arXiv subjects

Hyesung Kang

Publications and source records attributed to Hyesung Kang.

At least 19 recordsLinked to original sources

arXiv2025

Simulation Study of Binary Mergers of Galaxy Clusters I: Properties of Merger Shocks and Radio Emission

We investigate binary mergers of galaxy clusters, the formation of shocks, and the resulting radio relics using three-dimensional simulations. The initial setup consists of two idealized spherical subclusters with a mass ratio below three, each permeated by turbulent magnetic fields, and we follow their merger with a high-order accurate magnetohydrodynamic (MHD) code. In parallel, we track the acceleration of cosmic-ray electrons (CRe) via diffusive shock acceleration (DSA) at merger-driven shocks, together with radiative cooling and Fermi-II (turbulent) acceleration in the postshock region, employing a newly developed Eulerian Fokker-Planck solver. Synchrotron emission is computed from the simulated CRe distribution and magnetic fields. In this paper, we detail these numerical approaches and present the first results obtained with them. Two prominent axial shocks emerge along the merger axis; the shock ahead of the heavier subcluster systematically attains a higher Mach number, although it is more compact, than that ahead of the lighter subcluster. Turbulent magnetic fields, which are both inherited from the initial conditions and amplified during the merger, produce patchy, fine-scale structures in the radio surface brightness. Because of the combined effects of turbulent acceleration, spatially nonuniform magnetic fields, and the curved geometry of merger shocks, the volume-integrated radio spectra show deviations from the canonical power-law steepening expected for a planar shock with a uniform field. Reacceleration of preexisting fossil CRe enhances the surface brightness. Our results highlight the coupled roles of merger dynamics, MHD turbulence, and CRe physics in shaping the observed properties of radio relics in cluster outskirts.

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arXiv2025

Energy Spectrum and Mass Composition of Ultra-High-Energy Cosmic Rays Originating from Relativistic Jets of Nearby Radio Galaxies

Relativistic jets of radio galaxies (RGs) are possible sources of ultra-high-energy cosmic rays (UHECRs). Recent studies combining relativistic hydrodynamic simulations with Monte Carlo particle transport have demonstrated that UHECRs can be accelerated to energies beyond $10^{20}$ eV through shocks, turbulence, and relativistic shear in jet-induced flows of Fanaroff-Riley (FR) type RGs. The resulting time-asymptotic UHECR spectrum is well modeled by a double power law with an ``extended'' exponential cutoff, primarily shaped by relativistic shear acceleration. In this study, we adopt this novel source spectrum and simulate the propagation of UHECRs from nearby RGs using the CRPropa code. We focus on Virgo A, Centaurus A, Fornax A, and Cygnus A, expected to be the most prominent UHECR sources among RGs. We then analyze the energy spectrum and mass composition of UHECRs arriving at Earth. We find that, due to the extended high-energy tail in the source spectrum, UHECRs from Virgo A, which has a higher Lorentz factor, exhibit a higher flux at the highest energies and a lighter mass composition at Earth, compared to those from Centaurus A and Fornax A with lower Lorentz factors. Despite Cygnus A having an even higher Lorentz factor, the large distance limits its contribution. With a small number of nearby prominent RGs, our findings suggest that if RGs are the major sources of UHECRs, the energy spectrum and mass composition of observed UHECRs would exhibit hemispheric differences between the Northern and Southern skies at the highest energies.

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arXiv2024

Morphology and Mach Number Distribution of Merger Shock Surfaces in Merging Galaxy Clusters

