The intracluster medium (ICM) is expected to experience on average about three passages of weak shocks with low sonic Mach numbers, M . 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 diusive shock acceleration (DSA). We examine the eects of DSA by multiple shocks on the spectrum of accelerated CRs by including in situ injection/acceleration at each shock, followed by repeated re- acceleration at successive shocks in the test-particle regime. For simplicity, the accelerated particles are assumed to undergo adiabatic decompression without energy loss and escape from the system, before they encounter subsequent shocks. We show that in general the CR spectrum is attened by multiple shock passages, compared to a single episode of DSA, and that the acceleration eciency increases with successive shock passages. However, the decompression due to the expansion of shocks into the cluster outskirts may reduce the amplication and attening of the CR spectrum by multiple shock passages. The nal CR spectrum behind the last shock is determined by the accumulated eects of repeated re-acceleration by all previous shocks, but it is relatively insensitive to the ordering of the shock Mach numbers. Thus multiple passages of shocks may cause the slope of the CR spectrum to deviate from the canonical DSA power-law slope of the current shock.

We propose semi-analytic models for the electron momentum distribution in weak shocks that accounts for both in situ acceleration and re-acceleration through diffusive shock acceleration (DSA). In the former case, a small fraction of incoming electrons is assumed to be reflected at the shock ramp and pre-accelerated to the so-called injection momentum, pinj, above which particles can diffuse across the shock transition and participate in the DSA process. This leads to the DSA power-law distribution extending from the smallest momentum of reflected electrons, pref, all the way to the cutoff momentum, peq, constrained by radiative cooling. In the latter case, fossil electrons, specified by a power-law spectrum with a cutoff, are assumed to be re-accelerated from pref up to peq via DSA. We show that, in the in situ acceleration model, the amplitude of radio synchrotron emission depends strongly on the shock Mach number, whereas it varies rather weakly in the re-acceleration model. Considering the rather turbulent nature of shocks in the intracluster medium, such extreme dependence for the in situ acceleration might not be compatible with the relatively smooth surface brightness of observed radio relics.

Galaxy clusters are known to host many active galaxies (AGNs) with radio jets, which could expand to form radio bubbles with relativistic electrons in the intracluster medium (ICM). It has been suggested that fossil relativistic electrons contained in remnant bubbles from extinct radio galaxies can be re-accelerated to radio-emitting energies by merger-driven shocks via diffusive shock acceleration (DSA), leading to the birth of radio relics detected in clusters. In this study we assume that such bubble consist primarily of thermal gas entrained from the surrounding medium and dynamically-insignificant amounts of relativistic electrons. We also consider several realistic models for magnetic fields in the cluster outskirts, including the ICM field that scales with the gas density as BICM ∝ n0.5 ICM. Then we perform time-dependent DSA simulations of a spherical shock that runs into a lower-density but higher-temperature bubble with the ratio nb/nICM ≈ TICM/Tb ≈ 0.5. We find that inside the bubble the shock speed increases by about 20 %, but the Mach number decreases by about 15% in the case under consideration. In this re-acceleration model, the observed properties of a radio relic such as radio flux, spectral index, and integrated spectrum would be governed mainly by the presence of seed relativistic electrons and the magnetic field profile as well as shock dynamics. Thus it is crucial to understand how fossil electrons are deposited by AGNs in the ICM and how the downstream magnetic field evolves behind the shock in detailed modeling of radio relics.

We explore the shock acceleration model for giant radio relics, in which relativistic electrons are accelerated via diffusive shock acceleration (DSA) by merger-driven shocks in the outskirts of galaxy clusters. In addition to DSA, turbulent acceleration by compressive MHD modes downstream of the shock are included as well as energy losses of postshock electrons due to Coulomb scattering, synchrotron emission, and inverse Compton scattering off the cosmic background radiation. Considering that only a small fraction of merging clusters host radio relics, we favor a reacceleration scenario in which radio relics are generated preferentially by shocks encountering the regions containing low-energy ( e . 300) cosmic ray electrons (CRe). We perform time-dependent DSA simulations of spherically expanding shocks with physical parameters relevant for the Sausage radio relic, and calculate the radio synchrotron emission from the accelerated CRe. We find that significant level of postshock turbulent acceleration is required in order to reproduce broad profiles of the observed radio flux densities of the Sausage relic. Moreover, the spectral curvature in the observed integrated radio spectrum can be explained, if the putative shock should have swept up and exited out of the preshock region of fossil CRe about 10~Myr ago.

