The spectra are taken from the range (x−xsh)/rL,i= [0,+1] and the black dashed lines show the Maxwellian distributions in the upstream. The spectra are taken from the range (x−xsh)/rL,i = [0,+1] and the black dashed lines show the Maxwellian distributions in the upstream.
Numerics
Part of the shock kinetic energy is dissipated to accelerate the CR through the DSA and to heat the gas since ICM shocks are collisionless, as noted in the introduction. The red and blue arrows in the z=0.34 and 0.25 panels represent the axial shock before the LDMC and the axial shock before the HDMC, respectively.
Results
Moreover, ⟨vs⟩ and⟨Ms⟩ of axial shocks before HDMC are larger than those of axial shocks before LDMC. Axial shocks before LDMC should therefore have the best chance of being observed as X-ray shocks, especially at ∼1 Gyr after the launch of the shocks.
Summary and Discussion
Thus, ion repulsion when the shock potential is exceeded, self-excitation of turbulent waves, and SDA are components of ion injection in quasi-parallel shocks. And so the electron bounce is mainly governed by the magnetic mirror on the impact surface.
Numerics
Here xsh indicates the shock position and the length scale is expressed in the unit c/ωpe. The black and purple dashed lines indicate the power law spectrum of the test particles and the thermal Maxwellian distribution in the postshock region, respectively.
Results
The red dashed line indicates the inverse of the mean CR gyroradius, while the blue dashed line shows the characteristic power law,k(q−6)/2, due to the resonant flow instability. The red dashed line indicates the inverse of the mean CR gyroradius, while the blue dashed line shows the characteristic power law,k(q−6)/2, due to the resonant flow instability.
Summary
This method significantly reduces the computational cost of simulation compared to the PIC simulation. For example, calculated neutrinos due to the CRp produced at AGNs and SNRs in the ICM and cluster galaxies. Assuming that these CRp fill the cluster volume and serve as the pre-existing CRp, and adopt a simplified reacceleration model based on the "test particle" solution, we also estimate the boost of the CRp energy due to the multiple passes of the ICM plasma by shock.
CR protons in Simulated Clusters
Although the CRp production in the core of galaxy clusters may influence non-gravitational effects, we have. Note that dNCR(p)/dtd is defined in such a way that RdNCR(p)/dtd is the total rate of CRp production in the ICM. Note that ϕ is almost identical to the fraction of the shock kinetic energy dissipated in supercritical Q∥ shocks.
Gamma-Rays and Neutrinos from Simulated Clusters
While we focus on the GeV range γ-ray emission, our results can be extended to explain non-detection of γ-ray in the higher energy range such as TeV range. In this context, the cluster-wide γ-ray spectrum produced by weak ICM shocks is generally expected as a single power-law spectrum and our interpretation described by Figure 19 may also apply to non-detection of γ-ray in the higher energy to explain range. Therefore, we use the scaling ratioLν ∝TX5/2, together with the neutrino energy spectrum for αrp=2.4 in the top panel of Figure 19, to guess dLν/dEν for these nearby clusters.
Summary and Discussion
As found in previous kinetic plasma simulation studies, the electron acceleration process in shocks in various astrophysical environments is mediated by microinstabilities near the shock surface (e.g., according to previous numerical works for the simulation of Q⊥-shock self-excited waves in They argued that the temperature anisotropy (Te∥>Te⊥) due to the reflected electrons flowing back along the background magnetic fields with small inclination angles derives the electron tube instability (EFI, hereafter), which mainly excites non-propagating oblique waves in the upstream shock.
Linear Analysis of ETAFI and EBFI
Here are respectively the number density and the drift speed of the particle speciesa. This is consistent with the result of the ETAFI, shown in the right panels of Figure 23. Such β dependence is also seen in the case of the ETAFI, shown in the left panels of Figure 2 .
PIC Simulations of EBFI
Using its Fourier transform, δBy(k), we first compare ln(δB2y(k)/B20), calculated in the PIC simulations, with the linear growth rate, γ(k), since δBy(k)∝ exp(γ (k))in the linear regime. In the Su0.22 and Su0.26 models, the peak of δB2y(k)/B20 matches the location of the X mark quite well. This confirms that the development of the EBFI is not sensitive to both the non-linear and the linear regime.
Summary and Discussion
The ion anisotropy in the shock slope region on the left of Figure 8 is indeed Tp∥/Tp⊥∼0.7−1. Therefore, to investigate EFI in the shock front, the isotropic Maxwellian ions can be applicable. Particularly in the shock transition zone, Alfvén-Ion Cyclotron and/or ion level instabilities can be induced due to the Tp∥/Tp⊥<1.
