Standard Diffusive Shock Acceleration Research Articles

Flat Spectra of Energetic Particles in Interplanetary Shock Precursors

The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extending upstream of the shock for up to seven flux e-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy as ϵ −1, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from those traditionally employed in DSA models. We show that a standard (linear) DSA solution based on a widely accepted diffusive particle transport with an underlying resonant wave–particle interaction is inconsistent with the plateau in the particle flux. To resolve this contradiction, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivity κ on the particle flux F (nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. They lead to the particle diffusivity increasing with the particle energy as ∝ϵ 3/2 that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration.

Diffuse radio source candidate in CIZA J1358.9−4750

AbstractWe report on results of our upgraded Giant Metrewave Radio Telescope (uGMRT) observations for an early-stage merging galaxy cluster, CIZA J1358.9−4750 (CIZA1359), in Band-3 (300–500 MHz). We achieved the image dynamic range of ∼38000 using the direction dependent calibration and found a candidate of diffuse radio emission at 4σrms significance. The flux density of the candidate at 400 MHz, 24.04 ± 2.48 mJy, is significantly positive compared to noise, where its radio power, 2.40 × 1024 W Hz−1, is consistent with those of typical diffuse radio sources of galaxy clusters. The candidate is associated with a part of the X-ray shock front at which the Mach number reaches its maximum value of $\mathcal {M}\sim 1.7$. The spectral index (Fν ∝ να) of the candidate, α = −1.22 ± 0.33, is in agreement with an expected value derived from the standard diffusive shock acceleration (DSA) model. However, such a low Mach number with a short acceleration time would require seed cosmic rays supplied from active galactic nucleus (AGN) activities of member galaxies, as suggested in some other clusters. Indeed, we found seven AGN candidates inside the diffuse source candidate. Assuming the energy equipartition between magnetic fields and cosmic rays, the magnetic field strength of the candidate was estimated to be 2.1 μG. We also find head–tail galaxies and radio phoenixes or fossils near CIZA1359.

Theory of Electron Injection at Oblique Shock of Finite Thickness

Abstract A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion–convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of 0.1–1 MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high M A / cos θ Bn , where M A and θ Bn are the Alfvén Mach number and the shock obliquity, respectively. The theory suggests that efficient acceleration of electrons to ultrarelativistic energies will be more easily realized at high Mach number, young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.

Steep Cosmic-Ray Spectra with Revised Diffusive Shock Acceleration

Abstract Galactic cosmic rays (CRs) are accelerated at the forward shocks of supernova remnants (SNRs) via diffusive shock acceleration (DSA), an efficient acceleration mechanism that predicts power-law energy distributions of CRs. However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than E −2, the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of nonlinear DSA, we investigate the implications that these results have on the phenomenology of a wide range of SNRs. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than E −2 and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic SNRs (∝E −2.2) and the very steep spectra of young radio supernovae (∝E −3).

Mapping the spectral index of Cassiopeia A: evidence for flattening from radio to infrared

ABSTRACT Synchrotron radiation from supernova remnants is caused by electrons accelerated through diffusive shock acceleration (DSA). The standard DSA theory predicts an electron spectral index of p = 2, corresponding to a radio spectral index of α = −0.5. An extension of DSA theory predicts that the accelerated particles change the shock structure, resulting in a spectrum that is steeper than p > 2 (α < −0.5) at low energies and flattens with energy. For Cassiopeia A, a synchrotron spectral flattening was previously reported for a small part of the remnant in the mid-infrared regime. Here, we present new measurements for spectral flattening using archival radio (4.72 GHz) and mid-infrared (3.6 μm) data, and we produce a complete spectral index map to investigate the spatial variations within the remnant. We compare this to measurements of the radio spectral index from L-band (1.285 GHz) and C-band (4.64 GHz) maps. Our result shows overall spectral flattening across the remnant (αR-IR ∼ −0.5 to −0.7), to be compared with the radio spectral index of αR = −0.77. The flattest values coincide with the locations of most recent particle acceleration. In addition to overall flattening, we detect a relatively steeper region in the south-east of the remnant (αR-IR ∼ −0.67). We explore whether these locally steeper spectra could be the result of synchrotron cooling, which provides constraints on the local magnetic field strengths and the age of the plasma, suggesting B ≲ 2 mG for an age of 100 yr, and even B ≲ 1 mG using the age of Cas A, in agreement with other estimates.

