Shock Acceleration Theory Research Articles

An in situ Comparison of Electron Acceleration at Collisionless Shocks under Differing Upstream Magnetic Field Orientations

Abstract A leading explanation for the origin of Galactic cosmic rays is acceleration at high-Mach number shock waves in the collisionless plasma surrounding young supernova remnants. Evidence for this is provided by multi-wavelength non-thermal emission thought to be associated with ultrarelativistic electrons at these shocks. However, the dependence of the electron acceleration process on the orientation of the upstream magnetic field with respect to the local normal to the shock front (quasi-parallel/quasi-perpendicular) is debated. Cassini spacecraft observations at Saturn’s bow shock have revealed examples of electron acceleration under quasi-perpendicular conditions, and the first in situ evidence of electron acceleration at a quasi-parallel shock. Here we use Cassini data to make the first comparison between energy spectra of locally accelerated electrons under these differing upstream magnetic field regimes. We present data taken during a quasi-perpendicular shock crossing on 2008 March 8 and during a quasi-parallel shock crossing on 2007 February 3, highlighting that both were associated with electron acceleration to at least MeV energies. The magnetic signature of the quasi-perpendicular crossing has a relatively sharp upstream–downstream transition, and energetic electrons were detected close to the transition and immediately downstream. The magnetic transition at the quasi-parallel crossing is less clear, energetic electrons were encountered upstream and downstream, and the electron energy spectrum is harder above ∼100 keV. We discuss whether the acceleration is consistent with diffusive shock acceleration theory in each case, and suggest that the quasi-parallel spectral break is due to an energy-dependent interaction between the electrons and short, large-amplitude magnetic structures.

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).

X-ray Synchrotron Polarization from Turbulent Plasmas in Supernova Remnants

AbstractAs supernova remnants (SNRs) age, they become efficient cosmic ray accelerators at their outer shell shocks. The current paradigm for shock acceleration theory favors turbulent field environs in the proximity of these shocks, turbulence driven by current instabilities involving energetic ions. With the imminent prospect of dedicated X-ray polarimeters becoming a reality, the possibility looms of probing turbulence on scales that couple to the super-TeV electrons that emit X-rays. This paper presents model X-ray polarization signatures from energetic electrons moving in simulated MHD turbulence of varying levels of “chaos.” The emission volumes are finite slabs that represent the active regions of young SNR shells. We find that the turbulent field energy must be quite limited relative to that of the total field in order for the X-ray polarization degree to be as strong as the radio measures obtained in some remnants. Results presented are pertinent to the planned IXPE and XIPE polarimeters.

BARYON LOADING EFFICIENCY AND PARTICLE ACCELERATION EFFICIENCY OF RELATIVISTIC JETS: CASES FOR LOW LUMINOSITY BL LACS

ABSTRACT Relativistic jets launched by supermassive black holes, so-called active galactic nuclei (AGNs), are known as the most energetic particle accelerators in the universe. However, the baryon loading efficiency onto the jets from the accretion flows and their particle acceleration efficiencies have been veiled in mystery. With the latest data sets, we perform multi-wavelength spectral analysis of quiescent spectra of 13 TeV gamma-ray detected high-frequency-peaked BL Lacs (HBLs) following one-zone static synchrotron self-Compton (SSC) model. We determine the minimum, cooling break, and maximum electron Lorentz factors following the diffusive shock acceleration (DSA) theory. We find that HBLs have and the radiative efficiency , where P B and P e is the Poynting and electron power, respectively. By assuming 10 leptons per one proton, the jet power relates to the black hole mass as , where and is the jet power and the Eddington luminosity, respectively. Under our model assumptions, we further find that HBLs have a jet production efficiency of and a mass loading efficiency of . We also investigate the particle acceleration efficiency in the blazar zone by including the most recent Swift/BAT data. Our samples ubiquitously have particle acceleration efficiencies of , which is inefficient to accelerate particles up to the ultra-high-energy-cosmic-ray (UHECR) regime. This implies that the UHECR acceleration sites should not be the blazar zones of quiescent low power AGN jets, if one assumes the one-zone SSC model based on the DSA theory.

Observations of a new foreshock region upstream of a foreshock bubble's shock

AbstractEarth's foreshock is a region within the solar wind upstream of Earth's bow shock filled with backstreaming solar wind particles reflected at the shock. Within this region, when the interplanetary field is approximately radial, foreshock bubbles (FBs) can be formed when the backstreaming particles interact with approaching discontinuities embedded in the solar wind. Foreshock bubbles can grow to 5–10 RE in scale, well upstream of the bow shock. Having a high concentration of thermalized upstream ions and slow, or even sunward, speeds within them, these transient phenomena deflect the solar wind by forming a new shock ahead of them. Although FBs eventually succumb to solar wind dynamic pressure and crash onto Earth's bow shock and magnetopause, they may last long enough to allow solar wind reflection at their own shocks, which forms a new FB foreshock region upstream of them. The FB shock may be of different obliquity than the parent bow shock providing new and diverse opportunities for particle acceleration. Using a case study from Time History of Events and Macroscale Interactions during Substorms, we demonstrate that ions and electrons are reflected at the FB shock, where they acquire energies consistent with shock acceleration theory. These are the first definitive observations of a new ion and electron foreshock region upstream of the FB shock with implications for shock acceleration in general.