The Sausage radio relic is the arc-like radio structure in the cluster CIZA J2242.8+5301, whose observed properties can be best understood by synchrotron emission from relativistic electrons accelerated at a merger-driven shock. However, there remain a few puzzles that cannot be explained by the shock acceleration model with only in-situ injection. In particular, the Mach number inferred from the observed radio spectral index, Mradio  4.6, while the Mach number estimated from X-ray observations, MX−ray  2.7. In an attempt to resolve such a discrepancy, here we consider the re-acceleration model in which a shock of Ms  3 sweeps through the intracluster gas with a pre-existing population of relativistic electrons. We find that observed brightness profiles at multi frequencies provide strong constraints on the spectral shape of pre-existing electrons. The models with a power-law momentum spectrum with the slope, s  4.1, and the cutoff Lorentz factor, e,c  3−5×104, can reproduce reasonably well the observed spatial profiles of radio fluxes and integrated radio spectrum of the Sausage relic. The possible origins of such relativistic electrons in the intracluster medium remain to be investigated further.

The Toothbrush radio relic associated with the merging cluster 1RXS J060303.3 is presumed to be produced by relativistic electrons accelerated at merger-driven shocks. Since the shock Mach number inferred from the observed radio spectral index, Mradio  2:8, is larger than that estimated from X-ray observations, MX . 1:5, we consider the re-acceleration model in which a weak shock of Ms  1:2 - 1:5 sweeps through the intracluster plasma with a preshock population of relativistic electrons. We nd the models with a power-law momentum spectrum with the slope, s  4:6, and the cutoff Lorentz factor, e;c  7-8104 can reproduce reasonably well the observed proles of radio uxes and integrated radio spectrum of the head portion of the Toothbrush relic. This study conrms the strong connection between the ubiquitous presence of fossil relativistic plasma originated from AGNs and the shock-acceleration model of radio relics in the intracluster medium.

Most high energy cosmic rays (CRs) are thought to be produced by diffusive shock acceleration (DSA) in supernova remnants (SNRs) within the Galaxy. Plasma and MHD simulations have shown that the self-excitation of MHD waves and amplication of magnetic fields via plasma instabilities are an integral part of DSA for strong collisionless shocks. In this study we explore how plasma processes such as plasma instabilities and wave-particle interactions can affect the energy spectra of CR protons and electrons, using time-dependent DSA simulations of SNR shocks. We demonstrate that the time-dependent evolution of the shock dynamics, the self-amplified magnetic fields and Alfvenic drift govern the highest energy end of the CR energy spectra. As a result, the spectral cutoffs in nonthermal X-ray and γ-ray radiation spectra are regulated by the evolution of the highest energy particles, which are injected at the early phase of SNRs. We also nd that the maximum energy of CR protons can be boosted significantly only if the scale height of the magnetic field precursor is long enough to contain the diffusion lengths of the particles of interests. Thus, detailed understandings of nonlinear wave-particle interactions and time-dependent DSA simulations are crucial for understanding the nonthermal radiation from CR acceleration sources.

In Kang (2015) we calculated the acceleration of cosmic-ray electrons at weak spherical shocks that are expected to form in the cluster outskirts, and estimated the diffuse synchrotron radiation emitted by those electrons. 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 inject electrons decrease in time. In this study, we consider spherical blast waves propagating through a constant density core surrounded by an isothermal halo with  ∝ r−n in order to explore how the deceleration of the shock affects the radio emission from accelerated electrons. The surface brightness profile and the volumeintegrated 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 0.7 or 7 μG, at the shock age of ∼ 50 Myr, the volume-integrated radio spectrum steepens gradually with the spectral index from inj to inj + 0.5 over 0.1–10 GHz, where inj is the injection index at the shock position expected 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. (2015), if the relic shock is young enough so that the break frequency is around 1 GHz.

We study the evolution of the energy spectrum of cosmic-ray electrons accelerated at spherically expanding shocks with low Mach numbers and the ensuing spectral signatures imprinted in radio synchrotron emission. Time-dependent simulations of diffusive shock acceleration (DSA) of electrons in the test-particle limit have been performed for spherical shocks with parameters relevant for typical shocks in the intracluster medium. The electron and radiation spectra at the shock location can be described properly by the test-particle DSA predictions with instantaneous shock parameters. However, the volume integrated spectra of both electrons and radiation deviate significantly from the test-particle power-laws, because the shock compression ratio and the flux of injected electrons at the shock gradually decrease as the shock slows down in time. So one needs to be cautious about interpreting observed radio spectra of evolving shocks based on simple DSA models in the test-particle regime.

