Properties of the first-order Fermi acceleration in fast magnetic reconnection driven by turbulence in collisional magnetohydrodynamical flows

Abstract

Fast magnetic reconnection may occur in different astrophysical sources, producing flare-like emission and particle acceleration. Currently, this process is being studied as an efficient mechanism to accelerate particles via a first-order Fermi process. In this work we analyse the acceleration rate and the energy distribution of test particles injected in three-dimensional magnetohydrodynamical (MHD) domains with largescale current sheets where reconnection is made fast by the presence of turbulence. We study the dependence of the particle acceleration time with the relevant parameters of the embedded turbulence, i.e., the Alfvén speed V A , the injection power P inj and scale k inj (k inj = 1/l inj ). We find that the acceleration time follows a power-law dependence with the particle kinetic energy: t acc ∝ E α , with 0.2 < α < 0.6 for a vast range of values of c/V A ∼ 20 − 1000. The acceleration time decreases with the Alfvén speed (and therefore with the reconnection velocity) as expected, having an approximate dependence t acc ∝ (V A /c) −κ , with κ ∼ 2.1 − 2.4 for particles reaching kinetic energies between 1 − 100 m p c 2 , respectively. Furthermore, we find that the acceleration time is only weakly dependent on the P inj and l inj parameters of the turbulence. The particle spectrum develops a high-energy tail which can be fitted by a hard power-law already in the early times of the acceleration, in consistency with the results of kinetic studies of particle acceleration by magnetic reconnection in collisionless plasmas.

Magnetic reconnection, Cosmic Ray Acceleration and Gamma-Ray emission around Black Holes and Relativistic Jets

“…To probe this, we have performed in situ test particle acceleration injecting 1000 particles with initial Maxwellian velocity distribution into the relativistic jet of Figure 2 (see left diagram). Starting with energies ∼ 1 MeV, the particles undergo an exponential acceleration when they are trapped in the reconnection sheets and interact resonantly with plasma magnetic field fluctuations (as predicted in [18], and successfully tested in [49,50,22]), until a saturation level when then the accelerated particles Larmor radius become larger than the acceleration regions. The initial background magnetic field in this simulation had a maximum initial value B = 0.13 G, but we have also considered simulations with values about 100 times larger.…”

“…To assess the Fermi process in the large scales of the collisional MHD flows commonly observed in astrophyisical systems, the tracking of test particle distributions in such flows is a very useful and complementary tool to help in the understanding of the overall process through the scales. Such studies have been also successfully tested both in 2D and 3D MHD simulations with the injection of thousands of test particles in the reconnection domain by our and other groups [49,50,22,61,29,34,25].…”

“…Our recent studies, in particular, have revealed that test protons injected in large scale 3D MHD current sheets with turbulence embedded in order to make reconnection fast [50,22], undergo efficient particle acceleration with a rate t −1 acc ∝ E −α , with 0.2 < α < 0.6, for a vast range of values of c/V A ∼ 20−1000. The accelerated particles produce power-law spectra with indices in the initial times of the simulations N(E) ∝ E −1,−2 , where E is the particle kinetic energy [22]. These powerlaw indices are compatible with the values derived in PIC studies of highly relativistic magnetized, non-radiative plasmas, both of electron-positron pairs (e.g, [35,36,74]) and electron-ion pairs (e.g., [38,75,6]) 1 .…”

The feasibility of magnetic reconnection powered blazar flares from synchrotron self-Compton emission

“…particle acceleration with spectral indices between 1 and 2 (Sironi & Spitkovsky 2014;Guo et al 2014;Ball et al 2018). Whilst the exact attribution of the acceleration mechanisms remains unclear, it has been postulated that the mean energy gain of the particles is approximately first order and therefore analogous to the exponential increase in energy provided by shock models (de Gouveia dal Pino & Lazarian 2005;Guo et al 2014;de Gouveia Dal Pino & Kowal 2015;del Valle et al 2016). Other hypotheses include those where the acceleration is dominated by the reconnection electric field (E ≈ −v × B) (e.g.…”

On the energization of charged particles by fast magnetic reconnection

“…This is a difficult question to study numerically because in-principle one has to also take into account the electromagnetic fields created by the energised ions and electrons, which can be done by performing kinetic simulations, e.g., by using particles-in-cell (PIC) algorithms (see, e.g., Zenitani & Hoshino 2007;Hoshino 2012;Hoshino et al 2001;Sironi & Spitkovsky 2014;Guo et al 2014). Another option is to work with the test-particle approximation (see, e.g., Ambrosiano et al 1988;Kowal et al 2011Kowal et al , 2012de Gouveia Dal Pino & Kowal 2015;del Valle et al 2016) where one solves numerically the partial differential equations of MHD and uses the resultant electromagnetic field to calculate the energisation of a number of charged particles, ignoring the electromagnetic field generated by these energized charged particles. Furthermore, an additional approximation -quasistationary -is also often employed, where one assumes that the evolution of the particles are so fast that time-evolution of the fields (velocity and magnetic) can be ignored or approximated (see, e.g., Threlfall et al 2016, for a recent example).…”