Spectra of accelerated particles at supernova shocks in the presence of neutral hydrogen: the case of Tycho

The presence of neutral hydrogen in the shock proximity changes the structure of the shock and affects the spectra of particles accelerated through the first-order Fermi mechanism. This phenomenon has profound implications for the interpretation of the multifrequency spectra of radiation from supernova remnants. Neutrals that undergo charge exchange with hot ions downstream of the shock may result in fast neutrals moving towards the upstream gas, where they can suffer additional charge exchange or ionisation reactions, thereby depositing energy and momentum upstream. Here we discuss the implications of this neutral return flux, which was already predicted in our previous work on neutral mediated supernova shocks, and show how the spectra of accelerated particles turn out to be appreciably steeper than $p^{-4}$, thereby affecting the gamma ray spectra from supernova remnants in general and from Tycho specifically. The theory that describes non-linear diffusive shock acceleration in the presence of neutral hydrogen has been developed in recent years. Here we use a semi-analytical theory developed in previous work and specialise our predictions to the case of the Tycho supernova shock, where there is evidence that the spectrum of the accelerated cosmic rays is steeper than expected from the traditional theory of diffusive shock acceleration. We show that, if the fraction of neutral hydrogen in the vicinity of the Tycho supernova shock is, as suggested by observations, ~70-90, then spectra of accelerated protons steeper than $p^{-4}$ may be a natural consequence of charge exchange reactions and the associated neutral return flux. The spectral shape is affected by this phenomenon for particles with energies below ~100-1000 GeV, for which the diffusion length is less than or at most comparable to the pathlength of charge exchange and ionisation upstream of the shock.

SIMULATION OF ENERGETIC PARTICLE TRANSPORT AND ACCELERATION AT SHOCK WAVES IN A FOCUSED TRANSPORT MODEL: IMPLICATIONS FOR MIXED SOLAR PARTICLE EVENTS

ABSTRACT We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock for which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturally reproduce the morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.

ION ACCELERATION AT THE QUASI-PARALLEL BOW SHOCK: DECODING THE SIGNATURE OF INJECTION

ABSTRACT Collisionless shocks are efficient particle accelerators. At Earth, ions with energies exceeding 100 keV are seen upstream of the bow shock when the magnetic geometry is quasi-parallel, and large-scale supernova remnant shocks can accelerate ions into cosmic-ray energies. This energization is attributed to diffusive shock acceleration; however, for this process to become active, the ions must first be sufficiently energized. How and where this initial acceleration takes place has been one of the key unresolved issues in shock acceleration theory. Using Cluster spacecraft observations, we study the signatures of ion reflection events in the turbulent transition layer upstream of the terrestrial bow shock, and with the support of a hybrid simulation of the shock, we show that these reflection signatures are characteristic of the first step in the ion injection process. These reflection events develop in particular in the region where the trailing edge of large-amplitude upstream waves intercept the local shock ramp and the upstream magnetic field changes from quasi-perpendicular to quasi-parallel. The dispersed ion velocity signature observed can be attributed to a rapid succession of ion reflections at this wave boundary. After the ions’ initial interaction with the shock, they flow upstream along the quasi-parallel magnetic field. Each subsequent wavefront in the upstream region will sweep the ions back toward the shock, where they gain energy with each transition between the upstream and the shock wave frames. Within three to five gyroperiods, some ions have gained enough parallel velocity to escape upstream, thus completing the injection process.

Suzaku observations of the galaxy cluster 1RXS J0603.3+4214: Implications of particle acceleration processes in the “Toothbrush” radio relic

Abstract We present the results of Suzaku observations of the galaxy cluster 1RXS J0603.3+4214 with the “Toothbrush” radio relic. Although a shock with Mach number M ≃ 4 is expected at the outer edge of the relic from the radio observation, our temperature measurements of the intracluster medium indicate a weaker temperature difference than expected. The Mach number estimated from the temperature difference at the outer edge of the relic is M ≃ 1.5, which is significantly lower than the value estimated from the radio data even considering both statistical and systematic errors. This suggests that a diffusive shock acceleration theory in the linear test particle regime, which is commonly used to link the radio spectral index to the Mach number, is invalid for this relic. We also measured the temperature difference across the western part of the relic, where a shock with M ≃ 1.6 is suggested from the X-ray surface brightness analysis of the XMM-Newton data, and obtained consistent results in an independent way. We searched for the non-thermal inverse Compton component in the relic region and the resultant upper limit on the flux is 2.4 × 10−13 erg cm−2 s−1 in the 0.3–10 keV band. The lower limit of the magnetic field strength becomes 1.6 μG, which means that magnetic energy density could be more than a few percent of the thermal energy.

