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Register a new userA critical shock Mach number for particle acceleration in the absence of pre-existing cosmic rays: $M=sqrt 5$
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It is shown that, under some generic assumptions, shocks cannot accelerate particles unless the overall shock Mach number exceeds a critical value M > sqrt(5). The reason is that for M <= sqrt(5) the work done to compress the flow in a particle precursor requires more enthalpy flux than the system can sustain. This lower limit applies to situations without significant magnetic field pressure. In case that the magnetic field pressure dominates the pressure in the unshocked medium, i.e. for low plasma beta, the resistivity of the magnetic field makes it even more difficult to fulfil the energetic requirements for the formation of shock with an accelerated particle precursor and associated compression of the upstream plasma. We illustrate the effects of magnetic fields for the extreme situation of a purely perpendicular magnetic field configuration with plasma beta = 0, which gives a minimum Mach number of M = 5/2. The situation becomes more complex, if we incorporate the effects of pre-existing cosmic rays, indicating that the additional degree of freedom allows for less strict Mach number limits on acceleration. We discuss the implications of this result for low Mach number shock acceleration as found in solar system shocks, and shocks in clusters of galaxies.
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An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters such as CIZA J2242.8+5301 which has well defined radio relics.
Electron acceleration associated with various plasma kinetic instabilities in a nonrelativistic, very-high-Alfven Mach-number ($M_A sim 45$) shock is revealed by means of a two-dimensional fully kinetic PIC simulation. Electromagnetic (ion Weibel) and electrostatic (ion-acoustic and Buneman) instabilities are strongly activated at the same time in different regions of the two-dimensional shock structure. Relativistic electrons are quickly produced predominantly by the shock surfing mechanism with the Buneman instability at the leading edge of the foot. The energy spectrum has a high-energy tail exceeding the upstream ion kinetic energy accompanying the main thermal population. This gives a favorable condition for the ion acoustic instability at the shock front, which in turn results in additional energization. The large-amplitude ion Weibel instability generates current sheets in the foot, implying another dissipation mechanism via magnetic reconnection in a three-dimensional shock structure in the very-high-$M_A$ regime.
When two galaxy clusters encounter each other, the interaction results in a collisionless shock that is characterized by a low (1-4) sonic Mach number, and a high Alfv{e}nic Mach number. Our goal is to determine if, and to what extent, such shocks can accelerate particles to sufficient velocities that they can contribute to the cosmic ray spectrum. We combine two different computational methods, magnetohydrodynamics (MHD) and particle-in-cell (PIC) into a single code that allows us to take advantage of the high computational efficiency of MHD while maintaining the ability to model the behaviour of individual non-thermal particles. Using this method, we perform a series of simulations covering the expected parameter space of galaxy cluster collision shocks. Our results show that for shocks with a sonic Mach number below 2.25 no diffusive shock acceleration can take place because of a lack of instabilities in the magnetic field, whereas for shocks with a sonic Mach number $geq,3$ the acceleration is efficient and can accelerate particles to relativistic speeds. In the regime between these two extremes, diffusive shock acceleration can occur but is relatively inefficient because of the time- and space-dependent nature of the instabilities. For those shocks that show efficient acceleration, the instabilities in the upstream gas increase to the point where they change the nature of the shock, which, in turn, will influence the particle injection process.
Clusters of galaxies are the largest known gravitationally-bound structures in the Universe. When clusters collide, they create merger shocks on cosmological scales, which transform most of the kinetic energy carried by the cluster gaseous halos into heat. Observations of merger shocks provide key information of the merger dynamics, and enable insights into the formation and thermal history of the large-scale structures. Nearly all of the merger shocks are found in systems where the clusters have already collided, knowledge of shocks in the pre-merger phase is a crucial missing ingredient. Here we report on the discovery of a unique shock in a cluster pair 1E 2216 and 1E 2215. The two clusters are observed at an early phase of major merger. Contrary to all the known merger shocks observed ubiquitously on merger axes, the new shock propagates outward along the equatorial plane of the merger. This discovery uncovers an important epoch in the formation of massive clusters, when the rapid approach of the cluster pair leads to strong compression of gas along the merger axis. Current theoretical models predict that the bulk of the shock energy might be dissipated outside the clusters, and eventually turn into heat of the pristine gas in the circum-cluster space.
We herein investigate shock formation and particle acceleration processes for both protons and electrons in a quasi-parallel high-Mach-number collisionless shock through a long-term, large-scale particle-in-cell simulation. We show that both protons and electrons are accelerated in the shock and that these accelerated particles generate large-amplitude Alfv{e}nic waves in the upstream region of the shock. After the upstream waves have grown sufficiently, the local structure of the collisionless shock becomes substantially similar to that of a quasi-perpendicular shock due to the large transverse magnetic field of the waves. A fraction of protons are accelerated in the shock with a power-law-like energy distribution. The rate of proton injection to the acceleration process is approximately constant, and in the injection process, the phase-trapping mechanism for the protons by the upstream waves can play an important role. The dominant acceleration process is a Fermi-like process through repeated shock crossings of the protons. This process is a `fast process in the sense that the time required for most of the accelerated protons to complete one cycle of the acceleration process is much shorter than the diffusion time. A fraction of the electrons is also accelerated by the same mechanism, and have a power-law-like energy distribution. However, the injection does not enter a steady state during the simulation, which may be related to the intermittent activity of the upstream waves. Upstream of the shock, a fraction of the electrons is pre-accelerated before reaching the shock, which may contribute to steady electron injection at a later time.
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