Linear Analysis
In the case of whistle and i-mirror volatility, on the other hand, in general, the growth rates are slightly lower for smaller mi/me. As a result, the enhancement of the whistle and mirror instabilities can be somewhat suppressed in shock simulations with reduced mass ratios. In the case of LM2.0β20, all instabilities are stable (see black lines in the upper panels).
Nonlinear Evolution of Induced Waves in Periodic-Box Simulations
On the other hand, in the LM3.0β5 model (red solid lines), the e-mirror mode is stable and the other modes are unstable. In the LM3.0β1 model (gray solid lines), all instabilities are stable with negative growth rates. The lower panels of Fig. 35 confirm that the waves in the LM2.0β50 model do not grow noticeably.
Implications for Shock Simulations
However, the ion density fluctuations of the rippling waves propagating along the shock surface behind the shock slope are quite significant in the shock simulation for the M3.0β50 model in HKRK2021. Note that here the quantities are averaged along the x direction over the shock transition zone, including the first and second overshoot oscillations behind the ramp. Therefore, the purely AIC-driven waves in the shock transition could be modified by such possible nonlinearities, leading to the enhancement of ion density fluctuations.
Summary
Note that the pre-shock magnetic field, Bup0, lies in the x-y plane, and the slant angle between Bup0 and their axis is θBn=63◦ in the shock simulation. It is expected that the inhomogeneity in the shock transition and the non-linear effects may lead to the generation of such large-amplitude fluctuations of the ion density along the shock surface. A detailed description of the shock structure and the electron pre-acceleration in such ICM shocks, realized in 2D PIC simulations, is reported in the following Section VII.
Basic Physics of Q ⊥ -Shocks
In the HT frame, the flow velocity is measured upstream ut,HT=ush/cosθBnwhereush stands for the shock velocity measured in the upstream rest frame. These two critical Mach numbers are closely related, as the shock transition oscillations due to ion reflection enhance the magnetic mirror and electron reflection. Although the EFI-driven waves can be broadly generated in the upstream region, depending on Te∥/Te⊥, the Fermi-like acceleration occurs primarily within the shock foot.
Numerics
Results
In the M2.3 model in panel (e), the electron-scale waves are relatively more dominant than the ion-scale waves, while the ion-scale waves are mainly driven by the ion mirror instability as indicated in panel (b). . Note that the trajectories are shown in the shock rest frame, so that the region of(x−xsh)ωpe/c≈[−5,5]. Thus, even in the new simulations (red), the electron energy spectra are extended to the energy below the injection momentum (γinj∼7), as shown in Figure 42(d).
Summary
Based on the results described in this section, we conclude that the pre-acceleration of electrons and the shock criticality are almost independent of mi/me, but depend somewhat weakly on β (≈20−100) for the ranges of values considered here. In the transition zone of supercritical shocks, ion-scale waves can be generated by AIC and ion-mirror instabilities due to the ion temperature anisotropy (Ti⊥/Ti∥>1), while electron-scale waves can be generated by the whistler and electron-mirror instabilities due to the electron temperature anisotropy (Te⊥/Te∥ >1). Therefore, we infer that our results on the shock criticality and the preacceleration can generally be applied to Q⊥ shocks in the ICM.
Numerics
In particular, according to the results shown in Section VII, electron pre-acceleration mechanisms mediated by multiscale plasma waves near the shock surface are inefficient in subcritical shocks with Ms≲2.3. As pointed out in the shock simulation model, we know that the electron energy spectrum undergoes a smoothing process at γ∼γmin due to interactions mediated by PPEs, and the saturation time scale is approximately ∼1000Ω−1ce = 20Ω -1ci. This indicates that wave generation due to electron dynamics near the shock surface is much faster than PPE-mediated wave generation in the upstream shock.
Results
Electron temperature anisotropy, Te∥/Te⊥, estimated in the immediate upstream region, 0≤(x−xsh)/rL,i≤1 (panel (c)), and Te⊥/Te∥estimated in the immediate downstream region , − 1≤(x−xsh)/rL,i≤0 (panel (d)). On the other hand, waves with λ≳rinj,2 are produced only at supercritical shocks (black and red lines), regardless of the presence of PBMs. In the M2.0-np0.1 model (green line in Figure 53(a)), where np/n0 is ten times larger than that of the fiducial model (green line in Figure 51(a)), the excitation is of waves has improved.
Summary and Discussion
Jones, "Cosmological shock waves and their role in the large-scale structure of the universe," vol. Ostriker, "Cosmological shock waves in the large-scale structure of the universe: Nongravitational effects," vol. Ando, "Constraints on diffuse gamma-ray emission from structure-forming processes in the coma cluster," vol.
