Diffusive Shock Acceleration Process Research Articles

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).

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.

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.

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.

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.

Gamma rays from supernova remnants

The recent galactic plane surveys with space- and ground-based detectors revealed a number of high and very-high energy γ-ray sources associated with young and middle-aged supernova remnants (SNRs). These results imply effective production of relativistic particles, most likely through the process of diffusive shock acceleration. The interpretation of γ-ray data from several prominent representatives of young SNRs within the so-called ‘hadronic models’ demands hard proton spectra extending to 100TeV, and total energy released in accelerated protons and ions WCR⩾1050erg. This can be treated as a support of the SNR paradigm of galactic cosmic rays. However, the hadronic models are not free of pitfalls, and pose in fact non-trivial challenges. Moreover, in many cases γ-ray data can be successfully explained also by the inverse Compton scattering of directly accelerated electrons. Future deep spectroscopic and morphological studies of SNRs with the planned Cherenkov Telescope Array (CTA) over four decades in energy, from approximately 30GeV to 300TeV, promise a breakthrough regarding the identification of radiation mechanisms. The extension of studies beyond the shells of SNRs will be another important objective aimed at the extraction of information about the highest energy particles which have left remnants at the early epochs of their evolution. These particles, which potentially carry an answer to a key question whether SNRs operate as PeVatrons, can be traced via γ-ray emission outside the remnants. Finally, the expected significant increase of the number of γ-ray emitting SNRs by CTA should allow compelling population studies – a key issue for the proof of the SNR origin of galactic cosmic rays.

Two-dimensional magnetohydrodynamics simulations of young Type Ia supernova remnants

Using two-dimensional magnetohydrodynamics (MHD) simulations, we investigate the dynamical properties of Type Ia supernova remnants (SNRs) evolved either in a uniform ambient medium or from an interaction with a dense clump. The initial conditions assume that the expansion of the supernova ejecta is of free inertia with a power-law density distribution in the outer part of the ejecta. To include the effects of the diffusive shock acceleration process and the escape of the accelerated particles from the shock front, we use different adiabatic indices in the simulations to study the dynamical evolution of the Type Ia SNRs. Moreover, we investigate the interactions of a SNR with either a small or a large clump. A double-shock structure with a contact discontinuity is produced as the ejecta flow supersonically in the ambient medium; RayleighTaylor instability is clearly shown as fingers near the contact discontinuity in the contour maps of density, and a high density and a high magnetic field can be triggered because of the instability around the RayleighTaylor fingers. We perform simulations with different adiabatic indices, and the results show that a narrower intershock region is produced with a smaller adiabatic index because a larger compression ratio for the SNR shock is induced. The influence of the RayleighTaylor instability on the morphologies of both the forward and reverse shocks is more significant with a smaller adiabatic index. Finally, the simulations of a SNR interacting with a dense clump show that the morphology of the remnant is greatly twisted after the collision, and a filament with a high density and a high magnetic field can be produced as a SNR colliding with a large dense clump.

THE IMPACT OF EFFICIENT PARTICLE ACCELERATION ON THE EVOLUTION OF SUPERNOVA REMNANTS IN THE SEDOV-TAYLOR PHASE

We investigate the effects of the efficient production of cosmic rays on the evolution of supernova remnants (SNRs) in the adiabatic Sedov-Taylor phase. We model the SNR by coupling the hydrodynamic evolution with nonlinear diffusive shock acceleration (DSA), and track self-consistently the ionization state of the shock-heated plasma. Using a plasma emissivity code and the results of the model, we predict the thermal X-ray emission and combine it with the non-thermal component in order to obtain the complete spectrum in this energy range. Hence, we study how the interpretation of thermal X-ray observations is affected by the efficiency of the DSA process, and find that, compared to test particle cases, the efficient DSA example yields a smaller shock radius and speed, a larger compression ratio, and lower intensity X-ray thermal emission. We also find that a model where the shock is not assumed to produce CRs can fit the X-ray observational properties of an example with efficient particle acceleration, with a different set of input parameters, and in particular a much lower explosion energy. Additionally, we model the broadband non-thermal emission, and investigate what signatures result from the acceleration of particles.

