• 천문학회지
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• 제37권5호
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• pp.405-412
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• 2004

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc $\ge$ 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to ${\~}50\%$ in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks ($M_s {\le} 5$), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

• 천문학회보
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• 제36권1호
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• pp.45.1-45.1
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• 2011

Shock waves form in the intergalactic medium as a consequence of accretion, merger, and turbulent motion during the structure formation of the universe. They not only heat gas but also govern non-thermal processes through the acceleration of cosmic rays (CRs), production of magnetic fields, and generation of vorticity. We examine diffusive shock acceleration of the pre-existing as well as freshly injected populations of nonthermal, CR particles at weak cosmological shocks. Since the injection is extremely inefficient at weak shocks, the pre-existing CR population dominates over the injected population. If the pressure due to pre-existing CR protons is about 5 % of the gas thermal pressure in the upstream flow, the downstream CR pressure can absorb typically a few to 10 % of the shock ram pressure at shocks with the Mach number M<3. Yet, the re-acceleration of CR electrons can result in a substantial synchrotron emission behind the shock. The implication of our findings for observed bright radio relics is discussed.

• 천문학회보
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• 제45권1호
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• pp.52.1-52.1
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• 2020

We propose semi-analytic models for the electron momentum distribution in weak shocks that accounts for both in situ acceleration and reacceleration through diffusive shock acceleration (DSA). In the former case, a small fraction of incoming electrons is assumed to be reflected at the shock ramp and pre-accelerated to the so-called injection momentum, pinj, above which particles can diffuse across the shock transition and participate in the DSA process. This leads to the DSA power-law distribution extending from the smallest momentum of reflected electrons, pref, all the way to the cutoff momentum, peq, constrained by radiative cooling. In the latter case, fossil electrons, specified by a power-law spectrum with a cutoff, are assumed to be re-accelerated from pref up to peq via DSA. We show that, in the in situ acceleration model, the amplitude of radio synchrotron emission depends strongly on the shock Mach number, whereas it varies rather weakly in the re-acceleration model.

• 천문학회보
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• 제42권1호
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• pp.36.4-37
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• 2017

Although most of observed properties of giant radio relics detected in the outskirts of galaxy clusters could be explained by relativistic electrons accelerated at merger-driven shocks, a few significant puzzles remain. In some relics the shock Mach number inferred from X-ray observations is smaller than that estimated from radio spectral index. Such a discrepancy could be understood, if either the shock Mach number is nder-estimated in X-ray observation due to projection effects, or if pre-existing electrons with a flat spectrum are re-accelerated by a weak shock, retaining the flat spectral form. In this study, we explore these two scenarios by comparing the results of shock acceleration simulations with observed features of the so-called Toothbrush relic in the merging cluster 1RXS J060303.3. We find that both models could reproduce reasonably well the observed radio flux and spectral index profiles and the integrated radio spectrum. Either way, the broad transverse relic profile requires additional post shock electron acceleration by downstream turbulence.

• 천문학회지
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• 제37권5호
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• pp.393-398
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• 2004

This paper describes some recent developments in our understanding of particle acceleration by shocks. It is pointed out that while good agreement now exists as to steady nonlinear modifications to the shock structure, there is. also growing evidence that the mesoscopic scales may not in fact be steady and that siginficant instabilties associated with magnetic field amplification may be a feature of strong collisionless plasma shocks.

• 천문학회지
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• 제49권3호
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• pp.83-92
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• 2016

The Toothbrush radio relic associated with the merging cluster 1RXS J060303.3 is presumed to be produced by relativistic electrons accelerated at merger-driven shocks. Since the shock Mach number inferred from the observed radio spectral index, M_radio ≈ 2.8, is larger than that estimated from X-ray observations, M_X ≲ 1.5, we consider the re-acceleration model in which a weak shock of M_s ≈ 1.2 - 1.5 sweeps through the intracluster plasma with a preshock population of relativistic electrons. We find the models with a power-law momentum spectrum with the slope, s ≈ 4.6, and the cutoff Lorentz factor, γ_e,c ≈ 7-8×10⁴ can reproduce reasonably well the observed profiles of radio uxes and integrated radio spectrum of the head portion of the Toothbrush relic. This study confirms the strong connection between the ubiquitous presence of fossil relativistic plasma originated from AGNs and the shock-acceleration model of radio relics in the intracluster medium.

