Prescriptions for electron injection into the diffusive shock acceleration process are required in many practical considerations of cosmic-ray astrophysics, particularly in modeling of the synchrotron emission of astrophysical sources. In particle-in-cell simulations of quasi-parallel magnetized collisionless shocks, we analyse the evolution of particle spectra. We find that in the later stages of shock evolution, the initially strong suprathermal part in the ion spectra fades, thus leaving the spectra composed of a Maxwellian and a power law. Once the electron and ion spectra flatten and become parallel, we find that the amounts of cosmic ray ions and electrons become similar. We make the step towards relating the micro and macro-scale physics by applying this injection rule to Blasi's semi-analytical model of non-linear diffusive shock acceleration, in order to obtain the particle spectra and electron-to-proton ratio $K_{\mathrm{ep}}$ at high energies. By using shock jump conditions that include the electron heating, we find $K_{\mathrm{ep}}$ as a function of Mach number. For Mach number $\sim$ 100, our model finely reproduces the typically observed ratio for Galactic cosmic-rays $K_{\mathrm{ep}} \sim$ 1:100 in the test particle regime.
Recently, the {\it{Fermi}} space telescope has discovered two large $γ$-ray emission regions, the so-called "Fermi bubbles", that extend up to $\sim 50^\circ$ above and below the Galactic center. The $γ$-ray emission from the bubbles are found to follow a hard spectrum with no significant spatial variation in intensity and spectral shape. The origin of the emission is still not clearly understood. Suggested explanations include injection of cosmic-ray nuclei from the Galactic center by high-speed Galactic winds, electron acceleration by multiple shocks and stochastic electron acceleration insi…
We consider a phenomenological model for the thermal leakage injection in the diffusive shock acceleration (DSA) process, in which suprathermal protons and electrons near the shock transition zone are assumed to have the so-called $κ$-distributions produced by interactions of background thermal particles with pre-existing and/or self-excited plasma/MHD waves or turbulence. The $κ$-distribution has a power-law tail, instead of an exponential cutoff, well above the thermal peak momentum. So there are a larger number of potential seed particles with momentum, above that required for participation…
We present a three-dimensional hybrid simulation of a collisionless perpendicular shock in a partially ionized plasma for the first time. In this simulation, the shock velocity and the upstream ionization fraction are Vsh ~ 1333 km/s and fi ~ 0.5, that are typical values for isolated young supernova remnants in the interstellar medium. We confirm previous two-dimensional simulation results that downstream hydrogen atoms leak into the upstream region, they are accelerated by the pickup process in the upstream region, and large magnetic field fluctuations are generated both in the upstream and d…
We examine the test-particle solution for diffusive shock acceleration, based on simple models for thermal leakage injection and Alfv'enic drift. The critical injection rate, ξ_c, above which the cosmic ray (CR) pressure becomes dynamically significant, depends mainly on the sonic shock Mach number, M, and preshock gas temperature, T_1. In the hot-phase interstellar medium (ISM) and intracluster medium, ξ_c < 10^{-3} for shocks with M < 5, while ξ_c ~ 10^{-4}(T_1/10^6 K)^{1/2} for shocks with M > 10. For T_1=10^6 K, for example, the test-particle solution would be valid if the injection moment…
We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the traject…
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 equat…
Nonlinear diffusive shock acceleration with upstream escape reproduces DAMPE observations
State Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所粒子天体物理国家重点实验室）；Key Laboratory of cosmic ray, Ministry of education, Tibet University（西藏大学教育部宇宙射线重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Electron acceleration in collisionless shocks with arbitrary magnetic field orientations is discussed. It is shown that the injection of thermal electrons into 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 shock drift acceleration mechanism. The electron beam is able to excite whistler waves which can scatter the energetic electrons themselves when the Alfven Mach number of the shock is sufficiently high. A critical Mach number for the electron injection is obtained as a function of…
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 ($Q_\parallel$) shocks, previously suggested by \citet{kang2010}. In the model …
We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfvenic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is greater than 2x10^{-4}, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be ampl…
We have performed 2D hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles ("seeds"); such a study applies, for instance, to the re-acceleration of Galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call \emph{diffusive shock re-acceleration}. We find that reaccelerated seeds can drive the streaming instability in the shock upstream and produce effecti…