In a binary merger of two subclusters with comparable masses, a pair of merger shocks are typically generated, often manifesting as double radio relics. Using cosmological hydrodynamic simulations, we identify major merger events with mass ratio $\mathcal{M}_1/\mathcal{M}_2\lesssim4$ and impact parameter $b/r_{\rm vir,1}\lesssim1$, where $r_{\rm vir,1}$ is the virial radius of the larger subcluster. We analyze merger shock surfaces approximately 1 Gyr after the pericenter passage, focusing on their morphology and the distribution of the Mach number, $M_s$, of their constituent shock zones. The shock surfaces exhibit an elongated shape with a minor-to-major axis ratio of $\sim0.6-0.9$ and cover the area of $\sim5-20\%$ of the enclosed sphere. The area ratio of the two shock surfaces roughly scales with $\mathcal{M}_1/\mathcal{M}_2$, typically positioning the larger shock ahead of the smaller subcluster. The axis connecting the two subclusters generally does not pass through the centers of the shock surfaces, due to the nonzero impact parameter and the turbulent flows around them. The distribution of $M_s$ of shock zones on each surface can be approximated by a log-normal function, peaking at $M_{s,\rm{peak}}\approx2-4.5$ and extending up to $\sim10$. The surface-area-weighted and X-ray-emissivity-weighted average Mach numbers are comparable, with ${\langle{M_s}\rangle}_{\rm{area}}\approx2.3-4.4$ and ${\langle{M_s}\rangle}_{X}\approx2-4$. In contrast, the cosmic-ray-energy-flux-weighted average Mach numbers are higher with ${\langle{M_s}\rangle}_{\rm{CR}}\approx3-5$. This discrepancy aligns with the differences between Mach numbers derived from X-ray and radio observations of radio relic shocks. On the other hand, we find that mostly ${\langle{M_s}\rangle}_{X}\gtrsim2$ for simulated merger shocks, although shocks with $M_{\rm X-ray}\lesssim2$ are often reported in observations.

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arXiv2024

A Simulation Study of Low-Power Relativistic Jets: Flow Dynamics and Radio Morphology of FR-I Jets

Radio galaxies are classified into two primary categories based on their morphology: center-brightened FR-I and edge-brightened FR-II. It is believed that the jet power and interactions with the ambient medium govern the deceleration and decollimation of the jet-spine flows, which, in turn, influence this dichotomy. Using high-resolution, three-dimensional relativistic hydrodynamic simulations, we follow the development of flow structures on sub-kpc to kpc scales in kinetically dominant low-power relativistic jets. We find that the bulk Lorentz factor of the jet spine and the advance speed of the jet head, which depend on the energy injection flux and the jet-to-background density contrast, primarily determine the dynamics and structures of the jet-induced flows. The entrainment of ambient gas and the background density and pressure gradient may also play significant roles. To emulate radio morphology, we produce the synthetic maps of the synchrotron surface brightness for the simulated jets, by employing simple models for magnetic field distribution and nonthermal electron population and considering relativistic beaming effects at different inclination angles. Both the flow structures and radio maps capture the longitudinal and transverse structures of the jet-spine and shear layer, consistent with observations. We also compare different background effects and argue that the loss of pressure confinement beyond the galactic core may be a key factor in the flaring and disruption of FR-I jets. Our results confirm that mildly relativistic jets could explain the one-sidedness or asymmetries with the boosted main jet and deboosted counterjet pairs.

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arXiv2024

Diffusive Shock Acceleration Efficiencies for Weak ICM Shocks in the Test Particle Regime

During the formation of large-scale structures in the universe, weak internal shocks are induced within the hot ICM, while strong accretion shocks arise in the WHIM within filaments, and the warm-cold gas in voids surrounding galaxy clusters. These cosmological shocks are thought to accelerate cosmic ray (CR) protons and electrons via diffusive shock acceleration. Recent advances in particle-in-cell and hybrid simulations have provided deeper insights into the kinetic plasma processes that govern microinstabilities and particle acceleration in collisionless shocks in weakly magnetized astrophysical plasma. In this study, we adopt a thermal-leakage type injection model and DSA power-law distribution functions in the test-particle regime. The CR proton spectrum directly connects to the Maxwellian distribution of protons at the injection momentum $p_{\rm{inj}} = Q_p p_{\rm {th,p}}$. On the other hand, the CR electron spectrum extends down to $p_{\rm{min}}=Q_ep_{\rm{th,e}}$ and is linked to the Maxwellian distribution of electrons. Here, $p_{\rm{th,p}}$ and $p_{\rm{th,e}}$, are the proton and electron thermal momenta, respectively. Moreover, we propose that the postshock gas temperature and the injection parameters, $Q_p$ and $Q_e$ are self-regulated to maintain the test-particle condition, as the thermal energy is gradually transferred to the CR energy. Under these constraints, we estimate the self-regulated values of the temperature reduction factor, $R_T$, and the proton injection parameter, $Q_p$, along with the resulting CR efficiencies, $η_p$ and $η_e$. We then provide analytical fitting functions for these parameters as functions of the shock Mach number, $M_s$. These fitting formulas may serve as valuable tools for quantitatively assessing the impact of CR protons and electrons, as well as the resulting nonthermal emissions in galaxy clusters and cosmic filaments.

