Diffusive Shock Acceleration Mechanism Research Articles

Supernova Remnants in Gamma Rays

In the 1960s, the remnants of supernova explosions (SNRs) were indicated as a possible source of galactic cosmic rays through the Diffusive Shock Acceleration (DSA) mechanism. Since then, the observation of gamma-ray emission from relativistic ions in these objects has been one of the main goals of high-energy astrophysics. A few dozen SNRs have been detected at GeV and TeV photon energies in the last two decades. However, these observations have shown a complex phenomenology that is not easy to reduce to the standard paradigm based on DSA acceleration. Although the understanding of these objects has greatly increased, and their nature as efficient electron and proton accelerators has been observed, it remains to be clarified whether these objects are the main contributors to galactic cosmic rays. Here, we review the observations of γ-ray emission from SNRs and the perspectives for the future.

Particle acceleration test with Cas A multiwavelength emission

AbstractThe investigation of supernova remnants (SNRs) across the electromagnetic spectrum from radio up to very high energy gamma‐rays can serve as a test of the particle acceleration and touches on one of the unresolved problems of modern astrophysics, namely the origin of cosmic rays and the Galaxy's contribution to the overall cosmic ray spectrum. The multiwavelength observations of Cas A SNR demonstrated that structure and spectral features have clear signs of young SNRs and its overall properties make this object the best target to test a hypothesis of cosmic ray origin in SNRs. Studies of Cas A at very high energies by SHALON telescope showed the location of TeV gamma‐ray emission region relative to the position of reveres shock. Also, the spectral energy distribution was obtained at high and very high energies. To describe the spectral and structural features of this SNR viewed in non‐thermal emission, two approaches involving reverse and also both reverse and forward shocks to the mechanism of diffusive shock acceleration of cosmic rays in Cas A were applied. It is demonstrated that the observational properties of Cas A are well reproduced by the hadronic model with significant contribution of both the forward and reverse shocks in the generation of broadband emission. Calculation results suggest that the very high efficiency of particle acceleration in Cas A, which value is up to 25% of the supernova explosion energy with energy of accelerated particles not exceeding of eV. Whereas, the forward shock model predicts the spectral characteristics of the TeV‐gamma‐emission corresponding to ones detected at 800 GeV–40 TeV that are the evidence of acceleration of the hadronic cosmic rays in shells of SNRs up to eV

Electron Injection via Modified Diffusive Shock Acceleration in High-Mach-number Collisionless Shocks

The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters.

Self-consistent modeling of the energetic storm particle event of November 10, 2012

Context. It is thought that solar energetic ions associated with coronal and interplanetary shock waves are accelerated to high energies by the diffusive shock acceleration mechanism. For this mechanism to be efficient, intense magnetic turbulence is needed in the vicinity of the shock. The enhanced turbulence upstream of the shock can be produced self-consistently by the accelerated particles themselves via streaming instability. Comparisons of quasi-linear-theory-based particle acceleration models that include this process with observations have not been fully successful so far, which has motivated the development of acceleration models of a different nature. Aims. Our aim is to test how well our self-consistent quasi-linear SOLar Particle Acceleration in Coronal Shocks (SOLPACS) simulation code, developed earlier to simulate proton acceleration in coronal shocks, models the particle foreshock region. Methods. We applied SOLPACS to model the energetic storm particle (ESP) event observed by the STEREO A spacecraft on November 10, 2012. Results. All but one main input parameter of SOLPACS are fixed by the in situ plasma measurements from the spacecraft. By comparing a simulated proton energy spectrum at the shock with the observed one, we were able to fix the last simulation input parameter related to the efficiency of particle injection to the acceleration process. A subsequent comparison of simulated proton time-intensity profiles in a number of energy channels with the observed ones shows a very good correspondence throughout the upstream region. Conclusions. Our results strongly support the quasi-linear description of the foreshock region.