Estimating the cosmic-ray acceleration efficiency $ ε$ in supernova remnants (SNRs) through observations is a challenging task in general. Based on the Rankine-Hugoniot shock conditions, we find an anticorrelation between $ ε$ and the power-law spectral index $ α$ of relativistic particle distribution produced via diffusive particle acceleration by nonrelativistic shocks, implying more efficient acceleration in older SNRs with harder radio spectra. Then $ ε$ may be estimated from some hard radio spectral index measurements. Assuming the particle distribution in downstream of strong shocks to b…
Three approaches are considered to solve the equation which describes the time-dependent diffusive shock acceleration of test particles at the non-relativistic shocks. At first, the solution of Drury (1983) for the particle distribution function at the shock is generalized to any relation between the acceleration time-scales upstream and downstream and for the time-dependent injection efficiency. Three alternative solutions for the spatial dependence of the distribution function are derived. Then, the two other approaches to solve the time-dependent equation are presented, one of which does no…
The H.E.S.S. collaboration revealed the presence of a very high energy (VHE) diffuse emission in the inner 100pc of the Galaxy in close correlation with the Central Molecular Zone (CMZ). Recently, they deduced from this emission a cosmic-ray (CR) over-density in the region with a local peak toward the Galactic Center (GC) and proposed a diffusive scenario with a stationary source at the GC to explain it. However, the high supernovae (SN) rate in the GC must also create a sustained CR injection in the region via the shocks produced at the time of their explosion. Considering typical diffusion c…
Collisionless shocks with low sonic Mach numbers, $M_{\rm s} \lesssim 4$, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the ICM has yet to be established. Performing particle-in-cell simulations, we study the injection of protons into DSA and the early development of a nonthermal particle population in weak shocks in high $β$ ($\approx 100$) plasmas. Reflection of incident protons, self-excitation of plasma waves via CR-driven instabilities, and multiple cycles of sho…
The non-thermal acceleration of electrons and ions at an oblique, non-relativistic shock is studied using large scale particle-in-cell (PIC) simulations in one spatial dimension. Physical parameters are selected to highlight the role of electron pre-heating in injection and subsequent acceleration of particles at high Mach number shocks. Simulation results show evidence for the early onset of the diffusive shock acceleration process for both electrons and ions at a highly oblique subluminal shock. Ion acceleration efficiencies of $\lesssim 5\%$ are measured at late times, though this is not th…
The intracluster medium (ICM) is expected to experience on average about three passages of weak shocks with low sonic Mach numbers, $M\lesssim 3$, during the formation of galaxy clusters. Both protons and electrons could be accelerated to become high energy cosmic rays (CRs) at such ICM shocks via diffusive shock acceleration (DSA). We examine the effects of DSA by multiple shocks on the spectrum of accelerated CRs by including {\it in situ} injection/acceleration at each shock, followed by repeated re-acceleration at successive shocks in the test-particle regime. For simplicity, the accelerat…
Many bright radio relics in the outskirts of galaxy clusters have low inferred Mach numbers, defying expectations from shock acceleration theory and heliospheric observations that the injection efficiency of relativistic particles plummets at low Mach numbers. With a suite of cosmological simulations, we follow the diffusive shock acceleration as well as radiative and Coulomb cooling of cosmic ray electrons during the assembly of a cluster. We find a substantial population of fossil electrons. When reaccelerated at a shock (through diffusive shock acceleration), they are competitive with direc…
We reexamine nonlinear diffusive shock acceleration (DSA) at cosmological shocks in the large scale structure of the Universe, incorporating wave-particle interactions that are expected to operate in collisionless shocks. Adopting simple phenomenological models for magnetic field amplification (MFA) by cosmic-ray (CR) streaming instabilities and Alfv'enic drift, we perform kinetic DSA simulations for a wide range of sonic and Alfv'enic Mach numbers and evaluate the CR injection fraction and acceleration efficiency. In our DSA model the CR acceleration efficiency is determined mainly by the son…
Observations of the interplanetary shock provide us with strong evidence of particle acceleration to multi-MeV energies, even up to GeV energy, in a solar flare or coronal mass ejection (CME). Diffusive shock acceleration is an efficient mechanism for particle acceleration. For investigating the shock structure, the energy injection and energy spectrum of a CME-driven shock, we perform dynamical Monte Carlo simulation of the 14-Dec-2006 CME-driven shock using an anisotropic scattering law. The simulated results of the shock fine structure, particle injection, and energy spectrum are presented.…
