We study the survival of ultrahigh energy nuclei injected in clusters of galaxies, as well as their secondary neutrino and photon emissions, using a complete numerical propagation method and a realistic modeling of the magnetic, baryonic and photonic backgrounds. It is found that the survival of heavy nuclei highly depends on the injection position and on the profile of the magnetic field. Taking into account the limited lifetime of the central source could also lead in some cases to the detection of a cosmic ray afterglow, temporally decorrelated from neutrino and gamma ray emissions.We calculate that the diffusive neutrino flux around 1 PeV coming from clusters of galaxies may have a chance to be detected by current instruments. The observation of single sources in neutrinos and in gamma rays produced by ultrahigh energy cosmic rays will be more difficult. Signals coming from lower energy cosmic rays (E 1 PeV), if they exist, might however be detected by Fermi, for reasonable sets of parameters.

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We revisit the high-energy spectral cutoff originating from the electron−positron pair creation in the prompt phase of gamma-ray bursts (GRBs) with numerical and analytical calculations. We show that the conventional exponential and/or broken power law cutoff should be drastically modified to a shallower broken power-law in practical observations that integrate emissions from different internal shocks. Since the steepening is tiny for observations, this "smearing" effect can generally reduce the previous estimates of the Lorentz factor of the GRB outflows. We apply our formulation to GRB 080916C, recently detected by the Large Area Telescope detector on the Fermi satellite, and find that the minimum Lorentz factor can be ∼ 600 (or even smaller values), which is below but consistent with the previous result of ∼ 900. Observing the steepening energy (so-called "pair-break energy") is crucial to diagnose the Lorentz factor and/or the emission site in the future observations, especially current and future Cherenkov telescopes such as MAGIC, VERITAS, and CTA.

Shock‐acceleration theory predicts a power‐law energy spectrum in the test particle approximation, and there are two ways to calculate the power‐law index, namely Peacock's approximation and Vietri's formulation. In Peacock's approximation, it is assumed that particles cross a shock front many times and that the energy gain factors for each step are fully uncorrelated. By contrast, correlation of the distribution of the energy‐gain factors is considered in Vietri's formulation. We examine how Peacock's approximation differs from Vietri's formulation. It is useful to know when we can use Peacock's approximation, because in this approximation it is simple to derive the power‐law index. In addition, we focus on how the variance of the energy‐gain factor has an influence on the difference between Vietri's formulation and Peacock's approximation. The effect of the variance has not been examined in detail until now. As examples, we consider two cases for the scattering in the upstream region: large‐angle scattering (model A), and regular deflection by large‐scale magnetic fields (model B). In particular, there is no correlation among the distribution of an energy‐gain factor for every step in model A. In this model, it can be seen that the power‐law index derived from Peacock's approximation differs from that derived from Vietri's formulation when we consider a mildly relativistic shock, and the variance of the energy‐gain factor affects this difference. We can use Peacock's approximation for a non‐relativistic shock and a highly relativistic shock because the effect of the variance is hidden in these cases. In model B, we see the difference of the power‐law index, which converges along the shock velocity.

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., gamma-ray bursts (GRBs), active galactic nuclei (AGNs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations of relativistic electron-ion (electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In the presence of relativistic jets, instabilities such as the Buneman instability, other two-streaming instability, and the Weibel (filamentation) instability create colli-sionless shocks, which are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The "jitter" radiation from deflected electrons in small-scale magnetic fields has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation, a case of diffusive synchrotron radiation, may be important to understand the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.