Stochastic re-acceleration and magnetic-field damping in Tycho’s supernova remnant

Context. Tycho’s supernova remnant (SNR) is associated with the historical supernova (SN) event SN 1572 of Type Ia. The explosion occurred in a relatively clean environment, and was visually observed, providing an age estimate. This SNR therefore represents an ideal astrophysical test-bed for the study of cosmic-ray acceleration and related phenomena. A number of studies suggest that shock acceleration with particle feedback and very efficient magnetic-field amplification combined with Alfvénic drift are needed to explain the rather soft radio spectrum and the narrow rims observed in X-rays. Aims. We show that the broadband spectrum of Tycho’s SNR can alternatively be well explained when accounting for stochastic acceleration as a secondary process. The re-acceleration of particles in the turbulent region immediately downstream of the shock should be efficient enough to impact particle spectra over several decades in energy. The so-called Alfvénic drift and particle feedback on the shock structure are not required in this scenario. Additionally, we investigate whether synchrotron losses or magnetic-field damping play a more profound role in the formation of the non-thermal filaments. Methods. We solved the full particle transport equation in test-particle mode using hydrodynamic simulations of the SNR plasma flow. The background magnetic field was either computed from the induction equation or follows analytic profiles, depending on the model considered. Fast-mode waves in the downstream region provide the diffusion of particles in momentum space. Results. We show that the broadband spectrum of Tycho can be well explained if magnetic-field damping and stochastic re-acceleration of particles are taken into account. Although not as efficient as standard diffusive shock acceleration, stochastic acceleration leaves its imprint on the particle spectra, which is especially notable in the emission at radio wavelengths. We find a lower limit for the post-shock magnetic-field strength ∼330 μG, implying efficient amplification even for the magnetic-field damping scenario. Magnetic-field damping is necessary for the formation of the filaments in the radio range, while the X-ray filaments are shaped by both the synchrotron losses and magnetic-field damping.

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.

Cosmic-ray acceleration and escape from post-adiabatic supernova remnants

Context. Supernova remnants are known to accelerate cosmic rays on account of their nonthermal emission of radio waves, X-rays, and gamma rays. Although there are many models for the acceleration of cosmic rays in supernova remnants, the escape of cosmic rays from these sources has not yet been adequately studied. Aims. We aim to use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. Methods. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma in a volume large enough to keep all cosmic rays in the simulation. The transport equations for cosmic rays and magnetic turbulence were coupled via the cosmic-ray gradient and the spatial diffusion coefficient of the cosmic rays, while the cosmic-ray feedback onto the shock structure can be ignored. Our simulations span 100 000 years, thus covering the free-expansion, the Sedov–Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution. Results. At later stages of the evolution, cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration, and feature breaks in the 10 − 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. We further find the gamma-ray luminosity to peak around an age of 4000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media generally emit more inverse-Compton radiation, matching the fact that the brightest known supernova remnants – RCW86, Vela Jr., HESS J1731−347 and RX J1713.7−3946 – are all expanding in low density environments.

Shock acceleration efficiency in radio relics

Context. Radio relics in galaxy clusters are giant diffuse synchrotron sources powered in cluster outskirts by merger shocks. Although the relic–shock connection has been consolidated in recent years by a number of observations, the details of the mechanisms leading to the formation of relativistic particles in this environment are still not well understood. Aims. The diffusive shock acceleration (DSA) theory is a commonly adopted scenario to explain the origin of cosmic rays at astrophysical shocks, including those in radio relics in galaxy clusters. However, in a few specific cases it has been shown that the energy dissipated by cluster shocks is not enough to reproduce the luminosity of the relics via DSA of thermal particles. Studies based on samples of radio relics are required to further address this limitation of the mechanism. Methods. In this paper, we focus on ten well-studied radio relics with underlying shocks observed in the X-rays and calculate the electron acceleration efficiency of these shocks that is necessary to reproduce the observed radio luminosity of the relics. Results. We find that in general the standard DSA cannot explain the origin of the relics if electrons are accelerated from the thermal pool with an efficiency significantly smaller than 10%. Our results show that other mechanisms, such as shock re-acceleration of supra-thermal seed electrons or a modification of standard DSA, are required to explain the formation of radio relics.

The Acceleration of Energetic Particles at Coronal Shocks and Emergence of a Double Power-law Feature in Particle Energy Spectra

Abstract We present numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that the location on the shock where the high-energy particle intensity is the largest, depends on the energy of the particles and on time. The acceleration of particles to more than 100 MeV mainly occurs in the shock-streamer interaction region, due to perpendicular shock geometry and the trapping effect of closed magnetic fields. A comparison of the particle spectra to that in a radial magnetic field shows that the intensity at 100 MeV (200 MeV) is enhanced by more than one order (two orders) of magnitude. This indicates that the streamer-like magnetic field can be an important factor in producing large solar energetic particle events. We also show that the energy spectrum integrated over the simulation domain consists of two different power laws. Further analysis suggests that it may be a mixture of two distinct populations accelerated in the streamer and open field regions, where the acceleration rate differs substantially. Our calculations also show that the particle spectra are affected considerably by a number of parameters, such as the streamer tilt angle, particle spatial diffusion coefficient, and shock compression ratio. While the low-energy spectra agree well with standard diffusive shock acceleration theory, the break energy ranges from ∼1 MeV to ∼90 MeV and the high-energy spectra can extend to ∼1 GeV with a slope of ∼2–3.

