Shocks In Galaxy Clusters Research Articles

Electron Injection via Modified Diffusive Shock Acceleration in High-Mach-number Collisionless Shocks

The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters.

Electron Acceleration at Rippled Low-mach-number Shocks in High-beta Collisionless Cosmic Plasmas

Abstract Using large-scale fully kinetic two-dimensional particle-in-cell simulations, we investigate the effects of shock rippling on electron acceleration at low-Mach-number shocks propagating in high-β plasmas, in application to merger shocks in galaxy clusters. We find that the electron-acceleration rate increases considerably when the rippling modes appear. The main acceleration mechanism is stochastic shock-drift acceleration, in which electrons are confined at the shock by pitch-angle scattering off turbulence and gain energy from the motional electric field. The presence of multiscale magnetic turbulence at the shock transition and the region immediately behind the main shock overshoot is essential for electron energization. Wide-energy non-thermal electron distributions are formed both upstream and downstream of the shock. The maximum energy of the electrons is sufficient for their injection into diffusive shock acceleration. We show for the first time that the downstream electron spectrum has a power-law form with index p ≈ 2.5, in agreement with observations.

Discovering the most elusive radio relic in the sky: diffuse shock acceleration caught in the act?

ABSTRACT The origin of radio relics is usually explained via diffusive shock acceleration (DSA) or re-acceleration of electrons at/from merger shocks in galaxy clusters. The case of acceleration is challenged by the low predicted efficiency of low Mach number merger shocks, unable to explain the power observed in most radio relics. In this letter, we present the discovery of a new giant radio relic around the galaxy cluster Abell 2249 ($z$ = 0.0838) using Low-Frequency Array (LOFAR). It is special since it has the lowest surface brightness of all known radio relics. We study its radio and X-ray properties combining LOFAR data with uGMRT, JVLA, and XMM. This object has a total power of $L_{1.4\rm\, GHz}=4.1\pm 0.8 \times 10^{23}$ W Hz−1 and integrated spectral index α = 1.15 ± 0.23. We infer for this radio relic a lower bound on the magnetization of $B\ge 0.4\, \mu$G, a shock Mach number of $\mathcal {M}\approx 3.79$, and a low acceleration efficiency consistent with DSA. This result suggests that a missing population of relics may become visible, thanks to the unprecedented sensitivity of the new generation of radio telescopes.

Encounters of merger and accretion shocks in galaxy clusters and their effects on intracluster medium

ABSTRACT Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of ‘runaway merger shocks’, which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster centre. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius), affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper. We show examples of such MA-shocks in one-dimensioanal (1D) and three-dimensional (3D) simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a ‘flower-like’ morphology. In 3D, MA-shocks occupy space between the dense accreting filaments. (2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius.

Gamma-Ray and Neutrino Emissions due to Cosmic-Ray Protons Accelerated at Intracluster Shocks in Galaxy Clusters

Abstract We examine the cosmic-ray protons (CRp) accelerated at collisionless shocks in galaxy clusters using cosmological structure formation simulations. We find that in the intracluster medium (ICM) within the virial radius of simulated clusters, only ∼7% of shock kinetic energy flux is dissipated by the shocks that are expected to accelerate CRp—that is, supercritical, quasi-parallel (Q ∥) shocks with sonic Mach number M s ≥ 2.25. The rest is dissipated at subcritical shocks and quasi-perpendicular shocks, both of which may not accelerate CRp. Adopting the diffusive shock acceleration (DSA) model recently presented in Ryu et al., we quantify the DSA of CRp in simulated clusters. The average fraction of the shock kinetic energy transferred to CRp via DSA is assessed at ∼(1–2) × 10−4. We also examine the energization of CRp through reacceleration using a model based on the test-particle solution. Assuming that the ICM plasma passes through shocks three times on average through the history of the universe and that CRp are reaccelerated only at supercritical Q ∥-shocks, the CRp spectrum flattens by ∼0.05–0.1 in slope and the total amount of CRp energy increases by ∼40%–80% from reacceleration. We then estimate diffuse γ-ray and neutrino emissions, resulting from inelastic collisions between CRp and thermal protons. The predicted γ-ray emissions from simulated clusters lie mostly below the upper limits set by Fermi-LAT for observed clusters. The neutrino fluxes toward nearby clusters would be ≲10−4 of the IceCube flux at E ν = 1 PeV and ≲10−6 of the atmospheric neutrino flux in the energy range of E ν ≤ 1 TeV.

Diffusive shock acceleration of cosmic rays in low-Mach galaxy cluster shocks.

