Shock Acceleration Process Research Articles

AN INTERPRETATION OF THE POSSIBLE MECHANISMS OF TWO GROUND-LEVEL ENHANCEMENT EVENTS

We have carried out this work to clarify the possible mechanisms of two important high-energy particle events (GLE69 2005 January 20, 06: 46 UT and GLE70 2006 December 13, 02: 45 UT). For this purpose, the cosmic-ray intensities registered by neutron monitors at several sites have been analyzed and studied with concurrent solar flares of different energy bands. To determine whether the ground-level enhancement (GLE) might be caused by the energy released from a solar flare or a CME-driven shock, we identify the particle injection time in terms of the lowest value of the spectral indices deduced from proton fluxes. If the GLE is caused by the energy released from particle acceleration in a solar flare, the intensive phase of the flare representing extreme emission should lie within the injection time. While fulfilling this criterion, it is further necessary to understand the possible relativistic energy computed in terms of the possible travel time deduced by employing the observational time lag between the GLE and the concurrent solar flare. Accordingly, we have found that GLE69 is procured with sufficient possible relativistic energy (similar to 1.619 GeV) by the energy released from particle accelerations in the intensive phases of a solar flare components that have been corroborated by the injection time. The intensive phases of the flare components have also been justified with the prominent phases of a solar radio type III burst. For event GLE70, the particle injection time lies within the CME-driven shock justified by a solar radio type II burst which seems to be capable of procuring sufficient possible relativistic energies (similar to 1.231 to similar to 2.017 GeV). It is also noted that any fractional amount of energy (similar to 0.226 to similar to 0.694 GeV) from preceding flare components might be considered as a contribution to the shock acceleration process. Thus, GLE70 is presumably caused by the sum of the energy released mostly from a CME-driven shock and partially from preceding flare components.

Shock Acceleration of Ions in the Heliosphere

Energetic particles constitute an important component of the heliospheric plasma environment. They range from solar energetic particles in the inner heliosphere to the anomalous cosmic rays accelerated at the interface of the heliosphere with the local interstellar medium. Although stochastic acceleration by fluctuating electric fields and processes associated with magnetic reconnection may account for some of the particle populations, the majority are accelerated by the variety of shock waves present in the solar wind. This review focuses on “gradual” solar energetic particle (SEP) events including their energetic storm particle (ESP) phase, which is observed if and when an associated shock wave passes Earth. Gradual SEP events are the intense long-duration events responsible for most space weather disturbances of Earth’s magnetosphere and upper atmosphere. The major characteristics of gradual SEP events are first described including their association with shocks and coronal mass ejections (CMEs), their ion composition, and their energy spectra. In the context of acceleration mechanisms in general, the acceleration mechanism responsible for SEP events, diffusive shock acceleration, is then described in some detail including its predictions for a planar stationary shock, shock modification by the energetic particles, and wave excitation by the accelerating ions. Finally, some complexities of shock acceleration are addressed, which affect the predictive ability of the theory. These include the role of temporal and spatial variations, the distinction between the plasma and wave compression ratios at the shock, the injection of thermal plasma at the shock into the process of shock acceleration, and the nonlinear evolution of ion-excited waves in the vicinity of the shock.

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.

Cosmic rays and stochastic magnetic reconnection in the heliotail

Abstract. Galactic cosmic rays are believed to be generated by diffusive shock acceleration processes in Supernova Remnants, and the arrival direction is likely determined by the distribution of their sources throughout the Galaxy, in particular by the nearest and youngest ones. Transport to Earth through the interstellar medium is expected to affect the cosmic ray properties as well. However, the observed anisotropy of TeV cosmic rays and its energy dependence cannot be explained with diffusion models of particle propagation in the Galaxy. Within a distance of a few parsec, diffusion regime is not valid and particles with energy below about 100 TeV must be influenced by the heliosphere and its elongated tail. The observation of a highly significant localized excess region of cosmic rays from the apparent direction of the downstream interstellar flow at 1–10 TeV energies might provide the first experimental evidence that the heliotail can affect the transport of energetic particles. In particular, TeV cosmic rays propagating through the heliotail interact with the 100–300 AU wide magnetic field polarity domains generated by the 11 yr cycles. Since the strength of non-linear convective processes is expected to be larger than viscous damping, the plasma in the heliotail is turbulent. Where magnetic field domains converge on each other due to solar wind gradient, stochastic magnetic reconnection likely occurs. Such processes may be efficient enough to re-accelerate a fraction of TeV particles as long as scattering processes are not strong. Therefore, the fractional excess of TeV cosmic rays from the narrow region toward the heliotail direction traces sightlines with the lowest smearing scattering effects, that can also explain the observation of a harder than average energy spectrum.