A powerful double radio relic system discovered in PSZ1 G108.18-11.53: evidence for a shock with non-uniform Mach number?

Diffuse radio emission in the form of radio halos and relics has been found in a number of merging galaxy clusters. These structures indicate that shock and turbulence associated with the merger accelerate electrons to relativistic energies. We report the discovery of a radio relic + radio halo system in PSZ1 G108.18-11.53 (z=0.335). This cluster hosts the second most powerful double radio relic system ever discovered. We observed PSZ1 G108.18-11.53 with the Giant Meterwave Radio Telescope (GMRT) and the Westerbork Synthesis Radio Telescope (WSRT). We obtained radio maps at 147, 323, 607 and 1380 MHz. We also observed the cluster with the Keck telescope, obtaining the spectroscopic redshift for 42 cluster members. From the injection index we obtained the Mach number of the shocks generating the two radio relics. For the southern shock we found M = 2.33^{+0.19}_{-0.26}, while the northern shock Mach number goes from M = 2.20^{+0.07}_{-0.14} in the north part down to M = 2.00^{+0.03}_{-0.08} in the southern region. If the relation between the injection index and the Mach number predicted by diffusive shock acceleration (DSA) theory holds, this is the first observational evidence for a gradient in the Mach number along a galaxy cluster merger shock.

Evidence for superdiffusive shock acceleration at interplanetary shock waves

Recent analysis of time profiles of energetic particles accelerated at interplanetary shocks has shown evidence for superdiffusive transport upstream of the shock fronts, namely for a transport characterized by a particle mean square displacement that grows faster than linearly in time. While for normal, diffusive transport exponential particle time profiles are predicted, a large number of interplanetary shock events, included the termination shock of the solar wind, exhibits energetic particle time profiles that upstream decay as power laws. This power law trend has been derived in the framework of particle superdiffusion. The standard theory of diffusive shock acceleration has been further extended to the case of particle superdiffusive transport (superdiffusive shock acceleration), allowing for the derivation of harder energy spectral indices both for relativistic and non-relativistic particles. Here we test this theory for a couple of interplanetary shock waves that accelerate protons and that have been observed by the ACE spacecraft. We show that power law particle time profiles upstream of the shocks are common and clearly indicate superdiffusive transport. The particle energy spectra in some events are in a very good agreement with the superdiffusive shock acceleration prediction.

Particle acceleration at shocks propagating in partially ionized plasma

The shocks of several young supernova remnants (SNR) are often associated with very thin optical filaments dominated by Balmer emission resulting from charge-exchange and collisional excitation between neutral Hydrogen from the interstellar medium and shocked protons and electrons. Optical lines are a direct probe of the conditions at the shock, in particular the width of the narrow and broad components reflect the temperature upstream and downstream of the shock, respectively. When the shock accelerate efficiently non-thermal particles, the shock structure changes producing anomalous Balmer lines and it is possible to use their line shape and their spatial profile to check the efficiency of SNR shocks in accelerating cosmic rays. Here we illustrate the kinetic theory of shock acceleration in presence of neutrals with some applications to young SNRs. We show that in three cases (RCW 86, SNR 0509-67.5 and Tycho) anomalous Balmer lines can be explained assuming that a fraction of ∼ 10% of the total shock kinetic energy is converted into not thermal particles, while in one single case, the northwestern part of SN 1006, there is no evidence of efficient acceleration.

RAPID COSMIC-RAY ACCELERATION AT PERPENDICULAR SHOCKS IN SUPERNOVA REMNANTS

Perpendicular shocks are shown to be rapid particle accelerators that perform optimally when the ratio $u_{\rm s}$ of the shock speed to the particle speed roughly equals the ratio $1/\eta$ of the scattering rate to the gyro frequency. We use analytical methods and Monte-Carlo simulations to solve the kinetic equation that governs the anisotropy generated at these shocks, and find, for $\eta u_{\rm s}\approx1$, that the spectral index softens by unity and the acceleration time increases by a factor of two compared to the standard result of diffusive shock acceleration theory. These results provide a theoretical basis for the thirty-year-old conjecture that a supernova exploding into the wind of a Wolf-Rayet star may accelerate protons to an energy exceeding $10^{15}\,$eV.