Dynamical Coupling between Anomalous Cosmic Rays and Solar Wind in Outer Heliosphere

Voyager 2 (V2) observed that pickup ions (PUIs) and anomalous cosmic rays (ACRs) have a significant influence on the solar wind structures in the outer heliosphere. In particular, the maxima in energetic particle intensities often lagged behind the shock front, while the flow velocity in some cases featured a precursor in front of the shock. These two effects are believed to be caused by the cease of ACR injection from PUIs at large heliocentric distances, and the backward diffusion of ACRs, respectively. This paper investigates the dynamical coupling between the ACRs and the solar wind in the outer heliosphere by means of a time-dependent numerical MHD simulation, in which the ACRs are treated as a massless fluid that only contributes its pressure to the system. Two types of inner boundary conditions were used, namely a synthetic short-term shock event and an extended period of data-driven solar wind variability based on the OMNI database. The lag of the ACR pressure maximum relative to the shock front, and the extended shock precursor were reproduced by the numerical results. The increase rate of the lag is related to the corresponding diffusion coefficient and the injection efficiency from PUIs to ACRs. The model was also applied to the termination shock, where simulations likewise showed that the peak in the ACR distribution can be located a short distance downstream of the shock front, indicating that the time-dependent diffusive shock acceleration mechanism is a candidate to interpret the lag between the ACR pressure peak and the shock front observed by V2.

Numerical Modeling of Spectral Hardening at a Finite-width Shock

Spectral hardening has been identified in solar flare hard X-ray observations for several decades and remains a puzzle. We examine spectral hardening under the diffusive shock acceleration mechanism using numerical simulations. The hardening is related to the finite width of the shock and is controlled by the shock Péclet number. We implement two different types of Monte Carlo simulations. The first is based on the backward stochastic differential equation method, where the Parker transport equation is solved by casting it to a set of stochastic different equations, and by following the trajectories of individual quasiparticles. In the second approach, we follow real particles and particles are assumed to move freely between scatterings from magnetic turbulence in the plasma. The scattering is modeled as either large-angle hard-sphere elastic collision, or small-angle pitch-angle scattering. We show that the results from these two approaches agree well with each other and agree with analytical results. We also use a Pan-spectrum form to fit the resulting spectra.

SN 2008iy circumstellar interaction: bright and lesser light effects

ABSTRACT Optical photometry and spectra of the luminous type IIn supernova SN 2008iy are analysed in detail with implications for cosmic ray acceleration and the radio emission. The light curve and expansion velocities indicate ejecta with the kinetic energy of 3 × 1051 erg to collide with the ∼10 M⊙ circumstellar envelope. The luminous H α is explained as originated primarily from circumstellar clouds interacting with the forward shock. For the first time the fluorescent O i 8446 Å emission is used to demonstrate that the cloud fragmentation cascade spans a scale range >2.3 dex. The narrow circumstellar H α permitted us to estimate the acceleration efficiency of cosmic rays. The found value is close to the efficiency inferred in the same way for other two SNe IIn, SN 1997eg and SN 2002ic. The efficiency of cosmic ray acceleration is utilized to reproduce the radio flux from SN 2008iy for the amplified magnetic field consistent with the saturated turbulent magnetic field in the diffusive shock acceleration mechanism.

Backstreaming Pickup Ions

Abstract Ions that are reflected at the shock front and escape back into the upstream region can play the role of ions that start to be accelerated by a diffusive shock acceleration mechanism. Backstreaming ions have been shown to be generated from a superthermal tail of the solar wind at sufficiently high upstream temperatures. The number of such ions was found to be low and they were not found at shock angles exceeding 50°. The mechanism of production is multiple reflection when an ion changes the direction of motion inside the ramp for the first time, due to the cross-shock potential. Since pickup ions (PUIs) constitute a strongly superthermal population of protons a substantially stronger production of backstreaming PUIs can be expected. We study the reflection of PUIs in a planar stationary shock front using test particle analysis. The used model is inspired by the observed profile of the termination shock. The influence of magnetic compression, the shock angle, and the overshoot are analyzed. It is found that generation of backstreaming PUIs in this shock is substantially more efficient than the generation of backstreaming protons from thermal solar wind. The fraction of backstreaming PUIs rapidly increases with the increase of magnetic compression and the decrease of the shock angle. Overshoot enhances production of backstreaming PUIs and allows it for larger shock angles. No backstreaming ions have been found for shock angles larger than 60°. The results of the test particle analysis are supported by full-particle simulations.

