2nd-order Fermi Acceleration Research Articles

Investigating 1st and 2nd order Fermi acceleration of energetic particles by small-scale magnetic flux ropes at 1AU

A new telegrapher-type Parker transport equation was derived from the existing underlying focused transport equation to model the acceleration of energetic particles by contracting and reconnecting small-scale magnetic flux ropes (SMFRs) in the large-scale solar wind. Time-dependent and steady-state analytical solutions were found that unify all SMFR acceleration mechanisms present in the transport equation, showing that SMFR acceleration by the parallel reconnection electric field in the mixed spatial and momentum derivative transport term is constrained by and requires the presence of 2nd order Fermi SMFR acceleration. We explore the potential of these solutions in reproducing energetic proton flux enhancements and spectral evolution between ∼50 keV-5 MeV in dynamic SMFR regions near large-scale reconnecting current sheets in the solar wind at 1 AU. It is shown that both 2nd order Fermi SMFR acceleration involving the variance in SMFR compression and incompressible parallel shear flow, and 1st order SMFR Fermi acceleration due to mean SMFR compression are both workable options in reproducing observed flux amplification factors when using reasonable SMFR parameters. However, the predicted substantial quantitative differences in the spatial evolution of the accelerated spectra through the SMFR region might provide a diagnostic to distinguish between 1st and 2nd order Fermi SMFR acceleration in observations.

Searching for the high-energy neutrino counterpart signals: The case of the Fermi bubbles signal and of dark matter annihilation in the inner Galaxy

The recent uncovering of the \textit{Fermi} Bubbles/haze in the \textit{Fermi} gamma-ray data has generated theoretical work to explain such a signal of hard $\gamma$-rays in combination with the \textit{WMAP} haze signal. Many of these theoretical models can have distinctively different implications with regards to the production of high energy neutrinos. We discuss the neutrino signals from different models proposed for the explanation of the \textit{Fermi} Bubbles/haze, more explicitly, from Dark Matter annihilation in the galactic halo with conditions of preferential CR diffusion, from recent AGN jet activity, from periodic diffusive shock acceleration, from stochastic 2nd order Fermi acceleration and from long time-scale star formation in the galactic center in combination with strong galactic winds. We find that some of these models will be probed by the IceCube DeepCore detector. Moreover, with a km$^3$ telescope located at the north hemisphere, we will be able to discriminate between the hadronic, leptonic and the DM models. Additionally using the reconstructed neutrino spectra we will probe annihilation of TeV scale dark matter towards the galactic center.

A new analytic solution for 2nd-order Fermi acceleration

A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments.

Fermi Gamma-Ray “Bubbles” from Stochastic Acceleration of Electrons

Gamma-ray data from Fermi Large Area Telescope reveal a bilobular structure extending up to ∼50° above and below the Galactic Center. It has been argued that the gamma rays arise from hadronic interactions of high-energy cosmic rays which are advected out by a strong wind, or from inverse-Compton scattering of relativistic electrons accelerated at plasma shocks present in the bubbles. We explore the alternative possibility that the relativistic electrons are undergoing stochastic 2nd-order Fermi acceleration by plasma wave turbulence through the entire volume of the bubbles. The observed gamma-ray spectral shape is then explained naturally by the resulting hard electron spectrum modulated by inverse-Compton energy losses. Rather than a constant volume emissivity as in other models, we predict a nearly constant surface brightness, and reproduce the observed sharp edges of the bubbles.

Acceleration and Transport of Energetic Charged Particles in Space

Energetic charged particles or cosmic rays are found in space wherever the ambient matter density is small enough to allow them to exist. Their observed kinetic energies vary from just above the local thermal energies to in excess of 1020 eV. The energy spectrum is quite smooth, suggesting that a common mechanism is responsible for particles of all energies. Their arrival directions are distributed evenly in solid angle, with the observed anisotropies being quite small even at energies ∼ 1018 eV. Various scenarios for their acceleration are discussed, including 2nd-order Fermi acceleration, shocks and cosmic-ray viscosity. It is concluded that the most likely mechanism for the acceleration of most energetic particles to high energies is diffusive shock acceleration. This mechanism has the benefit of producing a power-law energy spectrum with a spectral index which is very insensitive to parameters and which is close in magnitude to that observed in a variety of contexts. It is also reasonably fast and efficient. Anomalous cosmic rays in the heliosphere are discussed as one example of the success of the shock-acceleration picture.

Effects from diffusive reacceleration on propagating cosmic rays

According to the diffusive reacceleration model the transport of cosmic ray particles is controlled by diffusion where the particles scatter on hydromagnetic waves. As a consequence they encounter stochastic 2nd order Fermi acceleration. This physical scenario can explain the cosmic ray observations but it leads to a mean escape length which is different from that obtained from Leaky Box calculations. We will explain how this works.

Cosmic-ray acceleration and transport, and diffuse galactic ?-ray emission

Cosmic-ray acceleration and transport is considered from the point of view of application to diffuse galactic γ-ray sources. As an introduction we review several source models, in particular supernovae exploding inside or near large interstellar clouds. The complex problem of cosmic ray transport in random electromagnetic fields is reduced to three cases which should be sufficient for practical purposes. As far as diffusive acceleration is concerned, apart from reviewing the basic physical principles, we point out the relation between shock acceleration and 2nd order Fermi acceleration, and the relative importance of the two processes around interstellar shock waves. For γ-ray source models the interaction of cosmic rays with dense clouds assumes great importance. Past discussions had been confined to static interactions of clouds with the ambient medium in the sense that no large scale mass motions in the ambient interstellar medium were considered. The well-known result then is that down to some tens of MeV or less, cosmic-ray nucleons should freely penetrate molecular clouds of typical masses and sizes. The self-exclusion of very low energy nucleons however may affect electron transport with consequences for the Bremsstrahlung γ-luminosity of such clouds.