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arXiv2024

Impact of Postshock Turbulence on the Radio Spectrum of Radio Relic Shocks in Merging Clusters

This study investigates the impact of magnetic turbulence on cosmic ray (CR) electrons through Fermi-II acceleration behind merger-driven shocks in the intracluster medium and examines how the ensuing synchrotron radio emission is influenced by the decay of magnetic energy through dissipation in the postshock region. We adopt simplified models for the momentum diffusion coefficient, specifically considering transit-time-damping resonance with fast-mode waves and gyroresonance with Alfvén waves. Utilizing analytic solutions derived from diffusive shock acceleration theory, at the shock location, we introduce a CR spectrum that is either shock-injected or shock-reaccelerated. We then track its temporal evolution along the Lagrangian fluid element in the time domain. The resulting CR spectra are mapped onto a spherical shell configuration to estimate the surface brightness profile of the model radio relics. Turbulent acceleration proves to be a significant factor in delaying the aging of postshock CR electrons, while decaying magnetic fields have marginal impacts due to the dominance of inverse Compton cooling over synchrotron cooling. However, the decay of magnetic fields substantially reduces synchrotron radiation. Consequently, the spatial distribution of the postshock magnetic fields affects the volume-integrated radio spectrum and its spectral index. We demonstrate that the Mach numbers estimated from the integrated spectral index tend to be higher than the actual shock Mach numbers, highlighting the necessity for accurate modeling of postshock magnetic turbulence in interpreting observations of radio relics.

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arXiv2024

Radio surface fluctuations in radio relics

Recent observations have revealed detailed structures of radio relics in a wide range of frequencies. In this work, we perform three-dimensional magnetohydrodynamical simulations of merger shocks propagating through a turbulent magnetized intracluster medium, and employ on-the-fly Lagrangian particles to explore the physical processes originating radio substructures and their appearances in high and low-frequency observations. We employ two cosmic-ray (CR) electron acceleration models: the fresh injection of electrons from the thermal pool and the re-acceleration of mildly relativistic electrons. We use the relative surface brightness fluctuations, $δS_ν$, to define a "degree of patchiness''. We find that: 1) Patchiness is produced if the shock's surface has a distribution of Mach numbers, rather than a single Mach number; 2) Radio relics appear patchier if the Mach number distribution consists of a large percentage of low Mach numbers ($\mathcal{M}\lesssim2.5$); 3) As the frequency increases, the patchiness also becomes larger. Nevertheless, if radio relics are patchy at high frequencies (e.g., 18.6 GHz), they are necessarily also at low frequencies (e.g., 150 MHz); 4) To produce noticeable differences in the patchiness at low and high frequencies, the shock front should have a Mach number spread of $σ_{\mathcal{M}}\gtrsim0.3$-0.4; 5) The amount of the patchiness depends on the Mach number distribution as well as the CR acceleration model. We propose $δS_ν$ as a potential tool for extracting merger shock properties and information about particle acceleration processes at shocks in radio observations.

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arXiv2023

Model Spectrum of Ultra-High-Energy Cosmic Rays Accelerated in FR-I Radio Galaxy Jets