ANOMALOUS TRANSPORT OF HIGH-ENERGY COSMIC RAYS IN GALACTIC SUPERBUBBLES. I. NUMERICAL SIMULATIONS

We present a simple continuous-time random-walk model for the transport of energetic particles accelerated by a collection of supernova explosions in a galactic superbubble, developed to simulate and highlight signatures of anomalous transport on the particles' evolution and their spectra in a multi-shock context. We assume standard diffusive shock acceleration (DSA) theory for each shock encounter. The superbubble (an OB stars association) is idealized as a heterogeneous region of particle sources and sinks bounded by a random surface. The model is based on two coupled stochastic differential equations and is applied for protons and alpha particles. Using characteristic values for a typical bubble, our simulations suggest that acceleration and transport in the bubble may be sub-diffusive. In addition, a spectral break in the particles' evolution and spectra is evident located at ≈1015 eV for protons and ≈3 × 1015 eV for alphas. Our simulations are consistent with a bubble's mean magnetic field strength of ≈1 μG and a shock separation distance ~0.1 × the characteristic radius of the bubble. The simulations imply that the diffusion coefficient (for the elementary shock acceleration process) is 1027 cm2 s–1 at 1 GeV/c. While the sub-diffusive transport is readily attributed to the stochastic nature of the acceleration time according to DSA theory, the spectral break appears to be an artifact of transport in a finite medium. These simulations point to a new and intriguing phenomenon associated with the statistical nature of collective acceleration of high-energy cosmic rays in galactic superbubbles.

Acceleration and radiation of ultra-high energy protons in galaxy clusters

Clusters of galaxies are believed to be capable to accelerate protons at accretion shocks to energies exceeding 10^18 eV. At these energies, the losses caused by interactions of cosmic rays with photons of the Cosmic Microwave Background Radiation (CMBR) become effective and determine the maximum energy of protons and the shape of the energy spectrum in the cutoff region. The aim of this work is the study of the formation of the energy spectrum of accelerated protons at accretion shocks of galaxy clusters and of the characteristics of their broad band emission. The proton energy distribution is calculated self-consistently via a time-dependent numerical treatment of the shock acceleration process which takes into account the proton energy losses due to interactions with the CMBR. We calculate the energy distribution of accelerated protons, as well as the flux of broad-band emission produced by secondary electrons and positrons via synchrotron and inverse Compton scattering processes. We find that the downstream and upstream regions contribute almost at the same level to the emission. For the typical parameters characterising galaxy clusters, the synchrotron and IC peaks in the spectral energy distributions appear at comparable flux levels. For an efficient acceleration, the expected emission components in the X-ray and gamma-ray band are close to the detection threshold of current generation instruments, and will be possibly detected with the future generation of detectors.

DIFFUSIVE PARTICLE ACCELERATION IN SHOCKED, VISCOUS ACCRETION DISKS: GREEN'S FUNCTION ENERGY DISTRIBUTION

The acceleration of relativistic particles in a viscous accretion disk containing a standing shock is investigated as a possible explanation for the energetic outflows observed around radio-loud black holes. The energy/space distribution of the accelerated particles is computed by solving a transport equation that includes the effects of first-order Fermi acceleration, bulk advection, spatial diffusion, and particle escape. The velocity profile of the accreting gas is described using a model for shocked viscous disks recently developed by the authors, and the corresponding Green's function distribution for the accelerated particles in the disk and the outflow is obtained using a classical method based on eigenfunction analysis. The accretion-driven, diffusive shock acceleration scenario explored here is conceptually similar to the standard model for the acceleration of cosmic rays at supernova-driven shocks. However, in the disk application, the distribution of the accelerated particles is much harder than would be expected for a plane-parallel shock with the same compression ratio. Hence the disk environment plays a key role in enhancing the efficiency of the shock acceleration process. The presence of the shock helps to stabilize the disk by reducing the Bernoulli parameter, while channeling the excess binding energy into the escaping relativistic particles. Inmore » applications to M87 and Sgr A*, we find that the kinetic power in the jet is {approx}0.01 M-dot c{sup 2}, and the outflowing relativistic particles have a mean energy {approx}300 times larger than that of the thermal gas in the disk at the shock radius. Our results suggest that a standing shock may be an essential ingredient in accretion onto underfed black holes, helping to resolve the long-standing problem of the stability of advection-dominated accretion disks.« less

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.

X-RAY OBSERVATION OF AM HERCULIS IN A VERY LOW STATE WITHSUZAKU

The X-ray observation of AM Her in a very low state was performed with {\it Suzaku} in October 2008. One flare event with a time scale of $\sim$ 3700 sec was detected at the X-ray luminosity of $6.0 \times 10^{29} {\rm ~erg ~sec}^{-1}$ in the 0.5 -- 10 keV band assuming at a distance of 91 pc. The X-ray spectrum is represented by a thermal plasma emission model with a temperature of $8.67_{-1.14}^{+1.31}$ keV. During the quiescence out of the flare interval, {\it Suzaku} also detected significant X-rays at a luminosity of $1.7 \times 10^{29} {\rm ~erg ~sec}^{-1}$ in the 0.5 -- 10 keV band, showing a clear spin modulation at a period of 0.1289273(2) days at BJD 2454771.581. The X-ray spectra in the quiescence were represented by a MEKAL + Power Law (PL) model or a single CEMEKL model, which are also supported by phase-resolved analyses. A correlation between the temperature and the volume emission measure was found together with historical X-ray measurements of AM Her in various states. In order to account for a possible non-thermal emission from AM Her, particle acceleration mechanisms in the AM Her system are also discussed, including a new proposal of a shock acceleration process on the top of the accretion column.

