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.

Massive stars blow powerful stellar winds throughout their evolutionary stages from the main sequence to Wolf-Rayet phases. The amount of mechanical energy deposited in the interstellar medium by the wind from a massive star can be comparable to the explosion energy of a core-collapse supernova that detonates at the end of its life. In this study, we estimate the kinetic energy deposition by massive stars in our Galaxy by considering the integrated Galactic initial mass function and modeling the stellar wind luminosity. The mass loss rate and terminal velocity of stellar winds during the main sequence, red supergiant, and Wolf-Rayet stages are estimated by adopting theoretical calculations and observational data published in the literature. We find that the total stellar wind luminosity due to all massive stars in the Galaxy is about Lw ≈ 1.1 × 1041 erg s−1, which is about 1/4 of the power of supernova explosions, LSN ≈ 4.8 × 1041 erg s−1. If we assume that ∼ 1 − 10 % of the wind luminosity could be converted to Galactic cosmic rays (GCRs) through collisonless shocks such as termination shocks in stellar bubbles and superbubbles, colliding-wind shocks in binaries, and bow-shocks of massive runaway stars, stellar winds might be expected to make a significant contribution to GCR production, though lower than that of supernova remnants.

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.