Nearby radio galaxies (RGs) of Fanaroff-Riley Class I (FR-I) are considered possible sites for the production of observed ultra-high-energy cosmic rays (UHECRs). Among those, some exhibit blazar-like inner jets, while others display plume-like structures. We reproduce the flow dynamics of FR-I jets using relativistic hydrodynamic simulations. Subsequently, we track the transport and energization of cosmic ray (CR) particles within the simulated jet flows using Monte Carlo simulations. The key determinant of flow dynamics is the mean Lorentz factor of the jet-spine flow, $\langleΓ\rangle_{\rm{spine}}$. When $\langleΓ\rangle_{\rm{spine}}\gtrsim$ several, the jet spine remains almost unimpeded, but for $\langleΓ\rangle_{\rm{spine}}\lesssim$ a few, substantial jet deceleration occurs. CRs gain energy mainly through diffusive shock acceleration for $E\lesssim1$~EeV and shear acceleration for $E\gtrsim1$~EeV. The time-asymptotic energy spectrum of CRs escaping from the jet can be modeled by a double power law, transitioning from $\sim E^{-0.6}$ to $\sim E^{-2.6}$ around a break energy, $E_{\rm{break}}$, with an exponential cutoff at $E_{\rm{break}}\langleΓ\rangle_{\rm{spine}}^2$. $E_{\rm{break}}$ is limited either by the Hillas confinement condition or by particle escape from the cocoon via fast spatial diffusion. The spectral slopes primarily arise from multiple episodes of shock and relativistic shear accelerations, and the confinement-escape processes within the cocoon. The exponential cutoff is determined by non-gradual shear acceleration that boosts the energy of high-energy CRs by a factor of $\sim \langleΓ\rangle_{\rm{spine}}^2$. We suggest that the model spectrum derived in this work could be employed to investigate the contribution of RGs to the observed population of UHECRs.

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arXiv2023

A Simulation Study of Ultra-relativistic Jets -- III. Particle Acceleration at FR-II Jets

We study the acceleration of ultra-high-energy cosmic rays (UHECRs) at FR-II radio galaxies by performing Monte Carlo simulations for the transport, scattering, and energy change of the CR particles injected into the time-evolving jet flows that are realized through relativistic hydrodynamic (RHD) simulations. Toward that end, we adopt physically motivated models for the magnetic field and particle scattering. By identifying the primary acceleration process among diffusive shock acceleration (DSA), turbulent shear acceleration (TSA), and relativistic shear acceleration (RSA), we find that CRs of $E\lesssim1$ EeV gain energy mainly through DSA in the jet-spine flow and the backflow containing many shocks and turbulence. After they attain $E\gtrsim$ a few EeV, CRs are energized mostly via RSA at the jet-backflow interface, reaching energies well above $10^{20}$ eV. TSA makes a relatively minor contribution. The time-asymptotic energy spectrum of escaping particles is primarily governed by the jet power, shifting to higher energies at more powerful jets. The UHECR spectrum fits well to the double-power-law form, whose break energy, $E_{\rm break}$, corresponds to the size-limited maximum energy. It is close to $d\mathcal{N}/dE\propto E^{-0.5}$ below $E_{\rm break}$, while it follows $d\mathcal{N}/dE\propto E^{-2.6}$ above $E_{\rm break}$, decreasing more gradually than the exponential. The power-law slope of the high-energy end is determined by the energy boosts via non-gradual shear acceleration across the jet-backflow interface and the confinement by the elongated cocoon. We conclude that giant radio galaxies could be major contributors to the observed UHECRs.

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arXiv2022

Cosmic Ray Acceleration and Nonthermal Radiation at Accretion Shocks in the Outer Regions of Galaxy Clusters

Cosmology models predict that external accretion shocks form in the outer region of galaxy clusters due to supersonic gas infall from filaments and voids in the cosmic web. They are characterized by high sonic and Alfvénic Mach numbers, $M_s\sim10-10^2$ and $M_A\sim10^2-10^3$, and propagate into weakly magnetized plasmas of $β\equiv P_g/P_B\gtrsim10^2$. Although strong accretion shocks are expected to be efficient accelerators of cosmic rays (CRs), nonthermal signatures of shock-accelerated CRs around clusters have not been confirmed, and detailed acceleration physics at such shocks has yet to be understood. In this study, we first establish through two-dimensional particle-in-cell simulations that at strong high-$β$ shocks electrons can be pre-energized via stochastic Fermi acceleration owing to the ion-Weibel instability in the shock transition region, possibly followed by injection into diffusive shock acceleration. Hence, we propose that the models derived from conventional thermal leakage injection may be employed for the acceleration of electrons and ions at accretion shocks as well. Applying these analytic models to numerical shock zones identified in structure formation simulations, we estimate nonthermal radiation, such as synchrotron and inverse-Compton (IC) emission due to CR electrons, and $π^0$-decay $γ$-rays due to CR protons, around simulated clusters. Our models with the injection parameter, $Q\approx3.5-3.8$, predict synthetic synchrotron maps, which seem consistent with recent radio observations of the Coma cluster. However, the detection of nonthermal IC X-rays and $γ$-rays from accretion shocks would be quite challenging. We suggest that the proposed analytic models may be adopted as generic recipes for CR production at cosmological shocks.

