We present a time-dependent approach to the one-zone hadronic model in the case where the photon spectrum is produced by ultrarelativistic protons interacting with soft photons that are produced from protons and low magnetic fields. Assuming that pro
tons are injected at a certain rate in a homogeneous spherical volume containing a magnetic field, the evolution of the system can be described by five coupled kinetic equations, for protons, electrons, photons, neutrons, and neutrinos. Photopair and photopion interactions are modelled using the results of Monte-Carlo simulations and, in particular from the SOPHIA code for the latter. The coupling of energy losses and injection introduces a self-consistency in our approach and allows the study of the comparative relevancy of processes at various conditions, the efficiency of the conversion of proton luminosity to radiation, the resulting neutrino spectra, and the effects of time variability on proton injection, among other topics. We present some characteristic examples of the temporal behaviour of the system and show that this can be very different from the one exhibited by leptonic models. Furthermore, we argue that, contrary to the wide-held belief, there are parameter regimes where the hadronic models can become quite efficient. However, to keep the free parameters at a minimum and facilitate an in-depth study of the system, we have only concentrated on the case where protons are injected; i.e., we did not consider the effects of a co-accelerated leptonic component.
Diffuse VHE gamma radiation from the Galactic Centre ridge observed by the H.E.S.S. telescope has been convincingly linked with the propagation of recently accelerated cosmic rays that interact with molecular hydrogen clouds during their diffusion. T
hrough a series of time-dependent simulations of that diffusion for different propagation parameters we have obtained the most probable values of the diffusion coefficient for the Galactic Centre region. Assuming that the diffusion coefficient is of the form kappa(E) = kappa_0*(E/E_0)^delta, then for different optimal combinations of kappa_0 and delta its value is obtained for cosmic rays originating from a central point (possibly Sgr A East) 10 kyr ago.
The non-linear back reaction of accelerated cosmic rays at the shock fronts, leads to the formation of a smooth precursor with a length scale corresponding to the diffusive scale of the energetic particles. Past works claimed that shocklets could be
created in the precursor region of a specific shock width, which might energize few thermal particles to sufficient acceleration and furthermore this precursor region may act as confining large angle scatterer for very high energy cosmic rays. On the other hand, it has been shown that the smoothing of the shock front could lower the acceleration efficiency. These controversies motivated us to investigate numerically by Monte Carlo simulations the particle acceleration efficiency in oblique modified shocks. The results show flatter spectra compared to the spectra of the pressumed sharp discontinuity shock fronts. The findings are in accordance with theoretical predictions, since the scattering inside the precursor confines high energy particles to further scattering, resulting in higher energies making the whole acceleration process more efficient.