SCATTTERING OF HIGH-ENERGY PARTICLES AT A COLLISIONLESS SHOCK FRONT: DEPENDENCE ON THE SHOCK ANGLE

Many shock acceleration theories deal with gyrophase-averaged particle distributions that depend only on the energy and pitch angle of the particles. Diffusive shock acceleration includes shock crossing as a necessary component. As long as the shock width is much smaller than the mean free path of a particle, the crossing is governed by the macroscopic fields inside the transition layer. The dynamics of high-energy particles in these fields is non-adiabatic and gyrophase dependent. The magnetic moment is not conserved in a wide range of shock angles, nor is the condition of reflection determined by the magnetic bottle relation. Instead, for a pitch angle and unknown gyrophase of an incident particle there is a finite probability of reflection. This probability varies between zero and unity in a wide range of pitch angles. In this work we investigate how the matching conditions at the shock front could be modified with the gyrophase dependence taken into account, e.g., in the form of the scattering probabilities.

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...

RADIO EMISSION FROM WEAK SPHERICAL SHOCKS IN THE OUTSKIRTS OF GALAXY CLUSTERS

In Kang (2015) we calculated the acceleration of cosmic-ray electrons and the ensuing radio synchrotron emission at weak spherical shocks that are expected to form in the outskirts of galaxy clusters.There we demonstrated that, at decelerating spherical shocks, the volume integrated spectra of both electrons and radiation deviate significantly from the test-particle power-laws predicted for constant planar shocks, because the shock compression ratio and the flux of injected electrons decrease in time. In this study, we consider spherical blast waves propagating into a constant density core surrounded by an isothermal halo with a decreasing density profile in order to explore how the deceleration rate of the shock speed affects the radio emission from accelerated electrons. The surface brightness profile and the volume-integrated radio spectrum of the model shocks are calculated by assuming a ribbon-like shock surface on a spherical shell and the associated downstream region of relativistic electrons. If the postshock magnetic field strength is about 7 microgauss, at the shock age of ~50 Myr, the volume-integrated radio spectrum steepens gradually with the spectral index from alpha_{inj} to alpha_{inj}+0.5 over 0.1-10 GHz, where alpha_{inj} is the injection index at the shock positionexpected from the diffusive shock acceleration theory. Such gradual steepening could explain the curved radio spectrum of the radio relic in cluster A2266, which was interpreted as a broken power-law by Trasatti et al. (2014), if the relic shock is young enough so that the break frequency falls in around 1 GHz.

Using optical lines to study particle acceleration at supernova remnants

The shocks of several young supernova remnants (SNR) are often associated with very thin optical filaments dominated by Balmer emission resulting from charge-exchange and collisional excitation between neutral Hydrogen from the interstellar medium and shocked protons and electrons. Optical lines are a direct probe of the conditions at the shock, in particular the width of the narrow and broad components reflect the temperature upstream and downstream of the shock, respectively. When the shock accelerate efficiently non-thermal particles, the shock structure changes producing anomalous Balmer lines and it is possible to use their line shape and their spatial profile to check the efficiency of SNR shocks in accelerating cosmic rays. Here we illustrate the kinetic theory of shock acceleration in presence of neutrals with some applications to young SNRs. We show that in three cases (RCW 86, SNR 0509-67.5 and Tycho) anomalous Balmer lines can be explained assuming that a fraction of ∼ 10% of the total shock kinetic energy is converted into not thermal particles, while in one single case, the northwestern part of SN 1006, there is no evidence of efficient acceleration.

Hybrid Simulations of Particle Acceleration at Shocks

We present the results of large hybrid (kinetic ions – fluid electrons) simulations of particle acceleration at non-relativistic collisionless shocks. Ion acceleration efficiency and magnetic field amplification are investigated in detail as a function of shock inclination and strength, and compared with predictions of diffusive shock acceleration theory, for shocks with Mach number up to 100. Moreover, we discuss the relative importance of resonant and Bell's instability in the shock precursor, and show that diffusion in the self-generated turbulence can be effectively parametrized as Bohm diffusion in the amplified magnetic field.

SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. II. MAGNETIC FIELD AMPLIFICATION

We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfv\'enic Mach number $M=100$, and scales with the square root of $M$. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately-strong shocks ($M\lesssim30$) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For $M\gtrsim30$, instead, Bell's non-resonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the free-escape boundary: the far upstream, where field amplification is provided by the current of escaping ions via NRH instability, and the shock precursor, where energetic particles are effectively magnetized, and field amplification is provided by the current in diffusing ions. The presented scalings of magnetic field amplification enable the inclusion of self-consistent microphysics into phenomenological models of ion acceleration at non-relativistic shocks.

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.