Shock Acceleration Research Articles

Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions

Abstract This paper provides the set of Rankine–Hugoniot (R–H) jump conditions for shocks in space and astrophysical plasmas described by kappa, distributions. The characteristic result is the development of a new R–H condition that transforms the values of kappa upstream and downstream the shock. The kappa index parameterizes and labels kappa distributions, and it is necessary for characterizing the thermodynamics of space plasmas. This first approach is restricted to non-magnetized plasmas, and the whole achievement is derived by following first principles of statistical mechanics and thermodynamics. The results show that, depending on the shock strength, the kappa indices across the shock may decrease or increase, indicating cases of shock acceleration or deceleration, respectively.

Runaway O-star Bow Shocks as Particle Accelerators? The Case of AE Aur Revisited

Abstract We present results of our Chandra/ACIS observations of the field centered on the fast, runaway O star AE Aur and its bow shock. Previous XMM-Newton observations revealed an X-ray “blob” near the IR arc tracing the bow shock, possibly a nonthermal source consistent with models of Inverse Compton scattering of dust IR photons by electrons accelerated at the shock. The new, subarcsecond-resolution Chandra data, while confirming the presence of the XMM-Newton source, clearly indicate that the latter is neither extended nor coincident with the IR arc and strongly suggest it is a background active galactic nucleus. Motivated by results published for the bow shock of BD+43°3654, we extended our study to the radio domain by analyzing archival EVLA data. We find no radio emission from the AE Aur bow shock either. The corresponding upper limits for the absorbed (unabsorbed) X-ray flux of 5.9(7.8) × 10−15 erg cm−2 s−1 (3σ) and, in the radio range of 2 mJy (1.4 GHz) and 0.4 mJy (5.0 GHz), are used to put constraints on model predictions for particle acceleration within the bow shock. In the “classical” framework of diffusive shock acceleration, we find that the predicted X-ray and radio emission by the bow shock is at least two orders of magnitude below the current upper limits, consistent with the systematic nondetections of up to 60 stellar bow shocks. The only exception so far remains that of BD+43°3654, which is probably the result of its very large mass-loss rate among runaway O stars.

Monte Carlo modelling of particle acceleration in collisionless shocks with effective mean electric field

Relativistic particle acceleration in collisionless shocks of supernova remnants is accompanied with magnetic field amplification by cosmic ray (CR) driven plasma instabilities. Bell’s fast CR-current instability is predicted to produce turbulence with a non-zero mean electric field in the shock precursor. We present a Monte Carlo model of Fermi shock acceleration explicitly taking into account an effective mean upstream electric field. Our model is nonlinear and includes the backreaction effects of efficient Fermi acceleration on the shock structure.

Global Energetics of Solar Flares and Coronal Mass Ejections

We investigate the global energetics and energy closure of various physical processes that are energetically important in solar flares and coronal mass ejections (CMEs), which includes: magnetic energies, thermal energies, nonthermal energies (particle acceleration), direct and indirect plasma heating processes, kinetic CME energies, gravitational CME energies, aerodynamic drag of CMEs, solar energetic particle events, EUV and soft X-ray radiation, white-light, and bolometric energies. Statistics on these forms of energies is obtained from 400 GOES M- and X-class events during the first 3.5 years of the Solar Dynamics Observatory (SDO) mission. A primary test addressed in this study is the closure of the various energies, such as the equivalence of the dissipated magnetic energies and the primary dissipated are energies (accelerated particles, direct heating, CME acceleration), which faciliate the energy of secondary processes (plasma heating, shock acceleration) and interactions with the solar wind (aerodynamic drag). Our study demonstrates energy closure in the statistical average, while individual events may have considerable uncertainties, requiring improved nonlinear force-free field models, and particle acceleration models with observationally constrained low-energy cutoffs.

Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

Cosmic rays (CRs) are thought to play a dynamically important role in several key aspects of galaxy evolution, including the structure of the interstellar medium, the formation of galactic winds, and the non-thermal pressure support of halos. We introduce a numerical model solving for the CR streaming instability and acceleration of CRs at shocks with a fluid approach in the adaptive mesh refinement code RAMSES. CR streaming is solved with a diffusion approach and its anisotropic nature is naturally captured. We introduce a shock finder for the RAMSES code that automatically detects shock discontinuities in the flow. Shocks are the loci for CR injection, and their efficiency of CR acceleration is made dependent on the upstream magnetic obliquity according to the diffuse shock acceleration mechanism. We show that the shock finder accurately captures shock locations and estimates the shock Mach number for several problems. The obliquity-dependent injection of CRs in the Sedov solution leads to situations where the supernova bubble exhibits large polar caps (homogeneous background magnetic field), or a patchy structure of the CR distribution (inhomogeneous background magnetic field). Finally, we combine both accelerated CRs with streaming in a simple turbulent interstellar medium box, and show that the presence of CRs significantly modifies the structure of the gas.