• 천문학회지
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• 제34권4호
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• pp.293-295
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• 2001

A numerical scheme that incorporates a self-consistent cosmic-ray (CR, hereafter) injection model into the combined gas dynamics and CR diffusion-convection code has been developed. The hydro/CR code can follow in a very cos-effective way the evolution of CR modified shocks by adopting subzone shock-tracking and multi-level Adaptive Mesh Refinement techniques. The injection model is based on interactions of the suprathermal particles with self-generated MHD waves in quasi-parallel shocks. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to upstream region according to a velocity-dependent transparency function, which represents the fraction of leaking suprathermal particles. In the strong shock limit of Mach numbers $\ge$20, significant physical processes such as the injection and acceleration seem to become independent of M, while they are sensitively dependent on M for M < 10. Although some particles injected early in the evolution continue to be accelerated to higher energies, the postshock CR pressure reaches a time asymptotic value due to balance between acceleration and diffusion of the CR particles.

• 천문학회지
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• 제51권6호
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• pp.185-195
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• 2018

Galaxy clusters are known to host many active galaxies (AGNs) with radio jets, which could expand to form radio bubbles with relativistic electrons in the intracluster medium (ICM). It has been suggested that fossil relativistic electrons contained in remnant bubbles from extinct radio galaxies can be re-accelerated to radio-emitting energies by merger-driven shocks via diffusive shock acceleration (DSA), leading to the birth of radio relics detected in clusters. In this study we assume that such bubble consist primarily of thermal gas entrained from the surrounding medium and dynamically-insignificant amounts of relativistic electrons. We also consider several realistic models for magnetic fields in the cluster outskirts, including the ICM field that scales with the gas density as $B_{ICM}{\infty}n^{0.5}_{ICM}$. Then we perform time-dependent DSA simulations of a spherical shock that runs into a lower-density but higher-temperature bubble with the ratio $n_b/n_{ICM}{\approx}T_{ICM}/T_b{\approx}0.5$. We find that inside the bubble the shock speed increases by about 20 %, but the Mach number decreases by about 15% in the case under consideration. In this re-acceleration model, the observed properties of a radio relic such as radio flux, spectral index, and integrated spectrum would be governed mainly by the presence of seed relativistic electrons and the magnetic field profile as well as shock dynamics. Thus it is crucial to understand how fossil electrons are deposited by AGNs in the ICM and how the downstream magnetic field evolves behind the shock in detailed modeling of radio relics.

• 천문학회지
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• 제35권4호
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• pp.159-174
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• 2002

Cosmological hydrodynamic simulations of large scale structure in the universe have shown that accretion shocks and merger shocks form due to flow motions associated with the gravitational collapse of nonlinear structures. Estimated speed and curvature radius of these shocks could be as large as a few 1000 km/s and several Mpc, respectively. According to the diffusive shock acceleration theory, populations of cosmic-ray particles can be injected and accelerated to very high energy by astrophysical shocks in tenuous plasmas. In order to explore the cosmic ray acceleration at the cosmic shocks, we have performed nonlinear numerical simulations of cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. We adopted the Bohm diffusion model for CRs, based on the hypothesis that strong Alfven waves are self-generated by streaming CRs. The shock formation simulation includes a plasma-physics-based 'injection' model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs for acceleration there. We found that, for strong accretion shocks, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to $20\%$, compared to pure gas dynamic shocks. For merger shocks with small Mach numbers, however, the energy transfer to CRs is only about $10-20\%$ with an associated CR particle fraction of $10^{-3}$. Nonlinear feedback due to the CR pressure is insignificant in the latter shocks. Although detailed results depend on models for the particle diffusion and injection, these calculations show that cosmic shocks in large scale structure could provide acceleration sites of extragalactic cosmic rays of the highest energy.

• 천문학회보
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• 제42권2호
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• pp.69.1-69.1
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• 2017

According to structure formation simulations, weak shocks with typical Mach number, M<3, are expected to form in merging galaxy clusters. The presence of such shocks has been indicated by X-ray and radio observations of many merging clusters. In particular, diffuse radio sources known as radio relics could be explained by synchrotron-emitting electrons accelerated via diffusive shock acceleration (Fermi I) at quasi-perpendicular shocks. Here we also consider possible roles of stochastic acceleration (Fermi II) by compressive MHD turbulence downstream of the shock. Then we explore a puzzling discrepancy that for some radio relics, the shock Mach number inferred from the radio spectral index is substantially larger than that estimated from X-ray observations. This problem could be understood, if shock surfaces associated with radio relics consist of multiple shocks with different strengths. In that case, X-ray observations tend to pick up the part of shocks with lower Mach numbers and higher kinetic energy flux, while radio emissions come preferentially from the part of shocks with higher Mach numbers and higher cosmic ray (CR) production. We also show that the Fermi I reacceleration model with preexisting fossil electrons supplemented by Fermi II acceleration due to postshock turbulence could reproduce observed profiles of radio flux densities and integrated radio spectra of two giant radio relics. This study demonstrates the CR electrons can be accelerated at collisionless shocks in galaxy clusters just like supernova remnant shock in the interstellar medium and interplanetary shocks in the solar wind.