Collisionless shocks and particle acceleration: Lessons from studies of heliospheric shocks

AbstractAcceleration processes at astrophysical collisionless shocks are reviewed with a special emphasis on the importance of in situ observations of heliospheric shocks. Topics to be included are nonlinear reaction of shock acceleration process, effect of neutral particles, and electron acceleration.

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.

On the non-thermal emission from the supernova remnant W51C

The middle-aged supernova remnant (SNR) W51C is an interesting source for the interaction of the shell with a molecular cloud. The shell emits intense radio synchrotron photons, and high-energy gamma-rays from the remnant have been detected using the {\it Fermi} Large Area Telescope (LAT), the H.E.S.S. telescope, and the Milagro gamma-ray observatory. Based on a semi-analytical approach to the nonlinear shock acceleration process, we investigate the multiband nonthermal emission from W51C. The result shows that the radio emission from the remnant can be explained as synchrotron radiation of the electrons accelerated by a part of the shock flowing into the ambient medium. On the other hand, the high-energy gamma-rays detected by the {\it Fermi} LAT are mainly produced via proton-proton collisions of the high-energy protons with the ambient matter in the molecular cloud overtaken by the other part of the shock. We propose a possible explanation of the multiband nonthermal emission from W51C, and it can be concluded that a molecular cloud overtaken by a shock wave can be an important emitter in GeV $\gamma$-rays.

MeV ion event observed at 0950 UT on 4 May 1998 at a quasi-perpendicular bow shock region: New observations and an alternative interpretation on its origin

[1] The region near the Earth's bow shock provides a chance to test and compare various charged particle acceleration models (magnetospheric versus bow shock acceleration processes). This kind of research attracted the interest of a large part of the space community in the last four decades. During the last decade, some ion events with spectrum extending to high energies (greater than ∼1.3 MeV) observed by Polar on 4 May 1998 provided the opportunity for a new debate. These ion events were analyzed in a large number of papers and were discussed in terms of acceleration processes in the cusp of the magnetosphere or at a quasi-parallel region of the bow shock. In this paper, we reexamine in detail one of the ion events observed during the period of interest, around ∼0950 UT, and we provide new crucial information and interpretation by focusing on data obtained very close to the shock (not examined so far). At ∼0950 UT, Polar crossed a quasi-perpendicular bow shock under special solar wind speed/bow shock conditions, which favor the efficient acceleration of the solar ambient energetic population via the shock drift acceleration (SDA) mechanism. We analyze in detail observations upstream and downstream from the bow shock crossing of 0945 UT, for instance, flux-time profiles, energy spectra, ion composition, and pitch angle distributions, and we find them, as expected, in excellent agreement with the predictions of the SDA theory.

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 multi-band non-thermal emission from the supernova remnant RX J1713.7−3946

Non-thermal X-rays and very high energy (VHE) y -rays have been detected from the supernova remnant (SNR) RX J1713.7-3946, and the recent observations with the Suzaku satellite clearly reveal a spectral cut-off in the X-ray spectrum, which directly relates to the cut-off of the energy spectrum of the parent electrons. However, whether the origin of the VHE γ-rays from the SNR is hadronic or leptonic is still in debate. We studied the multi-band non-thermal emission from RX J1713.7-3946 based on a semi-analytical approach towards the non-linear shock acceleration process by including the contribution of the accelerated electrons to the non-thermal radiation. The results show that the multi-band observations on RX J1713.7-3946 can be well explained in the model with appropriate parameters, and the TeV γ-rays have hadronic origin, i.e. they are produced via proton-proton interactions as the relativistic protons accelerated by the shock collide with the ambient matter.

Hadronic Interpretation of High-Energy Gamma-Rays from Two TeV Sources Coincident with Molecular Clouds Overtaken by Supernova Remnants

We present a possible hadronic explanation of the high-energy j-ray emission from two very high-energy (VHE) sources, HESS J1745-303 (A) and HESS J1714-385, which coincide with supernova remnants (SNRs) interacting with dense molecular clouds (MCs). We calculate the proton spectra and the corresponding hadronic γ-ray spectra for different Mach numbers of the shock wave in a semi-analytical model for the non-linear shock acceleration process, then apply the model to the two newly discovered TeV sources. The results show that the γ-ray spectra for the two sources with energies above 100MeV detected by HESS and EGRET can be reproduced with low Mach numbers about 2.5. Thus the high-energy γ-ray origin for each one of the two sources can be interpreted as proton-proton (p–p) collisions in MCs overtaken by an SNR shock wave.