X-rays from synchrotron radiation and the γ-rays produced via either inverse Compton scattering or proton–proton interaction for the supernova remnant RX J0852.0−4622 are investigated using a three-dimensional magnetohydrodynamic simulation. The simulation is initiated with the supernova ejecta imbedded in the turbulent environment, and the distributions of the density and the magnetic field within the shock wave can be obtained. Assuming that the number of the protons accelerated by the forward shock is proportional to the local density since more protons can be injected into the diffusive shock acceleration process with a higher density, the morphology of the emission produced via the inelastic collisions between the accelerated protons with the ambient matter is achieved. Furthermore, the X-ray map of the synchrotron radiation and the γ-ray image of the inverse Compton scattering can be obtained with the assumption that the relativistic electrons have a similar spatial distribution as the protons. The results show that the shock front is distorted by the turbulent medium, and the morphologies of the non-thermal emission from RX J0852.0−4622, which shows a broken shell with bright rims at the shock in the observed images both in the X-ray band and in the TeV γ-ray band, can be generally reproduced using the model. It can be concluded that the observed broken morphologies of the non-thermal emission with bright regions along the shock are the result of the remnant evolving in a turbulent plasma.

AN INTERPRETATION OF GLE71 CONCURRENT CME-DRIVEN SHOCK WAVE

Particle accelerations in solar flares and CME-driven shocks can sometimes result in very high-energy particle events (>= 1 GeV) that are known as ground level enhancements (GLEs). Recent studies on the first GLE event (GLE71 2012 May 17 01:50 UT) of solar cycle 24 suggested that CME-driven shock played a leading role in causing the event. To verify this claim, we have made an effort to interpret the GLE71 concurrent shock wave. For this, we have deduced the possible speed and height of the shock wave in terms of the frequency (MHz) of the solar radio type II burst and its drift rate (MHz min(-1)), and studied the temporal evolution of the particle intensity profiles at different heights of the solar corona. For a better perception of the particle acceleration in the shock, we have studied the solar radio type II burst with concurrent solar radio and electron fluxes. When the particle intensity profiles are necessarily shifted in time at similar to 1 AU, it is found that the growth phases of the electron and cosmic ray intensity fluxes are strongly correlated (>0.91; >= 0.87) with the frequency drift rate of the type II burst, which is also consistent with the intensive particle accelerations at upper coronal heights (similar to >= 0.80 R-S < 1.10 R-S). Thus, we conclude that the CME-driven shock was possibly capable of producing the high-energy particle event. However, since the peaks of some flare components are found to be strongly associated with the fundamental phase of the type II burst, the preceding flare is supposed to contribute to the shock acceleration process.

INJECTION OF κ-LIKE SUPRATHERMAL PARTICLES INTO DIFFUSIVE SHOCK ACCELERATION

We consider a phenomenological model for the thermal leakage injection in the diffusive shock acceleration (DSA) process, in which suprathermal protons and electrons near the shock transition zone are assumed to have the so-called $\kappa$-distributions produced by interactions of background thermal particles with pre-existing and/or self-excited plasma/MHD waves or turbulence. The $\kappa$-distribution has a power-law tail, instead of an exponential cutoff, well above the thermal peak momentum. So there are a larger number of potential seed particles with momentum, above that required for participation in the DSA process. As a result, the injection fraction for the $\kappa$-distribution depends on the shock Mach number much less severely compared to that for the Maxwellian distribution. Thus, the existence of $\kappa$-like suprathermal tails at shocks would ease the problem of extremely low injection fractions, especially for electrons and especially at weak shocks such as those found in the intracluster medium. We suggest that the injection fraction for protons ranges $10^{-4}-10^{-3}$ for a $\kappa$-distribution with $10 < \kappa_p < 30$ at quasi-parallel shocks, while the injection fraction for electrons becomes $10^{-6}-10^{-5}$ for a $\kappa$-distribution with $\kappa_e < 2$ at quasi-perpendicular shocks. For such $\kappa$ values the ratio of cosmic ray electrons to protons naturally becomes $K_{e/p}\sim 10^{-3}-10^{-2}$, which is required to explain the observed ratio for Galactic cosmic rays.

IS THE ACCELERATION OF ANOMALOUS COSMIC RAYS AFFECTED BY THE GEOMETRY OF THE TERMINATION SHOCK?