Recent radio observations have identified a class of structures, so-called radio relics, in clusters of galaxies. The radio emission from these sources is interpreted as synchrotron radiation from GeV electrons gyrating in microG-level magnetic fields. Radio relics, located mostly in the outskirts of clusters, seem to associate with shock waves, especially those developed during mergers. In fact, they seem to be good structures to identify and probe such shocks in intracluster media (ICMs), provided we understand the electron acceleration and re-acceleration at those shocks. In this paper, we …
The analytical theory of diffusive cosmic ray acceleration at parallel stationary shock waves with magnetostatic turbulence is generalized to arbitrary shock speeds $V_s=β_1c$, including in particular relativistic speeds. This is achieved by applying the diffusion approximation to the relevant Fokker-Planck particle transport equation formulated in the mixed comoving coordinate system. In this coordinate system the particle's momentum coordinates $p$ and $μ=p_{\parallel }/p$ are taken in the rest frame of the streaming plasma, whereas the time and space coordinates are taken in the observer's …
Galactic cosmic-ray source compositions, (Z/H)GCRS from H to Pb and ~10^8 - 10^14 eV, differ from solar-local interstellar, (Z/H)SS or (Z/H)ISM by ~20-200x. Both are mostly just mixes of core collapse (CCSN) and thermonuclear (SN Ia) supernova ejecta. The (Z/H)ISM come from steady unbiased accumulation over Gyrs. But the cosmic ray mass mixing ratio, universal ISM/CCSN ~4:1 of swept-up ISM and ~10x metallicity ejecta show that (Z/H)GCRS come from basic Sedov-Taylor bulk mixing of homologous, expanding CCSN in their OB cluster self-generated superbubbles, further enriched by highly biased grain…
High precision spectrometry of galactic cosmic rays (CR) has revealed the lack of our understanding of how different CR elements are extracted from the supernova environments to be further accelerated in their shocks. Comparing the spectra of accelerated particles with different mass to charge ratios is a powerful tool for studying the physics of particle injection into the diffusive shock acceleration (DSA). Recent AMS-02 demonstration of the similarity of He/$p$, C/$p$, and O/$p$ rigidity spectra has provided new evidence that injection is a mass-to-charge dependent process. We performed hyb…
Electron acceleration to non-thermal, ultra-relativistic energies (~ 10-100 TeV) is revealed by radio and X-ray observations of shocks in young supernova remnants (SNRs). The diffusive shock acceleration (DSA) mechanism is usually invoked to explain this acceleration, but the way in which electrons are initially energized or 'injected' into this acceleration process starting from thermal energies is an unresolved problem. In this paper we study the initial acceleration of electrons in non-relativistic shocks from first principles, using two- and three-dimensional particle-in-cell (PIC) plasma …
The origin of the bulk of cosmic rays (CRs) observed at Earth is the topic of a century long investigation, paved with successes and failures. From the energetic point of view, supernova remnants (SNRs) remain the most plausible sources of CRs up to rigidity ? 10^6-10^7 GV. This confidence somehow resulted in the construction of a paradigm, the so-called SNR paradigm: CRs are accelerated through diffusive shock acceleration in SNRs and propagate diffusively in the Galaxy in an energy dependent way. Qualitative confirmation of the SNR acceleration scenario has recently been provided by gamma ra…
We performed kinetic simulations of diffusive shock acceleration in Type Ia supernova remnants (SNRs) expanding into a uniform interstellar medium (ISM). The preshock gas temperature is the primary parameter that governs the cosmic ray (CR) acceleration, while magnetic field strength and CR injection rate are secondary parameters. SNRs in the hot ISM, with an injection fraction smaller than 10^{-4}, are inefficient accelerators with less than 10 % energy getting converted to CRs. The shock structure is almost test-particle like and the ensuing CR spectrum can be steeper than E^{-2}. Although t…
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 rays 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…
We perform kinetic simulations of diffusive shock acceleration (DSA) in Type Ia supernova remnants (SNRs) expanding into a uniform interstellar medium (ISM). Bohm-like diffusion assumed, and simple models for Alfvenic drift and dissipation are adopted. Phenomenological models for thermal leakage injection are considered as well. We find that the preshock gas temperature is the primary parameter that governs the cosmic ray (CR) acceleration efficiency and energy spectrum, while the CR injection rate is a secondary parameter. For SNRs in the warm ISM, if the injection fraction is larger than 10^…
In this paper, we develop a model for the radio and X-ray emissions from Type IIb Supernova (SN IIb) 2011dh in the first 100 days after the explosion, and investigate a spectrum of relativistic electrons accelerated at a strong shock wave. The widely-accepted theory of the particle acceleration, so-called diffusive shock acceleration (DSA) or Fermi mechanism, requires seed electrons with modest energy with gamma ~ 1 - 100, and little is known about this pre-acceleration mechanism: We derive the energy distribution of relativistic electrons in this pre-accelerated energy regime. We find that th…
