Solving Vlasov Equations Using NRxx Method

In this paper, we propose a moment method to numerically solve the Vlasov equations using the framework of the NRxx method developed in [6, 8, 7] for the Boltzmann equation. Due to the same convection term of the Boltzmann equation and the Vlasov equation, it is very convenient to use the moment expansion in the NRxx method to approximate the distribution function in the Vlasov equations. The moment closure recently presented in [5] is applied to achieve the globally hyperbolicity so that the local well-posedness of the moment system is attained. This makes our simulations using high order moment expansion accessible in the case of the distribution far away from the equilibrium which appears very often in the solution of the Vlasov equations. With the moment expansion of the distribution function, the acceleration in the velocity space results in an ordinary differential system of the macroscopic velocity, thus is easy to be handled. The numerical method we developed can keep both the mass and the momentum conserved. We carry out the simulations of both the Vlasov-Poisson equations and the Vlasov-Poisson-BGK equations to study the linear Landau damping. The numerical convergence is exhibited in terms of the moment number and the spatial grid size, respectively. The variation of discretized energy as well as the dependence of the recurrence time on moment order is investigated. The linear Landau damping is well captured for different wave numbers and collision frequencies. We find that the Landau damping rate linearly and monotonically converges in the spatial grid size. The results are in perfect agreement with the theoretic data in the collisionless case

Diffuse PeV neutrinos from gamma-ray bursts

The IceCube collaboration recently reported the potential detection of two cascade neutrino events in the energy range 1-10 PeV. We study the possibility that these PeV neutrinos are produced by gamma-ray bursts (GRBs), paying special attention to the contribution by untriggered GRBs that elude detection due to their low photon flux. Based on the luminosity function, rate distribution with redshift and spectral properties of GRBs, we generate, using Monte-Carlo simulation, a GRB sample that reproduce the observed fluence distribution of Fermi/GBM GRBs and an accompanying sample of untriggered GRBs simultaneously. The neutrino flux of every individual GRBs is calculated in the standard internal shock scenario, so that the accumulative flux of the whole samples can be obtained. We find that the neutrino flux in PeV energies produced by untriggered GRBs is about 2 times higher than that produced by the triggered ones. Considering the existing IceCube limit on the neutrino flux of triggered GRBs, we find that the total flux of triggered and untriggered GRBs can reach at most a level of ~10^-9 GeV cm^-2 s^-1 sr^-1, which is insufficient to account for the reported two PeV neutrinos. Possible contributions to diffuse neutrinos by low-luminosity GRBs and the earliest population of GRBs are also discussed.Comment: Accepted by ApJ, one more figure added to show the contribution to the diffuse neutrino flux by untriggered GRBs with different luminosity, results and conclusions unchange

On the origin of >10 GeV photons in gamma-ray burst afterglows

Fermi/LAT has detected long-lasting high-energy photons (>100 MeV) from gamma-ray bursts (GRBs), with the highest energy photons reaching about 100 GeV. One proposed scenario is that they are produced by high-energy electrons accelerated in GRB forward shocks via synchrotron radiation. We study the maximum synchrotron photon energy in this scenario, considering the properties of the microturbluence magnetic fields behind the shock, as revealed by recent Particle-in-Cell simulations and theoretical analyses of relativistic collisionless shocks. Due to the small-scale nature of the micro-turbulent magnetic field, the Bohm acceleration approximation breaks down at such high energies. This effect leads to a typical maximum synchrotron photon of a few GeV at 100 s after the burst and this maximum synchrotron photon energy decreases quickly with time. We show that the fast decrease of the maximum synchrotron photon energy leads to a fast decay of the synchrotron flux. The 10-100 GeV photons detected after the prompt phase can not be produced by the synchrotron mechanism. They could originate from the synchrotron self-Compton emission of the early afterglow if the circum-burst density is sufficiently large, or from the external inverse-Compton process in the presence of central X-ray emission, such as X-ray flares and prompt high-latitude X-ray emission.Comment: 13 pages, 3 figures, accepted by ApJ Letter