Fast Particle Acceleration at Perpendicular Shocks with Uniform Upstream Magnetic Field and Strong Downstream Turbulence

Abstract Shock waves produce relativistic particles via the diffusive shock acceleration (DSA) mechanism. Among various circumstances, fast acceleration has been expected for perpendicular shocks. We investigate the acceleration time and the energy spectrum of particles accelerated at a perpendicular shock. In our model, the upstream perpendicular magnetic field has no fluctuation, and the downstream region is highly turbulent. Then, the particle motion is the gyration in the upstream region and Bohm-like diffusion downstream. Under this situation, we derive an analytical form of the acceleration time. Using test particle simulations, the validity of our formula is verified. In addition, the energy spectrum of particles is the same as those predicted by standard DSA. Therefore, the presently proposed mechanism simultaneously realizes the rapid acceleration and the canonical spectrum, dN/dp ∝ p −2, even if there is no upstream magnetic amplification.

Extragalactic cosmic rays diffusing from two populations of sources

We consider the possibility of explaining the observed spectrum and composition of the cosmic rays with energies above ${10}^{17}\text{ }\text{ }\mathrm{eV}$ in terms of two different extragalactic populations of sources in the presence of a turbulent intergalactic magnetic field (including also a fading galactic cosmic-ray component). The populations are considered to be the superposition of different nuclear species having rigidity-dependent spectra. The first extragalactic population is dominant in the energy range ${10}^{17}\ensuremath{-}{10}^{18}\text{ }\text{ }\mathrm{eV}$ and consists of sources having a relatively large density ($>{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}$) and a steep spectrum. The second extragalactic population dominates the cosmic-ray flux above a few EeV; it has a harder spectral slope and has a high-energy cutoff at a few $Z$ EeV (where $eZ$ is the associated cosmic-ray charge). This population has a lower density of sources ($<{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}$), so that the typical intersource separation is larger than few tens of Mpc, being significantly affected by a magnetic horizon effect that strongly suppresses its flux for energies below $\ensuremath{\sim}Z$ EeV. We discuss how this scenario could be reconciled with the values of the cosmic-ray source spectral indices that are expected to result from the diffusive shock acceleration mechanism.

Particle acceleration in interstellar shocks

This review presents the fundamentals of the particle acceleration processes active in interstellar medium (ISM), which are essentially based on the so-called Fermi mechanism theory. More specifically, the review presents here in more details the first order Fermi acceleration process -- also known as diffusive shock acceleration (DSA) mechanism. In this case, acceleration is induced by the interstellar (IS) shock waves. These IS shocks are mainly associated with emission nebulae (HII regions, planetary nebulae and supernova remnants). Among all types of emission nebulae, the strongest shocks are associated with supernova remnants (SNRs). Due to this fact they also provide the most efficient manner to accelerate ISM particles to become {high energy particles}, i.e.~cosmic-rays (CRs). The review therefore focuses on the particle acceleration at the strong shock waves of supernova remnants.

Origin and impacts of the first cosmic rays

Nonthermal phenomena are ubiquitous in the Universe, and cosmic rays (CRs) play various roles in different environments. When, where, and how CRs are first generated since the Big Bang? We argue that blast waves from the first cosmic explosions at z~20 lead to Weibel mediated nonrelativistic shocks and CRs can be generated by the diffusive shock acceleration mechanism. We show that protons are accelerated at least up to sub-GeV energies, and the fast velocity component of supernova ejecta is likely to allow CRs to achieve a few GeV in energy. We discuss other possible accelerators of the first CRs, including accretion shocks due to the cosmological structure formation. These CRs can play various roles in the early universe, such as the ionization and heating of gas, the generation of magnetic fields, and feedbacks on the galaxy formation.

Cosmic-ray Spectrum Steepening in Supernova Remnants. I. Loss-free Self-similar Solution

Abstract The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical E −2 spectrum predicted by the standard diffusive shock acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The γ-ray “probes” of the acceleration spectra of CRs on the spot, inside the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the combination of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface, and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two “polar caps” of a spherical shock where the local magnetic field is within ≃45° to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at an expanding shock surface with an arbitrary energy dependence of particle diffusivity κ. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where κ cancels out.