Modelling of electron acceleration in relativistic supernovae

Radio and X-ray observations revealed a rare but a very interesting class of supernovae (SNe) with a sizeable fraction of the kinetic energy of ejecta moving with a trans-relativistic speed. These relativistic SNe are comprising a population of the objects intermediate between the numerous core collapse SNe expanding with non-relativistic velocities and the gamma-ray bursts with highly relativistic ejecta. An interpretation of the observed non-thermal emission from relativistic SNe requires a model of electron acceleration in trans-relativistic shocks. In this paper we present numerical Particle-in-Cell (PIC) simulation of electron spectra in trans-relativistic shock waves propagating in clumped stellar winds of the SN progenitors. It is shown here that the presence of background magnetic fluctuations has a drastical effect on the electron acceleration by the trans-relativistic shocks propagating transverse to the regular magnetic field in the clumped wind of a massive progenitor star.

Observation of Suprathermal Tails of He+ Pickup Ions across Solar Wind Compression Regions with STEREO PLASTIC

The presence of suprathermal tails of solar wind and pickup ions in interplanetary space has been widely observed, even during quiet times with no simultaneous observation of solar energetic particles. One of the persistent characteristics of these tails have been power law spectra of the velocity distribution function with a v−5 dependence in the solar wind reference frame and exponential fall-off at higher energies, but variations in the spectra including those of other species have also been observed. Several attempts to explain the formation of suprathermal tails during quiet times have been made, among them continuing acceleration by compressive fluctuations of the solar wind and the stochastic superposition of exponential, Gaussian, and variable power law spectra from diffusive shock, stochastic, and other acceleration processes. We find here that acceleration is effective within compression regions with and without shocks. In the context of a superposed epoch analysis of the evolution of He+ pickup ion distributions across compression regions, we report on a related study of He+ tails, using STEREO PLASTIC data from 2007 through 2014. Quiet times have been selected based on limiting energetic He fluxes above the tail energies and based on the tail fluxes themselves. We find that the suprathermal tail flux is dependent on the compression strength and varies substantially across the compression region. The strongest tails with spectra somewhat steeper than v−5 occur in the compressed fast solar wind, and they decrease rapidly with distance from the preceding and following compression into the rarefaction region, when using an unbiased data sample and applying a quiet time criterion based on higher energy ions. This may be consistent with the compressions being a potential source of the tails. When applying a quiet time criterion based on the observed tail fluxes, the temporal evolution disappears, possibly implicating a selection of the lower end of a Poisson distribution of tail count rates, rendering such a selection unusable for temporal evolution studies.

Chemistry of ion injection in supernova remnant shocks: hybrid simulations in the light of He/C/O data from AMS-02

The high precision spectrometry of galactic cosmic rays (CR), e.g. PAMELA experiment [1], accurately determined an approximately 0.1 difference between the rigidity spectral indices of protons and He ions. Similar deviations have been indicated earlier by other experiments [2] confirmed by the recent high-fidelity AMS-02 measurements [3]. These findings widen the window into a complicated selection process whereby collisionless shocks, such as supernova remnant (SNR) blast waves, extract different chemical elements from an interstellar matter mix. The similarity of He/p, C/p, and O/p rigidity spectra demonstrated by AMS-02 has provided new evidence that injection is a mass-to-charge (A/Z) dependent process. We investigate the particle injection into the diffusive shock acceleration using one- and two-dimensional self-consistent hybrid simulations. Our 1D simulations prove that an SNR shock can modify the chemical composition of accelerated CRs by preferentially extracting them from a homogeneous background plasma without additional, largely untestable assumptions. Our results confirm the earlier theoretical predictions of how the efficiency of injection depends on the shock Mach number MA. They show that selection rate of different ion species increases with A/Z, saturates, and peaks as a function of MA. The 2D simulations also evidence a deviation from the linear selection rate vs A/Z trend, pointing towards a saturation for higher A/Z. The integrated SNR rigidity spectrum for proton-to-helium flux ratio, obtained by the convolution of the time-dependent injection rates of protons and He ions with a decreasing shock strength over the active lives of SNRs, compares well with the AMS-02 and PAMELA data. The numerical results [4] correctly predict the decrease in p/He flux ratio with increasing rigidity at exactly the rate measured in the experiments for ℜ > 10 GV. Only at lower rigidities, ℜ < 10 GV, the difference between the data and our predictions becomes noticeable. Whether this deviation comes from the propagation through the interstellar medium or solar modulation, remains unclear. Except for this uncertainty, the suggested mechanism for A/Z-dependence of the injection fully explains the measured p/He ratio.

