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Register a new userProton Acceleration in Weak Quasi-parallel Intracluster Shocks: Injection and Early Acceleration
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Ji-Hoon Ha
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Collisionless shocks with low sonic Mach numbers, $M_{rm s} lesssim 4$, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the ICM has yet to be established. Performing particle-in-cell simulations, we study the injection of protons into DSA and the early development of a nonthermal particle population in weak shocks in high $beta$ ($approx 100$) plasmas. Reflection of incident protons, self-excitation of plasma waves via CR-driven instabilities, and multiple cycles of shock drift acceleration are essential to the early acceleration of CR protons in supercritical quasi-parallel shocks. We find that only in ICM shocks with $M_{rm s} gtrsim M_{rm s}^*approx 2.25$, a sufficient fraction of incoming protons are reflected by the overshoot in the shock electric potential and magnetic mirror at locally perpendicular magnetic fields, leading to efficient excitation of magnetic waves via CR streaming instabilities and the injection into the DSA process. Since a significant fraction of ICM shocks have $M_{rm s} < M_{rm s}^*$, CR proton acceleration in the ICM might be less efficient than previously expected. This may explain why the diffuse gamma-ray emission from galaxy clusters due to proton-proton collisions has not been detected so far.
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Low sonic Mach number shocks form in the intracluster medium (ICM) during the formation of the large-scale structure of the universe. Nonthermal cosmic-ray (CR) protons are expected to be accelerated via diffusive shock acceleration (DSA) in those ICM shocks, although observational evidence for the $gamma$-ray emission of hadronic origin from galaxy clusters has yet to be established. Considering the results obtained from recent plasma simulations, we improve the analytic test-particle DSA model for weak quasi-parallel ($Q_parallel$) shocks, previously suggested by citet{kang2010}. In the model CR spectrum, the transition from the postshock thermal to CR populations occurs at the injection momentum, $p_{rm inj}$, above which protons can undergo the full DSA process. As the shock energy is transferred to CR protons, the postshock gas temperature should decrease accordingly and the subshock strength weakens due to the dynamical feed of the CR pressure to the shock structure. This results in the reduction of the injection fraction, although the postshock CR pressure approaches an asymptotic value when the CR spectrum extends to the relativistic regime. Our new DSA model self-consistently accounts for such behaviors and adopts better estimations for $p_{rm inj}$. With our model DSA spectrum, the CR acceleration efficiency ranges $etasim10^{-3}-0.01$ for supercritical, $Q_parallel$-shocks with sonic Mach number $2.25lesssim M_{rm s}lesssim5$ in the ICM. Based on citet{ha2018b}, on the other hand, we argue that proton acceleration would be negligible in subcritical shocks with $M_{rm s}<2.25$.
We study diffusive shock acceleration (DSA) of electrons in non-relativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell (PIC) simulations. By exploring the parameter space of sonic and Alfv{e}nic Mach numbers we find that high Mach number quasi-perpendicular shocks can efficiently accelerate electrons to power-law downstream spectra with slopes consistent with DSA prediction. Electrons are reflected by magnetic mirroring at the shock and drive non-resonant waves in the upstream. Reflected electrons are trapped between the shock front and upstream waves and undergo multiple cycles of shock drift acceleration before the injection into DSA. Strong current-driven waves also temporarily change the shock obliquity and cause mild proton pre-acceleration even in quasi-perpendicular shocks, which otherwise do not accelerate protons. These results can be used to understand nonthermal emission in supernova remnants and intracluster medium in galaxy clusters.
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.
The theory of diffusive particle acceleration explains the spectral properties of the cosmic rays below energies of approx. 10^6 GeV as produced at strong shocks in supernova remnants (SNRs). To supply the observed flux of cosmic rays, a significant fraction of the energy released by a supernova has to be transfered to cosmic rays. The key to the question of the efficiency of SNRs in producing cosmic rays is the injection process from thermal energies. A self-consistent model has to take into account the interaction of the accelerated particles with magneto-hydrodynamic waves, which generate the particle diffusion, a requisite for the acceleration process. Such a nonlinear model of the turbulent background plasma has been developed recently (Malkov, 1998, Phys. Rev. E 58, 4911). We use this model for the first numerical treatment of the gas dynamics and the diffusion-convection equation at a quasi-parallel strong shock, which incorporates a plasma-physical injection model to investigate the cosmic ray production.
Electrons can be accelerated to ultrarelativistic energies at strong (high-Mach number) collisionless shock waves that form when stellar debris rapidly expands after a supernova. Collisionless shock waves also form in the flow of particles from the Sun (the solar wind), and extensive spacecraft observations have established that electron acceleration at these shocks is effectively absent whenever the upstream magnetic field is roughly parallel to the shock surface normal (quasi-parallel conditions). However, it is unclear whether this magnetic dependence of electron acceleration also applies to the far stronger shocks around young supernova remnants, where local magnetic conditions are poorly understood. Here we present Cassini spacecraft observations of an unusually strong solar system shock wave (Saturns bow shock) where significant local electron acceleration has been confirmed under quasi-parallel magnetic conditions for the first time, contradicting the established magnetic dependence of electron acceleration at solar system shocks. Furthermore, the acceleration led to electrons at relativistic energies (~MeV), comparable to the highest energies ever attributed to shock-acceleration in the solar wind. These observations demonstrate that at high-Mach numbers, like those of young supernova remnant shocks, quasi-parallel shocks become considerably more effective electron accelerators.
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