Nonthermal radiation from supernova remnants (SNRs) provides observational evidence and constraints on the diffusive shock acceleration (DSA) hypothesis for the origins of Galactic cosmic rays (CRs). Recently it has been recognized that a variety of plasma wave-particle interactions operate at astrophysical shocks and the detailed outcomes of DSA are governed by their complex and nonlinear interrelationships. Here we calculate the energy spectra of CR protons and electrons accelerated at Type Ia SNRs, using time-dependent, DSA simulations with phenomenological models for magnetic field amplification due to CR streaming instabilities, Alfv´enic drift, and free escape boundary. We show that, if scattering centers drift with the Alfv´en speed in the amplified magnetic fields, the CR energy spectrum is steepened and the acceleration efficiency is significantly reduced at strong CR modified SNR shocks. Even with fast Afv´enic drift, DSA can still be efficient enough to develop a substantial shock precursor due to CR pressure feedback and convert about 20-30% of the SN explosion energy into CRs. Since the high energy end of the CR proton spectrum is composed of the particles that are injected in the early stages, in order to predict nonthermal emissions, especially in X-ray and -ray bands, it is important to follow the time dependent evolution of the shock dynamics, CR injection process, magnetic field amplification, and particle escape. Thus it is crucial to understand the details of these plasma interactions associated with collisionless shocks in successful modeling of nonlinear DSA.

We calculate the energy spectra of cosmic ray (CR) protons and electrons at a plane shock with quasi-parallel magnetic fields, using time-dependent, diffusive shock acceleration (DSA) simulations, including energy losses via synchrotron emission and Inverse Compton (IC) scattering. A thermal leakage injection model and a Bohm type diffusion coefficient are adopted. The electron spectrum at the shock becomes steady after the DSA energy gains balance the synchrotron/IC losses, and it cuts off at the equilibrium momentum peq. In the postshock region the cutoff momentum of the electron spectrum decreases with the distance from the shock due to the energy losses and the thickness of the spatial distribution of electrons scales as p-1. Thus the slope of the downstream integrated spectrum steepens by one power of p for pb < p < peq, where the break momentum decreases with the shock age as pbr ∝ t-1. In a CR modified shock, both the proton and electron spectrum exhibit a concave curvature and deviate from the canonical test-particle power-law, and the upstream integrated electron spectrum could dominate over the downstream integrated spectrum near the cutoff momentum. Thus the spectral shape near the cutoff of X-ray synchrotron emission could reveal a signature of nonlinear DSA.

We calculate the evolution of multiple supernova (SN) explosions inside a pre-exiting bubble blown up by winds from massive stars, using one-dimensional hydrodynamic simulations including radiative cooling and thermal conduction effects. First, the development of the wind bubble driven by collective winds from multiple stars during the main sequence is calculated. Then multiple SN explosion is loaded at the center of the bubble and the evolution of the SN remnant is followed for 106 years. We find the size and mass of the SN-driven shell depend on the structure of the pre-existing wind bubble as well as the total SN explosion energy. Most of the explosion energy is lost via radiative cooling, while about 10% remains as kinetic energy and less than 10% as thermal energy of the expanding bubble shell. Thus the photoionization and heating by diffuse radiation emitted by the shock heated gas is the most dominant form of SN feedback into the surrounding interstellar medium.

The COREA (COsmic ray Research and Education Array in Korea) project aims to build a ground array of particle detectors distributed over Korean Peninsular, through collaborations of high school students, educators, and university researchers, in order to study the origin of ultra high energy cosmic rays. COREA array will consist of about 2000 detector stations covering several hundreds of km2 area at its final configuration and detect electrons and muons in extensive air-showers triggered by high energy particles. During the intial phase COREA array will start with a small number of detector stations in Seoul area schools. In this paper, we have studied by Monte Carlo simulations how to select detector sites for optimal detection efficiency for proton triggered air-showers. We considered several model clusters with up to 30 detector stations and calculated the effective number of air-shower events that can be detected per year for each cluster. The greatest detection efficiency is achieved when the mean distance between detector stations of a cluster is comparable to the effective radius of the air-shower of a given proton energy. We find the detection efficiency of a cluster with randomly selected detector sites is comparable to that of clusters with uniform detector spacing. We also considered a hybrid cluster with 60 detector stations that combines a small cluster with Δι≈100m and a large cluster with Deltaι≈1km . We suggest that it can be an ideal configuration for the initial phase study of the COREA project, since it can measure the cosmic rays with a wide range energy, i.e., 1016eV≤E≤1019eV , with a reasonable detection rate.

We introduce a method of identifying evidence of shocks in the X-ray emitting gas in clusters of galaxies. Using information from synthetic observations of simulated clusters, we do a blind search of the synthetic image plane. The locations of likely shocks found using this method closely match those of shocks identified in the simulation hydrodynamic data. Though this method assumes nothing about the geometry of the shocks, the general distribution of shocks as a function of Mach number in the cluster hydrodynamic data can be extracted via this method. Characterization of the cluster shock distribution is critical to understanding production of cosmic rays in clusters and the use of shocks as dynamical tracers.