Radio emission from interstellar shocks: Young type Ia supernova remnants and the case of N 103B in the Large Magellanic Cloud

Here we present a radio continuum study based on new and archival data from the Australia Telescope Compact Array towards N 103B, a young (<=1000 yrs) spectroscopically confirmed type Ia SNR in the Large Magellanic Cloud (LMC) and proposed to have originated from a single degenerate progenitor. The radio morphology of this SNR is asymmetrical with two bright regions towards the north-west and south-west of the central location as defined by radio emission. N 103B identified features include: a radio spectral index of -0.75+-0.01 (consistent with other young type Ia SNRs in the Galaxy); a bulk SNR expansion rate as in X-rays; morphology and polarised electrical field vector measurements where we note radial polarisation peak towards the north-west of the remnant at both 5500 and 9000 MHz. The spectrum is concave-up and the most likely reason is the non-linear diffusive shock acceleration effects or presence of two different populations of ultra-relativistic electrons. We also note unpolarized clumps near the south-west region which is in agreement with this above scenario. We derive a typical magnetic field strength for N 103B, of 16.4 microG for an average rotation measurement of 200 rad m^-2. However, we estimate the equipartition field to be of the order of ~235 microG with an estimated minimum energy of Emin=6.3*10^48 erg. The close (~0.5 degree) proximity of N 103B to the LMC mid-plane indicates that an early encounter with dense interstellar medium may have set an important constrain on SNR evolution. Finally, we compare features of N 103B, to six other young type Ia SNRs in the LMC and Galaxy, with a range of proposed degeneracy scenarios to highlight potential differences due to a different models. We suggest that the single degenerate scenario might point to morphologically asymmetric type Ia supernova explosions.

A possible explanation for the enhancement of energetic particles downstream of the heliospheric termination shock

Voyager 2 observations of the energetic particle “time-intensity” profiles from ~1.8 to ~40 MeV show that the flux peaks downstream of the heliospheric termination shock (HTS), which is inconsistent with the predictions of classical diffusive shock acceleration (DSA). Previous studies suggest that shocks are effective in generating downstream magnetic flux ropes, islands or plasmoids. These dynamically interacting small-scale structures can accelerate charged particles statistically through reconnection-related processes. We present a preliminary study of the magnetic field and plasma properties together with the energetic particle data during the V2 crossing of the HTS. We apply a local stochastic acceleration model associated with solar wind magnetic island dynamics to explain the unusual behavior of energetic particles observed in the vicinity of the HTS. An analytic solution for the particle velocity distribution function derived from the Zank et al. statistical transport theory is used to fit the observed particle flux amplification downstream of the HTS. The results show that stochastic acceleration by interacting magnetic islands can successfully predict the observed (i) peaking of particle intensities behind the HTS, instead of at the shock front; (ii) increasing of the particle flux amplification factor with increasing particle energy; and (iii) increase in distance between the particle intensity peak and the HTS with increasing particle energy; This study illustrates the possibility of local acceleration in the inner heliosheath due to the dynamical interaction of magnetic islands.

Steepening of Cosmic-Ray Spectra in Shocks with Varying Magnetic Field Direction

Abstract Cosmic-ray (CR) spectra, both measured upon their arrival at the Earth’s atmosphere and inferred from the emission in supernova remnants (SNRs), appear to be significantly steeper than the “standard” diffusive shock acceleration (DSA) theory predicts. Although the reconstruction of the primary spectra introduces an additional steepening due to propagation effects, there is a growing consensus in the CR community that these corrections fall short to explain the newest high-precision data. Using 2D hybrid simulations, we investigate a new mechanism that may steepen the spectrum during the acceleration in SNR shocks. Most of the DSA treatments are limited to homogeneous shock environments. To investigate whether inhomogeneity effects can produce the necessary extra steepening, we assume that the magnetic field changes its angle along the shock front. The rationale behind this approach is the strong dependence of the DSA efficiency upon the field angle, θ Bn. Our results show that the variation of shock obliquity along its face results in a noticeable steepening of the DSA spectrum. Compared to simulations of quasi-parallel shocks, we observe an increase of the spectral index by Δq = 0.1–0.15. Possible extrapolation of the limited simulation results to more realistic SNR conditions are briefly considered.