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arXiv2021

Effects of Forcing on Shocks and Energy Dissipation in Interstellar and Intracluster Turbulences

Observations indicate that turbulence in the interstellar medium (ISM) is supersonic ($M_{\rm turb}\gg1$) and strongly magnetized ($β\sim0.01-1$), while in the intracluster medium (ICM) it is subsonic ($M_{\rm turb}\lesssim1$) and weakly magnetized ($β\sim100$). Here, $M_{\rm turb}$ is the turbulent Mach number and $β$ is the plasma beta. We study the properties of shocks induced in these disparate environments, including the distribution of the shock Mach number, $M_s$, and the dissipation of the turbulent energy at shocks, through numerical simulations using a high-order accurate code based on the WENO scheme. In particular, we investigate the effects of different modes of the forcing that drives turbulence: solenoidal, compressive, and a mixture of the two. In the ISM turbulence, while the density distribution looks different with different forcings, the velocity power spectrum, $P_v$, on small scales exhibits only weak dependence. Hence, the statistics of shocks depend weakly on forcing either. In the ISM models with $M_{\rm turb}\approx10$ and $β\sim0.1$, the fraction of the turbulent energy dissipated at shocks is estimated to be $\sim15~\%$, not sensitive to the forcing mode. In contrast, in the ICM turbulence, $P_v$ as well as the density distribution show strong dependence on forcing. The frequency and average Mach number of shocks are greater for compressive forcing than for solenoidal forcing, so is the energy dissipation. The fraction of ensuing shock dissipation is in the range of $\sim10-35~\%$ in the ICM models with $M_{\rm turb}\approx0.5$ and $β\sim10^6$. The rest of the turbulent energy should be dissipated through turbulent cascade.

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arXiv2021

Electron Preacceleration at Weak Quasi-perpendicular Intracluster Shocks: Effects of Preexisting Nonthermal Electrons

Radio relics in the outskirts of galaxy clusters imply the diffusive shock acceleration (DSA) of electrons at merger-driven shocks with Mach number $M_{s}\lesssim3-4$ in the intracluster medium (ICM). Recent studies have suggested that electron preacceleration and injection, prerequisite steps for DSA, could occur at supercritical shocks with $M_{s}\gtrsim2.3$ in the ICM, thanks to the generation of multiscale waves by microinstabilities such as the Alfvén ion cyclotron (AIC) instability, the electron firehose instability (EFI), and the whistler instability (WI). On the other hand, some relics are observed to have subcritical shocks with $M_{s}\lesssim2.3$, leaving DSA at such weak shocks as an outstanding problem. Reacceleration of preexisting nonthermal electrons has been contemplated as one of possible solutions for that puzzle. To explore this idea, we perform Particle-in-Cell (PIC) simulations for weak quasi-perpendicular shocks in high-$β$ ($β=P_{\rm gas}/P_{B}$) plasmas with power-law suprathermal electrons in addition to Maxwellian thermal electrons. We find that suprathermal electrons enhance the excitation of electron-scale waves via the EFI and WI. However, they do not affect the ion reflection and the ensuing generation of ion-scale waves via the AIC instability. The presence of ion-scale waves is the key for the preacceleration of electrons up to the injection momentum, thus the shock criticality condition for electron injection to DSA is preserved. Based on the results, we conclude that preexisting nonthermal electrons in the preshock region alone would not resolve the issue of electron preacceleration at subcritical ICM shocks.