High-energy Emission from Interacting Supernovae: New Constraints on Cosmic-Ray Acceleration in Dense Circumstellar Environments

Abstract Supernovae (SNe) with strong interactions with circumstellar material (CSM) are promising candidate sources of high-energy neutrinos and gamma-rays and have been suggested as an important contributor to Galactic cosmic rays (CRs) beyond 1015 eV. Taking into account the shock dissipation by a fast velocity component of SN ejecta, we present comprehensive calculations of the nonthermal emission from SNe powered by shock interactions with a dense wind or CSM. Remarkably, we consider electromagnetic cascades in the radiation zone and subsequent attenuation in the pre-shock CSM. A new time-dependent phenomenological prescription provided by this work enables us to calculate gamma-ray, hard X-ray, radio, and neutrino signals, which originate from CRs accelerated by the diffusive shock acceleration (DSA) mechanism. We apply our results to Type IIn SN 2010jl and Type Ib/IIn SN 2014C, for which the model parameters can be determined from the multiwavelength data. For SN 2010jl, the more promising case, by using the the latest Fermi Large Area Telescope Pass 8 data release, we derive new constraints on the CR energy fraction, ϵ p ≲ 0.05–0.1. We also find that the late-time radio data of these interacting SNe are consistent with our model. Further multimessenger and multiwavelength observations of nearby interacting SNe should give us new insights into the DSA in dense environments, as well as pre-SN mass-loss mechanisms.

Radio evolution of supernova remnants including non-linear particle acceleration

Supernova remnants (SNRs) are believed to accelerate particles up to high energies, at least reaching a few PeV, through the mechanism of diffusive shock acceleration (DSA). Detection of synchrotron radio emission from cosmic ray (CR) electrons supports this picture. We give preliminary results for the global radio emission evolution for SNRs, based on two-dimensional hydrodynamic simulations of SNRs evolving through a homogeneous ambient medium, coupled with particle acceleration and magnetic field amplification (MFA). We coupled a simple Blasi's semi-analytical model that deals with these non-linear effects in a quantitative way and changes hydrodynamics by means of an effective adiabatic index. We obtained the radio flux density increasing with time in the free expansion phase, achieving its peak value slightly before the beginning of the Sedov phase, and then decreasing during later phases.

Modeling a Single SEP Event from Multiple Vantage Points Using the iPATH Model

Abstract Using the recently extended 2D improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, we model an example gradual solar energetic particle event as observed at multiple locations. Protons and ions that are energized via the diffusive shock acceleration mechanism are followed at a 2D coronal mass ejection-driven shock where the shock geometry varies across the shock front. The subsequent transport of energetic particles, including cross-field diffusion, is modeled by a Monte Carlo code that is based on a stochastic differential equation method. Time intensity profiles and particle spectra at multiple locations and different radial distances, separated in longitudes, are presented. The results shown here are relevant to the upcoming Parker Solar Probe mission.

Modeling Particle Acceleration and Transport at a 2‐D CME‐Driven Shock

AbstractWe extend our earlier Particle Acceleration and Transport in the Heliosphere (PATH) model to study particle acceleration and transport at a coronal mass ejection (CME)‐driven shock. We model the propagation of a CME‐driven shock in the ecliptic plane using the ZEUS‐3D code from 20 solar radii to 2 AU. As in the previous PATH model, the initiation of the CME‐driven shock is simplified and modeled as a disturbance at the inner boundary. Different from the earlier PATH model, the disturbance is now longitudinally dependent. Particles are accelerated at the 2‐D shock via the diffusive shock acceleration mechanism. The acceleration depends on both the parallel and perpendicular diffusion coefficients κ|| and κ⊥ and is therefore shock‐obliquity dependent. Following the procedure used in Li, Shalchi, et al. (), we obtain the particle injection energy, the maximum energy, and the accelerated particle spectra at the shock front. Once accelerated, particles diffuse and convect in the shock complex. The diffusion and convection of these particles are treated using a refined 2‐D shell model in an approach similar to Zank et al. (). When particles escape from the shock, they propagate along and across the interplanetary magnetic field. The propagation is modeled using a focused transport equation with the addition of perpendicular diffusion. We solve the transport equation using a backward stochastic differential equation method where adiabatic cooling, focusing, pitch angle scattering, and cross‐field diffusion effects are all included. Time intensity profiles and instantaneous particle spectra as well as particle pitch angle distributions are shown for two example CME shocks.