Kinetic Simulations of Nonrelativistic Perpendicular Shocks of Young Supernova Remnants. II. Influence of Shock-surfing Acceleration on Downstream Electron Spectra

Abstract We explore electron preacceleration at high-Mach-number nonrelativistic perpendicular shocks at, e.g., young supernova remnants, which are a prerequisite of further acceleration to very high energies via diffusive shock acceleration. Using fully kinetic particle-in-cell simulations of shocks and electron dynamics in them, we investigate the influence of shock-surfing acceleration (SSA) at the shock foot on the nonthermal population of electrons downstream of the shock. The SSA is followed by further energization at the shock ramp where the Weibel instability spawns a type of second-order Fermi acceleration. The combination of these two processes leads to the formation of a nonthermal electron population, but the importance of SSA becomes smaller for larger ion-to-electron mass ratios in the simulation. We discuss the resulting electron spectra and the relevance of our results to the physics of systems with real ion-to-electron mass ratios and fully three-dimensional behavior.

Exploring particle escape in supernova remnants through gamma rays

ABSTRACT The escape process of particles accelerated at supernova remnant (SNR) shocks is one of the poorly understood aspects of the shock acceleration theory. Here we adopt a phenomenological approach to study the particle escape and its impact on the gamma-ray spectrum resulting from hadronic collisions both inside and outside of a middle-aged SNR. Under the assumption that in the spatial region immediately outside of the remnant the diffusion coefficient is suppressed with respect to the average Galactic one, we show that a significant fraction of particles are still located inside the SNR long time after their nominal release from the acceleration region. This fact results into a gamma-ray spectrum that resembles a broken power law, similar to those observed in several middle-aged SNRs. Above the break, the spectral steepening is determined by the diffusion coefficient outside of the SNR and by the time dependence of maximum energy. Consequently, the comparison between the model prediction and actual data will contribute to determining these two quantities, the former being particularly relevant within the predictions of the gamma-ray emission from the halo of escaping particles around SNRs, which could be detected with future Cherenkov telescope facilities. We also calculate the spectrum of runaway particles injected into the Galaxy by an individual remnant. Assuming that the acceleration stops before the SNR enters the snowplow phase, we show that the released spectrum can be a featureless power law only if the accelerated spectrum is ∝ p−α with α &gt; 4.

Acceleration of Interstellar Pickup He+ at Earth's Perpendicular Bow Shock

AbstractOn 05 December 2015 the Magnetospheric MultiScale constellation observed interstellar pickup ion distributions during an inbound crossing of Earth's perpendicular bow shock near the subsolar point, which provides new insights into shock acceleration of pickup ions throughout the heliosphere. In this study we analyze the upstream and downstream velocity distributions of H+ and He+ using data from the Hot Plasma Composition Analyzer on Magnetospheric MultiScale. We derive average two‐dimensional pitch angle distributions in the upstream and downstream field‐aligned bulk plasma frame, as well as integrated one‐dimensional velocity distributions. By comparing the upstream and downstream distributions, we find evidence of accelerated H+ and He+ downstream of the shock. By comparing measured and theoretical reflection ratios for He+, we attribute a significant part of this acceleration to a single reflection at the shock.

Interaction of a Singular Surface with a Characteristic Shock in a Relaxing Gas with Dust Particles

Abstract A system of hyperbolic differential equations outlining one-dimensional planar, cylindrical symmetric and spherical symmetric flow of a relaxing gas with dust particles is considered. Singular surface theory used to study different aspects of wave propagation and its culmination to the steepened form. The evolutionary behavior of the characteristic shock is studied. A particular solution of the governing system of equations is used to discuss the steepened wave form, characteristic shock and their interaction. The results of the interaction between the steepened wave front and the characteristic shock using the general theory of wave interaction are discussed. Also, the influence of relaxation and dust parameters on the steepened wave front, the formation of a characteristic shock, reflected and transmitted waves after interaction and a jump in shock acceleration are investigated.