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arXiv2021

Re-acceleration of Cosmic Ray Electrons by Multiple ICM Shocks

Radio relics could be generated by multiple shocks induced in the turbulent intracluster medium during galaxy mergers. Kang (2021) demonstrated that the re-acceleration of cosmic ray (CR) protons via diffusive shock acceleration (DSA) by multiple shocks could enhance the acceleration efficiency and flatten the CR spectrum, compared to a single episode of DSA. Here we examine the CR electron acceleration through multiple re-acceleration by considering energy losses and decompression of the particle distribution and magnetic fields in the postshock region between consecutive shock passages. We find that the accumulated effects of repeated re-acceleration are significant, if preceding shocks are stronger than the last shock and the shock passage interval is $\lesssim20$ Myr. In such cases, both the CR spectrum and the ensuing radiation spectrum behind the last shock are enhanced and become flatter than the canonical DSA power-law forms. As a result, the shock Mach number estimated from radio observations tends be higher than the actual Mach number of the last shock. Thus, multiple episodes of DSA may explain the enhanced acceleration efficiency for CR electrons and the discrepancy of shock Mach numbers, $M_{\rm X} \lesssim M_{\rm rad}$, inferred for some observed radio relics.

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arXiv2021

A Simulation Study of Ultra-relativistic Jets -- II. Structures and Dynamics of FR-II Jets

We study the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, through three-dimensional relativistic hydrodynamic (RHD) simulations. To that end, we have developed a high-order accurate RHD code, equipped with a weighted essentially non-oscillatory (WENO) scheme and a realistic equation of state (Seo et al. 2021, Paper I). Using the code, we explore a set of jet models with the parameters relevant to FR-II radio galaxies. We confirm that the overall jet morphology is primarily determined by the jet power, and the jet-to-background density and pressure ratios play secondary roles. Jets with higher powers propagate faster, resulting in more elongated structures, while those with lower powers produce more extended cocoons. Shear interfaces in the jet are dynamically unstable, and hence, chaotic structures with shocks and turbulence develop. We find that the fraction of the jet-injected energy dissipated through shocks and turbulence is greater in less powerful jets, although the actual amount of the dissipated energy is larger in more powerful jets. In lower power jets, the backflow is dominant in the energy dissipation owing to the broad cocoon filled with shocks and turbulence. In higher power jets, by contrast, both the backflow and jet spine flow are important for the energy dissipation. Our results imply that different mechanisms, such as diffusive shock acceleration, shear acceleration, and stochastic turbulent acceleration, may be involved in the production of ultra-high energy cosmic rays in FR-II radio galaxies.

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arXiv2021

A Simulation Study of Ultra-Relativistic Jets -- I. A New Code for Relativistic Hydrodynamics

In an attempt to investigate the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, we have developed a new special relativistic hydrodynamic (RHD) code in the Cartesian coordinates, based on the weighted essentially non-oscillatory (WENO) scheme. It is a finite difference scheme of high spatial accuracy, which has been widely employed for solving hyperbolic systems of conservation equations. The code is equipped with different WENO versions, such as the 5th-order accurate WENO-JS (Jiang & Shu 1996), WENO-Z, and WENO-ZA, and different time integration methods, such as the 4th-order accurate Runge-Kutta (RK4) and strong stability preserving RK (SSPRK), as well as the implementation of the equations of state (EOSs) that closely approximate the EOS of the single-component perfect gas in relativistic regime. In addition, it incorporates a high-order accurate averaging of fluxes along the transverse directions to enhance the accuracy of multi-dimensional problems, and a modification of eigenvalues for the acoustic modes to effectively control the carbuncle instability. Through extensive numerical tests, we assess the accuracy and robustness of the code, and choose WENO-Z, SSPRK, and the EOS suggested in Ryu et al. (2006) as the fiducial setup for simulations of ultra-relativistic jets. The results of our study of ultra-relativistic jets using the code is reported in an accompanying paper (Seo et al. 2021, Paper II).