Historically, anomalous cosmic rays (ACRs) were thought to be accelerated at the solar-wind termination shock (TS) by the diffusive shock acceleration process. When Voyager 1 crossed the TS in 2004, the measured ACR spectra did not match the theoretical prediction of a continuous power law, and the source of the high-energy ACRs was not observed. When the Voyager 2 crossed the TS in 2007, it produced similar results. Several possible explanations have since appeared in the literature, but we follow the suggestion that ACRs are still accelerated at the shock, only away from the Voyager crossing points. To investigate this hypothesis closer, we study ACR acceleration using a three-dimensional, non-spherical model of the heliosphere that is axisymmetric with respect to the interstellar flow direction. We then compare the results with those obtained for a spherical TS. A semi-analytic model of the plasma and magnetic field backgrounds is developed to permit an investigation over a wide range of parameters under controlled conditions. The model is applied to helium ACRs, whose phase-space trajectories are stochastically integrated backward in time until a pre-specified, low-energy boundary, taken to be 0.5 MeV n?1 (the so-called injection energy), is reached. Our results show that ACR acceleration is quite efficient on the heliotail-facing part of the TS. For small values of the perpendicular diffusion coefficient, our model yields a positive intensity gradient between the TS and about midway through the heliosheath, in agreement with the Voyager observations.

NONTHERMAL RADIATION FROM SUPERNOVA REMNANTS: EFFECTS OF MAGNETIC FIELD AMPLIFICATION AND PARTICLE ESCAPE

We explore nonlinear effects of wave-particle interactions on the diffusive shock acceleration (DSA) process in Type Ia-like, SNR blast waves, by implementing phenomenological models for magnetic field amplification, Alfv'enic drift, and particle escape in time-dependent numerical simulations of nonlinear DSA. For typical SNR parameters the CR protons can be accelerated to PeV energies only if the region of amplified field ahead of the shock is extensive enough to contain the diffusion lengths of the particles of interest. Even with the help of Alfv'enic drift, it remains somewhat challenging to construct a nonlinear DSA model for SNRs in which order of 10 % of the supernova explosion energy is converted to the CR energy and the magnetic field is amplified by a factor of 10 or so in the shock precursor, while, at the same time, the energy spectrum of PeV protons is steeper than E^{-2}. To explore the influence of these physical effects on observed SNR emissions, we also compute resulting radio-to-gamma-ray spectra. Nonthermal emission spectra, especially in X-ray and gamma-ray bands,depend on the time dependent evolution of CR injection process, magnetic field amplification, and particle escape, as well as the shock dynamic evolution. This result comes from the fact that the high energy end of the CR spectrum is composed of the particles that are injected in the very early stages of blast wave evolution. Thus it is crucial to understand better the plasma wave-particle interactions associated with collisionless shocks in detail modeling of nonthermal radiation from SNRs.

Electron-Ion Temperature Equilibration in Collisionless Shocks: The Supernova Remnant-Solar Wind Connection

Collisionless shocks are loosely defined as shocks where the transition between pre-and post-shock states happens on a length scale much shorter than the collisional mean free path. In the absence of collision to enforce thermal equilibrium post-shock, electrons and ions need not have the same temperatures. While the acceleration of electrons for injection into shock acceleration processes to produce cosmic rays has received considerable attention, the related problem of the shock heating of quasi-thermal electrons has been relatively neglected. In this paper we review that state of our knowledge of electron heating in astrophysical shocks, mainly associated with supernova remnants (SNRs), shocks in the solar wind associated with the terrestrial and Saturnian bowshocks, and galaxy cluster shocks. The solar wind and SNR samples indicate that the ratio of electron temperature to ion temperature declines with increasing shock speed or Alfvenic Mach number. We discuss the extent to which such behavior can be understood via cosmic ray-generated waves in a shock precursor, which then subsequently damp by heating electrons. Finally, we speculate that a similar mechanism may be at work for both solar wind and SNR shocks.

Diffusive Ion Acceleration by CME‐Driven Shocks

The acceleration of solar energetic ions in events at coronal/ interplanetary shocks is reviewed including: a brief observational motivation for a shock origin of gradual events, the historical development of the theory of shock acceleration as applied to solar energetic particles, the basic features of the process of diffusive shock acceleration (first-order Fermi acceleration at the shock, wave excitation by the energetic protons, magnetic focusing and upstream escape of the ions), challenges to developing a successful theory, the basic equations of ion transport and acceleration, and current theoretical research. Finally, outstanding issues which must be addressed by future work are listed including: ion injection into the process of diffusive shock acceleration, careful evaluation of the wave intensity upstream of the shock, acceleration and injection at quasi-perpendicular shocks, long-time behavior of gradual events, the inclusion of wave propagation velocities in the effective shock compression ratio, and a rigorous treatment of the time-dependence.