The Filamentary Radio Lobes of the Seyfert–Starburst Composite Galaxy NGC 3079

Abstract We present results from multifrequency polarization-sensitive Very Large Array observations of the Seyfert–starburst composite galaxy NGC 3079. Our sensitive radio observations reveal a plethora of radio “filaments” comprising the radio lobes in this galaxy. We analyze the origin of these radio filaments in the context of existing Chandra X-ray and HST emission-line data. We do not find a one-to-one correlation of the radio filaments with the emission-line filaments. The northeastern lobe is highly polarized with polarization fractions ∼33% at 5 GHz. The magnetic fields are aligned with the linear extents of the optically thin filaments, as observed in our, as well as other, observations in the literature. Our rotation measure images show evidence for rotation measure inversion in the northeastern lobe. Our data best fit a model where the cosmic rays follow the magnetic field lines generated as a result of the dynamo mechanism. There could be additional effects like shock acceleration that might also be playing a role. We speculate that the peculiar radio lobe morphology is a result of an interplay between both the superwinds and the active galactic nucleus jet that are present in the galaxy. The jet, in fact, might be playing a major role in providing the relativistic electron population that is present in the radio lobes.

Test Research on Airdrop Shock Vibration of Armored Vehicles

In view of the airdrop adaptability of a lightweight high-mobility wheeled armored vehicle, the shock vibration of the vehicle’s onboard electronic equipment under simulated airdrop was tested and the shock characteristic of the equipment was analyzed. The test results show that the onboard equipment of the airdrop vehicle is mainly subjected to three stages of shock vibration, which includes the crash of the lifting rope, shock of the cushion airbag and the rebound shock. The cushion airbags can effectively reduce the shock acceleration peak of the onboard electronic equipment of the light wheeled armored vehicle, and the shock peak of the onboard computer and power supply is about 9-10 g with the shock duration of 0.15-0.2 s. While compared with the shock of the base, the buffering effect of the isolators to the airdrop shock vibration is not satisfied. Resonances of the isolation system are caused by the airdrop shock and the shock peaks of the tested electronic equipment are higher than that of the base.

Particle acceleration in interstellar shocks

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

All-optical cascaded ion acceleration in segmented tubes driven by multiple independent laser pulses

A scheme to achieve all-optical cascaded ion acceleration driven by intense laser pulses is proposed, where a series of segmented tubes are used. First, the high-flux ion beam is produced via collisionless shock acceleration in the first tube segment driven by an intense picosecond laser, and then undergoes successive post-accelerations in a cascaded manner via magnetic vortex acceleration driven by low-power terawatt-femtosecond lasers when it propagates through each subsequent tube segment into the vacuum gaps between them. By controlling the delay of the femtosecond lasers as well as the vacuum gap between the tube segments, not only the maximum energy of the ion beam can be boosted, but also its energy spectrum can be tuned to be quasi-monoenergetic. Two-dimensional particle-in-cell simulations show that the maximum energy of the primary proton beam, produced by the picosecond laser at intensity 8.8 × 1019 W cm−2, can be boosted from 123 to 181 MeV with only two post-accelerations by using 100 fs lasers at the same intensities.

A Diffusive Shock Acceleration Model for Protons in Weak Quasi-parallel Intracluster Shocks

Abstract Low sonic Mach number shocks form in the intracluster medium (ICM) during the formation of the large-scale structure of the universe. Nonthermal cosmic-ray (CR) protons are expected to be accelerated via diffusive shock acceleration (DSA) in those ICM shocks, although observational evidence for the γ-ray emission of hadronic origin from galaxy clusters has yet to be established. Considering the results obtained from recent plasma simulations, we improve the analytic test-particle DSA model for weak quasi-parallel ( ) shocks, previously suggested by Kang &amp; Ryu. In the model CR spectrum, the transition from the postshock thermal to CR populations occurs at the injection momentum, p inj, above which protons can undergo the full DSA process. As the shock energy is transferred to CR protons, the postshock gas temperature should decrease accordingly and the subshock strength weakens due to the dynamical feed of the CR pressure to the shock structure. This results in the reduction of the injection fraction, although the postshock CR pressure approaches an asymptotic value when the CR spectrum extends to the relativistic regime. Our new DSA model self-consistently accounts for such behaviors and adopts better estimations for p inj. With our model DSA spectrum, the CR acceleration efficiency ranges from η ∼ 10−3–0.01 for supercritical, -shocks with sonic Mach number 2.25 ≲ M s ≲ 5 in the ICM. Based on Ha et al., on the other hand, we argue that proton acceleration would be negligible in subcritical shocks with M s &lt; 2.25.