ELECTRON INJECTION BY WHISTLER WAVES IN NON-RELATIVISTIC SHOCKS

Electron acceleration to non-thermal, ultra-relativistic energies (∼10–100 TeV) is revealed by radio and X-ray observations of shocks in young supernova remnants (SNRs). The diffusive shock acceleration (DSA) mechanism is usually invoked to explain this acceleration, but the way in which electrons are initially energized or "injected" into this acceleration process starting from thermal energies is an unresolved problem. In this paper we study the initial acceleration of electrons in non-relativistic shocks from first principles, using two- and three-dimensional particle-in-cell (PIC) plasma simulations. We systematically explore the space of shock parameters (the Alfvénic Mach number, MA, the shock velocity, vsh, the angle between the upstream magnetic field and the shock normal, θBn, and the ion to electron mass ratio, mi/me). We find that significant non-thermal acceleration occurs due to the growth of oblique whistler waves in the foot of quasi-perpendicular shocks. This acceleration strongly depends on using fairly large numerical mass ratios, mi/me, which may explain why it had not been observed in previous PIC simulations of this problem. The obtained electron energy distributions show power-law tails with spectral indices up to α ∼ 3–4. The maximum energies of the accelerated particles are consistent with the electron Larmor radii being comparable to that of the ions, indicating potential injection into the subsequent DSA process. This injection mechanism, however, requires the shock waves to have fairly low Alfénic Mach numbers, MA ≲ 20, which is consistent with the theoretical conditions for the growth of whistler waves in the shock foot (MA ≲ (mi/me)1/2). Thus, if the whistler mechanism is the only robust electron injection process at work in SNR shocks, then SNRs that display non-thermal emission must have significantly amplified upstream magnetic fields. Such field amplification is likely achieved by the escaping cosmic rays, so electron and proton acceleration in SNR shocks must be interconnected.

SIGN FOR SUPER-DIFFUSIVE TRANSPORT OF ENERGETIC IONS ASSOCIATED WITH A CORONAL-MASS-EJECTION-DRIVEN INTERPLANETARY SHOCK

We study the transport properties of energetic particles in the upstream region of an interplanetary shock, considering the possibility of anomalous diffusion. We investigated the energetic storm particle event on 2006 December 14 observed by the ACE spacecraft at 1 AU. The spatial decay profile of the energetic particle flux does not exhibit an exponential behavior, as expected for the standard diffusive shock acceleration process, but a power-law behavior in anomalous or super-diffusive transport. The spatial profiles of the energetic ions with energy ranges of 0.546-0.761, 0.761-1.22, and 1.22-4.97 MeV are well fitted by a power-law distribution; we observe the relation ({Delta}x {sup 2}) {proportional_to} t {sup {alpha}} for {alpha}{approx} 1.28-1.33, where {Delta}x is the particle displacement within the timescale t, and the bracket denotes an ensemble average. This implies that particle propagation around a near-Earth orbit can be intermediate between normal diffusion ({alpha} = 1) and ballistic motion ({alpha} = 2), even though the power of the electromagnetic wave is sufficiently large to scatter the particles, and that an entirely different wave-particle interaction process based on linear or quasi-linear theories is responsible for the ion motion upstream of an interplanetary shock observed around the Earth's orbit.

EVIDENCE FOR PARTICLE ACCELERATION TO THE KNEE OF THE COSMIC RAY SPECTRUM IN TYCHO ’S SUPERNOVA REMNANT

Supernova remnants (SNRs) have long been assumed to be the source of cosmic rays (CRs) up to the "knee" of the CR spectrum at 10^15 eV, accelerating particles to relativistic energies in their blast waves by the process of diffusive shock acceleration (DSA). Since cosmic ray nuclei do not radiate efficiently, their presence must be inferred indirectly. Previous theoretical calculations and X-ray observations show that CR acceleration modifies significantly the structure of the SNR and greatly amplifies the interstellar magnetic field. We present new, deep X-ray observations of the remnant of Tycho's supernova (SN 1572, henceforth Tycho), which reveal a previously unknown, strikingly ordered pattern of non-thermal high-emissivity stripes in the projected interior of the remnant, with spacing that corresponds to the gyroradii of 10^14 - 10^15 eV} protons. Spectroscopy of the stripes shows the plasma to be highly turbulent on the (smaller) scale of the Larmor radii of TeV energy electrons. Models of the shock amplification of magnetic fields produce structure on the scale of the gyroradius of the highest energy CRs present, but they do not predict the highly-ordered pattern we observe. We interpret the stripes as evidence for acceleration of particles to near the knee of the CR spectrum in regions of enhanced magnetic turbulence, while the observed highly ordered pattern of these features provides a new challenge to models of DSA.

A Critical Mach Number for Electron Injection in Collisionless Shocks

Electron acceleration in collisionless shocks with arbitrary magnetic field orientations is discussed. It is shown that the injection of thermal electrons into the diffusive shock acceleration process is achieved by an electron beam with a loss cone in velocity space that is reflected back upstream from the shock through the shock drift acceleration mechanism. The electron beam is able to excite whistler waves which can scatter the energetic electrons themselves when the Alfvén Mach number of the shock is sufficiently high. A critical Mach number for the electron injection is obtained as a function of upstream parameters. The application to supernova remnant shocks is discussed.

COMPRESSION ACCELERATION IN ASTROPHYSICAL PLASMAS AND THE PRODUCTION OFf(v) ∝v–5SPECTRA IN THE HELIOSPHERE

We present a new derivation of the acceleration of fast charged particles by random compressions and expansions based on a quasilinear approximation applied to the Parker transport equation, and explore its consequences. This process has been suggested in a recent series of papers by Fisk & Gloeckler (F&G) as the origin of the quiet-time suprathermal ion population observed throughout the inner heliosphere with an omnidirectional distribution function close to the form f(v) v ?5. Our derivation does not agree with a recent equation derived by F&G. We show that, while our equation conserves particles, the F&G equation does not. Solutions of the correct quasilinear equation are presented, which show that the compressive acceleration process does not produce power-law velocity spectra with indices less than (i.e., softer than) ?3. We show that the transport equations for two other types of stochastic acceleration, by a spectrum of Alfv?n waves and by transit-time damping of oblique magnetosonic waves, yield comparable acceleration rates but also do not produce power-law spectra with indices less than ?3. Conversely, the process of diffusive shock acceleration, responsible for energetic storm particle events, corotating ion events and probably most large solar energetic particle (SEP) events, readily produces power-law velocity spectra with indices in a range including ?5. It is suggested that the quiet-time suprathermal ion population is composed predominantly of remnant ions from these events as well as a contribution from impulsive SEP events.