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.

An Unusual Energetic Particle Flux Enhancement Associated with Solar Wind Magnetic Island Dynamics

Abstract The possibility that charged particles are accelerated statistically in a “sea” of small-scale interacting magnetic flux ropes in the supersonic solar wind is gaining credence. In this Letter, we extend the Zank et al. statistical transport theory for a nearly isotopic particle distribution by including an escape term corresponding to particle loss from a finite acceleration region. Steady-state 1D solutions for both the accelerated particle velocity distribution function and differential intensity are derived. We show Ulysses observations of an energetic particle flux enhancement event downstream of a shock near 5 au that is inconsistent with the predictions of classical diffusive shock acceleration (DSA) but may be explained by local acceleration associated with magnetic islands. An automated Grad-Shafranov reconstruction approach is employed to identify small-scale magnetic flux ropes behind the shock. For the first time, the observed energetic particle “time-intensity” profile and spectra are quantitatively compared with theoretical predictions. The results show that stochastic acceleration by interacting magnetic islands accounts successfully for the observed (i) peaking of particle intensities behind the shock instead of at the shock front as standard DSA predicts; (ii) increase in the particle flux amplification factor with increasing particle energy; (ii) increase in distance between the particle intensity peak and the shock front with increasing energy; and (iv) hardening of particle power-law spectra with increasing distance downstream of the shock.

Acceleration of Solar Energetic Particles at a Fast Traveling Shock in Non-uniform Coronal Conditions

Time-dependent solar energetic particle (SEP) acceleration is investigated at a fast, nearly parallel spherical traveling shock in the strongly non-uniform corona by solving the standard focused transport equation for SEPs and transport equations for parallel propagating Alfvén waves that form a set of coupled equations. This enables the modeling of self-excitation of Alfvén waves in the inertial range by SEPs ahead of the shock and its role in enhancing the efficiency of the diffusive shock acceleration (DSA) of SEPs in a self-regulatory fashion. Preliminary results suggest that, because of the highly non-uniform coronal conditions that the shock encounters, both DSA and wave excitation are highly time-dependent processes. Thus, DSA spectra of SEPs strongly deviate from the simple power-law prediction of standard steady-state DSA theory and initially strong wave excitation weakens rapidly. Consequently, the ability of DSA to produce high energy SEPs in the corona of ∼1 GeV, as observed in the strongest gradual SEP events, appears to be strongly curtailed at a fast nearly parallel shock, but further research is needed before final conclusions can be drawn.

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).

COMBINING DIFFUSIVE SHOCK ACCELERATION WITH ACCELERATION BY CONTRACTING AND RECONNECTING SMALL-SCALE FLUX ROPES AT HELIOSPHERIC SHOCKS

ABSTRACT Computational and observational evidence is accruing that heliospheric shocks, as emitters of vorticity, can produce downstream magnetic flux ropes and filaments. This led Zank et al. to investigate a new paradigm whereby energetic particle acceleration near shocks is a combination of diffusive shock acceleration (DSA) with downstream acceleration by many small-scale contracting and reconnecting (merging) flux ropes. Using a model where flux-rope acceleration involves a first-order Fermi mechanism due to the mean compression of numerous contracting flux ropes, Zank et al. provide theoretical support for observations that power-law spectra of energetic particles downstream of heliospheric shocks can be harder than predicted by DSA theory and that energetic particle intensities should peak behind shocks instead of at shocks as predicted by DSA theory. In this paper, a more extended formalism of kinetic transport theory developed by le Roux et al. is used to further explore this paradigm. We describe how second-order Fermi acceleration, related to the variance in the electromagnetic fields produced by downstream small-scale flux-rope dynamics, modifies the standard DSA model. The results show that (i) this approach can qualitatively reproduce observations of particle intensities peaking behind the shock, thus providing further support for the new paradigm, and (ii) stochastic acceleration by compressible flux ropes tends to be more efficient than incompressible flux ropes behind shocks in modifying the DSA spectrum of energetic particles.

