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تسجيل مستخدم جديدProton 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 IC
M 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
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