A possible explanation of the knee of cosmic light component spectrum from 100 TeV to 3 PeV**Supported by the National Natural Science Foundation of China (11433004, 11363006, 11103016, 11173020), Top Talents Program of Yunnan Province (2015HA030) and the Natural Science Foundation of Yunnan Province(2015FB103)

A mixed hydrogen and helium (H + He) spectrum with a clear steepening at ∼ 700 TeV has been detected by the ARGO-YBJ experiments. In this paper, we demonstrate that the observed H + He spectrum can be reproduced well with a model of cosmic rays escaping from the supernova remnants (SNRs) in our Galaxy. In this model, particles are accelerated in a SNR through a non-linear diffusive shock acceleration mechanism. Three components of high energy light nuclei escaped from the SNR are considered. It should be noted that the proton spectrum observed by KASCADE can be also explained by this model given a higher acceleration efficiency.

Suzakuobservations of the merging galaxy cluster Abell 2255: The northeast radio relic

We present the results of deep 140 ks Suzaku X-ray observations of the north-east (NE) radio relic of the merging galaxy cluster Abell2255. The temperature structure of Abell2255 is measured out to 0.9 times the virial radius (1.9 Mpc) in the NE direction for the first time. The Suzaku temperature map of the central region suggests a complex temperature distribution, which agrees with previous work. Additionally, on a larger-scale, we confirm that the temperature drops from 6 keV around the cluster center to 3 keV at the outskirts, with two discontinuities at {\it r}$\sim$5\arcmin~(450 kpc) and $\sim$12\arcmin~(1100 kpc) from the cluster center. Their locations coincide with surface brightness discontinuities marginally detected in the XMM-Newton image, which indicates the presence of shock structures. From the temperature drop, we estimate the Mach numbers to be ${\cal M}_{\rm inner}\sim$1.2 and, ${\cal M}_{\rm outer}\sim$1.4. The first structure is most likely related to the large cluster core region ($\sim$350--430 kpc), and its Mach number is consistent with the XMM-Newton observation (${\cal M}\sim$1.24: Sakelliou & Ponman 2006). Our detection of the second temperature jump, based on the Suzaku key project observation, shows the presence of a shock structure across the NE radio relic. This indicates a connection between the shock structure and the relativistic electrons that generate radio emission. Across the NE radio relic, however, we find a significantly lower temperature ratio ($T_1/T_2\sim1.44\pm0.16$ corresponds to~${\cal M}_{\rm X-ray}\sim1.4$) than the value expected from radio wavelengths, based on the standard diffusive shock acceleration mechanism ($T_1/T_2>$ 3.2 or ${\cal M}_{\rm Radio}>$ 2.8).

Positive charge prevalence in cosmic rays: Room for dark matter in the positron spectrum

The unexpected energy spectrum of the positron/electron ratio is interpreted astrophysically, with a possible exception of the 100-300 GeV range. The data indicate that this ratio, after a decline between $0.5-8$ GeV, rises steadily with a trend towards saturation at 200-400GeV. These observations (except for the trend) appear to be in conflict with the diffusive shock acceleration (DSA) mechanism, operating in a \emph{single} supernova remnant (SNR) shock. We argue that $e^{+}/e^{-}$ ratio can still be explained by the DSA if positrons are accelerated in a \emph{subset} of SNR shocks which: (i) propagate in clumpy gas media, and (ii) are modified by accelerated CR \emph{protons}. The protons penetrate into the dense gas clumps upstream to produce positrons and, \emph{charge the clumps positively}. The induced electric field expels positrons into the upstream plasma where they are shock-accelerated. Since the shock is modified, these positrons develop a harder spectrum than that of the CR electrons accelerated in other SNRs. Mixing these populations explains the increase in the $e^{+}/e^{-}$ ratio at $E>8$ GeV. It decreases at $E<8$ GeV because of a subshock weakening which also results from the shock modification. Contrary to the expelled positrons, most of the antiprotons, electrons, and heavier nuclei, are left unaccelerated inside the clumps. Scenarios for the 100-300 GeV AMS-02 fraction exceeding the model prediction, including, but not limited to, possible dark matter contribution, are also discussed.