We study the thermalization, injection, and acceleration of ions with different mass/charge ratios, $A/Z$, in non-relativistic collisionless shocks via hybrid (kinetic ions-fluid electrons) simulations. In general, ions thermalize to a post-shock temperature proportional to $A$. When diffusive shock acceleration is efficient, ions develop a non-thermal tail whose extent scales with $Z$ and whose normalization is enhanced as $(A/Z)^2$, so that incompletely-ionized heavy ions are preferentially accelerated. We discuss how these findings can explain observed heavy-ion enhancements in Galactic cos…
In this paper we investigate the effect of stochasticity in the spatial and temporal distribution of supernova remnants on the spectrum and chemical composition of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) experienced by cosmic rays during propagation in the Galaxy. In particular, at high energies we assume that D(E)\sim E^δ, with $δ=1/3$ and $δ=0.6$ being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars, with and without accoun…
Observations of large-scale radio emissions prove the existence of shock accelerated cosmic-ray electrons in galaxy clusters, while the lack of detected $γ$-rays limits the acceleration of cosmic-ray protons in galaxy clusters. This challenges our understanding of how diffusive shock acceleration works. In this work, we couple the most updated recipes for shock acceleration in the intracluster medium to state-of-the-art magneto-hydrodynamical simulations of massive galaxy clusters. Furthermore, we use passive tracer particles to follow the evolution of accelerated cosmic-rays. We show that whe…
Cosmology models predict that external accretion shocks form in the outer region of galaxy clusters due to supersonic gas infall from filaments and voids in the cosmic web. They are characterized by high sonic and Alfvénic Mach numbers, $M_s\sim10-10^2$ and $M_A\sim10^2-10^3$, and propagate into weakly magnetized plasmas of $β\equiv P_g/P_B\gtrsim10^2$. Although strong accretion shocks are expected to be efficient accelerators of cosmic rays (CRs), nonthermal signatures of shock-accelerated CRs around clusters have not been confirmed, and detailed acceleration physics at such shocks has yet to…
Thermal electrons cannot directly participate in the process of diffusive acceleration at electron-ion shocks because their Larmor radii are smaller than the shock transition width: this is the well-known electron injection problem of diffusive shock acceleration. Instead, an efficient pre-acceleration process must exist that scatters electrons off of electromagnetic fluctuations on scales much shorter than the ion gyro radius. The recently found intermediate-scale instability provides a natural way to produce such fluctuations in parallel shocks. The instability drives comoving (with the upst…
Supernova remnants (SNRs) are believed to produce the majority of galactic cosmic rays (CRs). SNRs harbor non-relativistic collisionless shocks responsible for acceleration of CRs via diffusive shock acceleration (DSA), in which particles gain their energies via repeated interactions with the shock front. As the DSA theory involves pre-existing mildly energetic particles, a means of pre-acceleration is required, especially for electrons. Electron injection remains one of the most troublesome and still unresolved issues and our physical understanding of it is essential to fully comprehend the p…
Radio relics in the outskirts of galaxy clusters imply the diffusive shock acceleration (DSA) of electrons at merger-driven shocks with Mach number $M_{s}\lesssim3-4$ in the intracluster medium (ICM). Recent studies have suggested that electron preacceleration and injection, prerequisite steps for DSA, could occur at supercritical shocks with $M_{s}\gtrsim2.3$ in the ICM, thanks to the generation of multiscale waves by microinstabilities such as the Alfvén ion cyclotron (AIC) instability, the electron firehose instability (EFI), and the whistler instability (WI). On the other hand, some relics…
The much-anticipated proof of cosmic ray (CR) acceleration in supernova remnants (SNR) must hinge on full consistency of acceleration theory with the observations; direct proof is impossible because of the orbit scrambling of CR particles. The PAMELA orbital telescope revealed deviation between helium and proton CR spectra deemed inconsistent with the theory, since the latter does not differentiate between elements of ultrarelativistic rigidity. By considering an initial (injection-) phase of the diffusive shock acceleration (DSA), where elemental similarity does not apply, we demonstrate that…
Cosmic Ray Diffusion and the Origin of Very High Energy Gamma-Ray Emission in Young Massive Stellar Clusters
Instituto de Astronomia, Geofísica e Ciências Atmosféricas da USP（圣保罗大学天文、地球物理与大气科学研究所）；Sorbonne Université, Institut d’Astrophysique de Paris, CNRS（索邦大学巴黎天体物理学研究所（CNRS））
We study diffusive shock acceleration (DSA) of electrons in non-relativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell (PIC) simulations. By exploring the parameter space of sonic and Alfvénic Mach numbers we find that high Mach number quasi-perpendicular shocks can efficiently accelerate electrons to power-law downstream spectra with slopes consistent with DSA prediction. Electrons are reflected by magnetic mirroring at the shock and drive non-resonant waves in the upstream. Reflected electrons are trapped between the shock front and upstream waves and …