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arXiv2021

Diffusive Shock Acceleration by Multiple Weak Shocks

The intracluster medium (ICM) is expected to experience on average about three passages of weak shocks with low sonic Mach numbers, $M\lesssim 3$, during the formation of galaxy clusters. Both protons and electrons could be accelerated to become high energy cosmic rays (CRs) at such ICM shocks via diffusive shock acceleration (DSA). We examine the effects of DSA by multiple shocks on the spectrum of accelerated CRs by including {\it in situ} injection/acceleration at each shock, followed by repeated re-acceleration at successive shocks in the test-particle regime. For simplicity, the accelerated particles are assumed to undergo adiabatic decompression without energy loss and escape from the system, before they encounter subsequent shocks. We show that in general the CR spectrum is flattened by multiple shock passages, compared to a single episode of DSA, and that the acceleration efficiency increases with successive shock passages. However, the decompression due to the expansion of shocks into the cluster outskirts may reduce the amplification and flattening of the CR spectrum by multiple shock passages. The final CR spectrum behind the last shock is determined by the accumulated effects of repeated re-acceleration by all previous shocks, but it is relatively insensitive to the ordering of the shock Mach numbers. Thus multiple passages of shocks may cause the slope of the CR spectrum to deviate from the canonical DSA power-law slope of the current shock.

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arXiv2021

Effects of Multi-scale Plasma Waves on Electron Preacceleration at Weak Quasi-perpendicular Intracluster Shocks

Radio relics associated with merging galaxy clusters indicate the acceleration of relativistic electrons in merger-driven shocks with low sonic Mach numbers ($M_{\rm s}\lesssim 3$) in the intracluster medium (ICM). Recent studies have suggested that electron injection to diffusive shock acceleration (DSA) could take place through the so-called Fermi-like acceleration in the shock foot of $β=P_{\rm gas}/P_{\rm B}\approx 20-100$ shocks and the stochastic shock drift acceleration (SSDA) in the shock transition of $β\approx 1-5$ shocks. Here we explore how the SSDA can facilitate electron preacceleration in weak quasi-perpendicular ($Q_{\perp}$) shocks in $β\approx 20-100$ plasmas by performing particle-in-cell simulations in the two-dimensional domain large enough to encompass ion-scale waves. We find that in supercritical shocks with $M_{\rm s}\gtrsim M_{\rm AIC}^*\sim 2.3$, multi-scale waves are excited by the ion and electron temperature anisotropies in the downstream of the shock ramp, and that through stochastic pitch-angle scattering off the induced waves, electrons are confined in the shock transition for an extended period. Gaining energy through the gradient-drift along the motional electric field, electrons could be preaccelerated all the way to injection to DSA at such ICM shocks. Our findings imply that the electron DSA process at weak ICM shocks could explain the origin of radio relics. However, a further investigation of electron acceleration at subcritical shocks with $M_{\rm s}< 2.3$ is called for, since the Mach numbers of some observed radio relic shocks derived from radio or X-ray observations are as low as $M_{\rm s}\sim 1.5$.

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arXiv2021

Microinstabilities in the Transition Region of Weak Quasi-Perpendicular Intracluster Shocks

Microinstabilities play important roles in both entropy generation and particle acceleration in collisionless shocks. Recent studies have suggested that in the transition zone of quasi-perpendicular ($Q_{\perp}$) shocks in the high-beta ($β=P_{\rm gas}/P_{\rm B}$) intracluster medium (ICM), the ion temperature anisotropy due to the reflected-gyrating ions could trigger the Alfvén ion cyclotron (AIC) instability and the ion-mirror instability, while the electron temperature anisotropy induced by magnetic field compression could excite the whistler instability and the electron-mirror instability. Adopting the numerical estimates for ion and electron temperature anisotropies found in particle-in-cell (PIC) simulations of $Q_{\perp}$-shocks with sonic Mach numbers, $M_{\rm s}=2-3$, we carry out a linear stability analysis for these microinstabilities. The kinetic properties of the microinstabilities and the ensuing plasma waves on both ion and electron scales are described for wide ranges of parameters, including the dependence on $β$ and the ion-to-electron mass ratio. In addition, the nonlinear evolution of induced plasma waves are examined by performing 2D PIC simulations with periodic boundary conditions. We find that for $β\approx 20-100$, the AIC instability could induce ion-scale waves and generate shock surface ripples in supercritical shocks above the AIC critical Mach number, $M_{\rm AIC}^{*} \approx 2.3$. Also electron-scale waves are generated primarily by the whistler instability in these high-$β$ shocks. The resulting multi-scale waves from electron to ion scales are thought to be essential in electron injection to the diffusive shock acceleration mechanism in $Q_{\perp}$-shocks in the ICM.

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