TURBULENT COSMIC-RAY REACCELERATION AT RADIO RELICS AND HALOS IN CLUSTERS OF GALAXIES

Radio relics are synchrotron emission found on the periphery of galaxy clusters. From the position and the morphology, it is often believed that the relics are generated by cosmic-ray (CR) electrons accelerated at shocks through a diffusive shock acceleration (DSA) mechanism. However, some radio relics have harder spectra than the prediction of the standard DSA model. One example is observed in the cluster 1RXS J0603.3+4214, which is often called the ``Toothbrush Cluster''. Interestingly, the position of the relic is shifted from that of a possible shock. In this study, we show that these discrepancies in the spectrum and the position can be solved if turbulent (re)acceleration is very effective behind the shock. This means that for some relics turbulent reacceleration may be the main mechanism to produce high-energy electrons, contrary to the common belief that it is the DSA. Moreover, we show that for efficient reacceleration, the effective mean free path of the electrons has to be much smaller than their Coulomb mean free path. We also study the merging cluster 1E 0657-56 or the ``Bullet Cluster'', in which a radio relic has not been found at the position of the prominent shock ahead of the bullet. We indicate that a possible relic at the shock is obscured by the observed large radio halo that is generated by strong turbulence behind the shock. We propose a simple explanation if the morphological differences of radio emission among the Toothbrush, the Bullet, and the Sausage (CIZA J2242.8+5301) Clusters.

Parameter estimation of superdiffusive motion of energetic particles upstream of heliospheric shocks

In-situ spacecraft observations recently suggested that the transport of energetic particles accelerated at heliospheric shocks can be anomalous, i.e. the mean square displacement can grow non-linearly in time. In particular, a new analysis technique has permitted the study of particle transport properties from energetic particle time profiles upstream of interplanetary shocks. Indeed, the time/spatial power laws of the differential intensity upstream of several shocks are indicative of superdiffusion. A complete determination of the key parameters of superdiffusive transport comprises the power-law index, the superdiffusion coefficient, the related transition scale at which the energetic particle profiles turn to decay as power laws, and the energy spectral index of the shock accelerated particles. Assuming large-scale spatial homogeneity of the background plasma, the power-law behaviour can been derived from both a (microscopic) propagator formalism and a (macroscopic) fractional transport equation. We compare the two approaches and find a relation between the diffusion coefficients used in the two formalisms. Based on the assumption of superdiffusive transport, we quantitatively derive these parameters by studying energetic particle profiles observed by the Ulysses and Voyager 2 spacecraft upstream of shocks in the heliosphere, for which a superdiffusive particle transport has previously been observed. Further, we have jointly studied the electron energy spectra, comparing the values of the spectral indices observed with those predicted by the standard diffusive shock acceleration theory and by a model based on superdiffusive transport. For a number of interplanetary shocks and for the solar wind termination shock, for the first time we obtain the anomalous diffusion constants and the scale at which the probability of particle free paths changes to a power-law...

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.

No shock across part of a radio relic in the merging galaxy cluster ZwCl 2341.1+0000?

The galaxy cluster ZwCl 2341.1+0000 is a merging system at z=0.27, which hosts two radio relics and a central, faint, filamentary radio structure. The two radio relics have unusually flat integrated spectral indices of -0.49 +/- 0.18 and -0.76 +/- 0.17, values that cannot be easily reconciled with the theory of standard diffusive shock acceleration of thermal particles at weak merger shocks. We present imaging results from XMM-Newton and Chandra observations of the cluster, aimed to detect and characterise density discontinuities in the ICM. As expected, we detect a density discontinuity near each of the radio relics. However, if these discontinuities are the shock fronts that fuelled the radio emission, then their Mach numbers are surprisingly low, both <=2. We studied the aperture of the density discontinuities, and found that while the NW discontinuity spans the whole length of the NW radio relic, the arc spanned by the SE discontinuity is shorter than the arc spanned by the SE relic. This startling result is in apparent contradiction with our current understanding of the origin of radio relics. Deeper X-ray data are required to confirm our results and to determine the nature of the density discontinuities.

PARTICLE ACCELERATION AT THE HELIOSPHERIC TERMINATION SHOCK WITH A STOCHASTIC SHOCK OBLIQUITY APPROACH

Observations by the plasma and magnetic field instruments on board the Voyager 2 spacecraft suggest that the termination shock is weak with a compression ratio of ∼2. However, this is contrary to the observations of accelerated particle spectra at the termination shock, where standard diffusive shock acceleration theory predicts a compression ratio closer to ∼2.9. Using our focused transport model, we investigate pickup proton acceleration at a stationary spherical termination shock with a moderately strong compression ratio of 2.8 to include both the subshock and precursor. We show that for the particle energies observed by the Voyager 2 Low Energy Charged Particle (LECP) instrument, pickup protons will have effective length scales of diffusion that are larger than the combined subshock and precursor termination shock structure observed. As a result, the particles will experience a total effective termination shock compression ratio that is larger than values inferred by the plasma and magnetic field instruments for the subshock and similar to the value predicted by diffusive shock acceleration theory. Furthermore, using a stochastically varying magnetic field angle, we are able to qualitatively reproduce the multiple power-law structure observed for the LECP spectra downstream of the termination shock.