We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and "smooth" the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoni…
The interaction between the strong winds of the stars in colliding-wind binary (CWB) systems produces two shock fronts, delimiting the wind collision region (WCR). There, particles are expected to be accelerated mainly via diffusive shock acceleration, and to produce $γ$-rays, in processes involving relativistic electrons and/or protons. We investigate the injection and the acceleration of protons in typical CWB systems by means of Monte Carlo simulations, with a test-particle approach. We use magnetohydrodynamic simulations to determine the background conditions in the wind collision region. …
We use kinetic simulations of diffusive shock acceleration (DSA) to study the time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified shocks. Thermal leakage injection of low energy CRs and finite Alfvén wave propagation and dissipation are included. Bohm diffusion as well as the diffusion with the power-law momentum dependence are modeled. As long as the acceleration time scale to relativistic energies is much shorter than the dynamical evolution time scale of the shocks, the precursor and subshock transition approach the time-asymptotic state, which depends on the shock s…
Cosmic Ray (CR) acceleration still challenges the researchers. Fast particles may be accelerated in astrophysical environments by a variety of processes. Acceleration in magnetic reconnection sites in particular, has lately attracted the attention of researchers not only for its potential importance in the solar system context, but also in other astrophysical environments, like compact stellar sources, AGNs and GRBs, and even in diffusive media like the ISM and the IGM, especially when the environment is magnetically dominated. In this talk we review this process and also present three-dimensi…
Anisotropic diffusion modeling of cosmic-ray lepton propagation
Faculty of Physics, M.V. Lomonosov Moscow State University (MSU)（莫斯科国立大学物理系）；Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University (MSU)（莫斯科国立大学索别尔廷核物理研究所）
We present three-dimensional hybrid simulations of collisionless shocks that propagate parallel to the background magnetic field to study the acceleration of protons that forms a high-energy tail on the distribution. We focus on the initial acceleration of thermal protons and compare it with results from one-dimensional simulations. We find that for both one- and three-dimensional simulations, particles that end up in the high-energy tail of the distribution later in the simulation gained their initial energy right at the shock. This confirms previous results but is the first to demonstrate th…
Multiwavelength Probes of Cosmic Ray Transport in Molecular Cloud Structures
University College London（伦敦大学学院）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先导研究本部）；The University of Tokyo（东京大学）；Institute for Cosmic Ray Research, The University of Tokyo（东京大学宇宙线研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学中心）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Institute of Astronomy, National Tsing Hua University（国立清华大学天文研究所）；The University of Osaka（大阪大学）
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 1…
When two galaxy clusters encounter each other, the interaction results in a collisionless shock that is characterized by a low (1-4) sonic Mach number, and a high Alfv{é}nic Mach number. Our goal is to determine if, and to what extent, such shocks can accelerate particles to sufficient velocities that they can contribute to the cosmic ray spectrum. We combine two different computational methods, magnetohydrodynamics (MHD) and particle-in-cell (PIC) into a single code that allows us to take advantage of the high computational efficiency of MHD while maintaining the ability to model the behaviou…
Radio relics associated with merging galaxy clusters indicate the acceleration of relativistic electrons in merger-driven shocks with low sonic Mach numbers ($M_{\rm s}\lesssim 3$) in the intracluster medium (ICM). Recent studies have suggested that electron injection to diffusive shock acceleration (DSA) could take place through the so-called Fermi-like acceleration in the shock foot of $β=P_{\rm gas}/P_{\rm B}\approx 20-100$ shocks and the stochastic shock drift acceleration (SSDA) in the shock transition of $β\approx 1-5$ shocks. Here we explore how the SSDA can facilitate electron preaccel…
Using large-scale fully-kinetic two-dimensional particle-in-cell simulations, we investigate the effects of shock rippling on electron acceleration at low-Mach-number shocks propagating in high-$β$ plasmas, in application to merger shocks in galaxy clusters. We find that the electron acceleration rate increases considerably when the rippling modes appear. The main acceleration mechanism is stochastic shock-drift acceleration, in which electrons are confined at the shock by pitch-angle scattering off turbulence and gain energy from the motional electric field. The presence of multi-scale magnet…