PARTICLE ACCELERATION IN RELATIVISTIC MAGNETIZED COLLISIONLESS PAIR SHOCKS: DEPENDENCE OF SHOCK ACCELERATION ON MAGNETIC OBLIQUITY

We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to "subluminal" shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For increasing magnetic inclination in the subluminal range, the high-energy tail accounts for an increasing fraction of particles (from ~1% to ~2%) and energy (from ~4% to ~12%). The spectral index of the power law increases with angle from -2.8+-0.1 to -2.3+-0.1. Particle energization is driven by the Diffusive Shock Acceleration process for nearly parallel shocks, and switches to Shock-Drift Acceleration for larger subluminal inclinations. For "superluminal" shocks, the downstream particle spectrum does not show any significant suprathermal tail. As seen from the upstream frame, efficient acceleration in relativistic (Lorentz factor gamma0 > 5) magnetized (sigma > 0.03) flows exists only for a very small range of magnetic inclination angles (< 34/gamma0 degrees), so relativistic astrophysical pair shocks have to be either nearly parallel or weakly magnetized to generate nonthermal particles. These findings place constraints on the models of AGN jets, Pulsar Wind Nebulae and Gamma Ray Bursts that invoke particle acceleration in relativistic magnetized shocks. (Abridged)

Dynamical feedback of self-generated magnetic fields in cosmic ray modified shocks

We present a semi-analytical kinetic calculation of the process of non-linear diffusive shock acceleration (NLDSA) which includes the magnetic field amplification due to cosmic ray induced streaming instability, the dynamical reaction of the amplified magnetic field and the possible effects of turbulent heating. The approach is specialized to parallel shock waves, and the parameters we chose are the ones appropriate to forward shocks in supernova remnants. Our calculation allows us to show that the net effect of the amplified magnetic field is to enhance the maximum momentum of accelerated particles while reducing the concavity of the spectra, with respect to the standard predictions of NLDSA. This is mainly due to the dynamical reaction of the amplified field on the shock, which notably reduces the modification of the shock precursor. The total compression factors which are obtained for parameters typical of supernova remnants are Rtot∼ 7–10, in good agreement with the values inferred from observations. The strength of the magnetic field produced through excitation of streaming instability is found in good agreement with the values inferred for several remnants if the thickness of the X-ray rims is interpreted as due to severe synchrotron losses of high-energy electrons. We also discuss the relative role of turbulent heating and magnetic dynamical reaction in driving the reduction of the precursor modification.

The transport of cosmic rays in self-excited magnetic turbulence

The process of diffusive shock acceleration relies on the efficacy with which hydromagnetic waves can scatter charged particles in the precursor of a shock. The growth of self-generated waves is driven by both resonant and non-resonant processes. We perform high-resolution magnetohydrodynamic simulations of the non-resonant cosmic ray driven instability, in which the unstable waves are excited beyond the linear regime. In a snapshot of the resultant field, particle transport simulations are carried out. The use of a static snapshot of the field is reasonable given that the Larmor period for particles is typically very short relative to the instability growth time. The diffusion rate is found to be close to, or below, the Bohm limit for a range of energies. This provides the first explicit demonstration that self-excited turbulence reduces the diffusion coefficient and has important implications for cosmic-ray transport and acceleration in supernova remnants.

Electron Injection at High Mach Number Quasi‐perpendicular Shocks: Surfing and Drift Acceleration

Electron injection process at high Mach number collisionless quasi-perpendicular shock waves is investigated by means of one-dimensional electromagnetic particle-in-cell simulations. We find that energetic electrons are generated through the following two steps: (1) electrons are accelerated nearly perpendicular to the local magnetic field by shock surfing acceleration at the leading edge of the shock transition region. (2) the preaccelerated electrons are further accelerated by shock drift acceleration. As a result, energetic electrons are preferentially reflected back to the upstream. Shock surfing acceleration provides sufficient energy required for the reflection. Therefore, it is important not only for the energization process by itself, but also for triggering the secondary acceleration process. We also present a theoretical model of the two-step acceleration mechanism based on the simulation results, which can predict the injection efficiency for subsequent diffusive shock acceleration process. We show that the injection efficiency obtained by the present model agrees well with the value obtained by Chandra X-ray observations of SN 1006. At typical supernova remnant shocks, energetic electrons injected by the present mechanism can self-generate upstream Alfven waves, which scatter the energetic electrons themselves.