Astrophysical shocks are known to accelerate particles to high relativistic velocities. This process requires the particles to repeatedly cross the shock, a process that can only occur if the particle is reflected by the local magnetic field. Such particles are observed on Earth as cosmic rays. This phenomenon has been studied in considerable detail for high-Mach shocks, such as the shocks that occur in colliding stellar winds and supernova explosions, but remains relatively unexplored for low-Mach shocks, such as the shocks of colliding clusters of galaxies. Recent simulations using the particle-in-cell (PIC) method have shown that, depending on the exact Mach number, even low-Mach shocks can accelerate charged particles to the point where they start to deviate from the thermal velocity distribution. However, the computationally intensive nature of the PIC calculations makes it difficult to continue the simulations to determine whether the particles can reach relativistic speeds. We now present new simulations, using a combined PIC and magnetohydrodynamics (MHD) technique. This model, which takes advantage of the computational efficiency of MHD, allows us to simulate a much larger physical volume and study the behaviour of the particles over a longer period of time in order to determine to what extent the acceleration process continues and whether these shocks are capable of contributing to the cosmic ray spectrum.

Using Combined PIC and MHD to Model Particle Acceleration in Galaxy Cluster Shocks

Using Combined PIC and MHD to Model Particle Acceleration in Galaxy Cluster Shocks

Standoff distance of bow shocks in galaxy clusters as proxy for Mach number

X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre- (post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre- and post-merger stages.

Detection of gamma-ray emission from the Coma cluster with Fermi Large Area Telescope and tentative evidence for an extended spatial structure

Many galaxy clusters have giant halos of non-thermal radio emission, indicating the presence of relativistic electrons in the clusters. Relativistic protons may also be accelerated by merger and/or accretion shocks in galaxy clusters. These cosmic-ray (CR) electrons and/or protons are expected to produce gamma-rays through inverse-Compton scatterings or inelastic $pp$ collisions respectively. Despite of intense efforts in searching for high-energy gamma-ray emission from galaxy clusters, conclusive evidence is still missing so far. Here we report the discovery of $\ge 200$ MeV gamma-ray emission from the Coma cluster direction with an unbinned likelihood analysis of the 9 years of {\it Fermi}-LAT Pass 8 data. The gamma-ray emission shows a spatial morphology roughly coincident with the giant radio halo, with an apparent excess at the southwest of the cluster. Using the test statistic analysis, we further find tentative evidence that the gamma-ray emission at the Coma center is spatially extended. The extended component has an integral energy flux of $\sim 2\times 10^{-12}{\rm \ erg\ cm^{-2}\ s^{-1}}$ in the energy range of 0.2 - 300 GeV and the spectrum is soft with a photon index of $\simeq-2.7$. Interpreting the gamma-ray emission as arising from CR proton interaction, we find that the volume-averaged value of the CR to thermal pressure ratio in the Coma cluster is about $\sim 2\%$. Our results show that galaxy clusters are likely a new type of GeV gamma-ray sources, and they are probably also giant reservoirs of CR protons.

Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions

Abstract Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. In this work, the second of a series, we investigate the efficiency of irreversible electron heating in perpendicular low Mach number shocks, by means of two-dimensional particle-in-cell simulations. We consider values of plasma beta (the ratio of thermal and magnetic pressures) in the range 4 ≲ β p0 ≲ 32, and sonic Mach number (the ratio of shock speed to pre-shock sound speed) in the range 2 ≲ M s ≲ 5, as appropriate for galaxy cluster shocks. As shown in Paper I, magnetic field amplification—induced by shock compression of the pre-shock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy—can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We find that the post-shock electron temperature T e2 exceeds the adiabatic expectation by an amount (here, T e0 is the pre-shock temperature), which depends only weakly on the plasma beta over the range 4 ≲ β p0 ≲ 32 that we have explored, as well as on the proton-to-electron mass ratio (the coefficient of ≃0.044 is measured for our fiducial , and we estimate that it will decrease to ≃0.03 for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev–Zel’dovich effect) and at X-ray frequencies.

Electron Heating in Low-Mach-number Perpendicular Shocks. I. Heating Mechanism

Abstract Recent X-ray observations of merger shocks in galaxy clusters have shown that the postshock plasma has two temperatures, with the protons hotter than the electrons. By means of two-dimensional particle-in-cell simulations, we study the physics of electron irreversible heating in low-Mach-number perpendicular shocks, for a representative case with sonic Mach number of 3 and plasma beta of 16. We find that two basic ingredients are needed for electron entropy production: (1) an electron temperature anisotropy, induced by field amplification coupled to adiabatic invariance; and (2) a mechanism to break the electron adiabatic invariance itself. In shocks, field amplification occurs at two major sites: at the shock ramp, where density compression leads to an increase of the frozen-in field; and farther downstream, where the shock-driven proton temperature anisotropy generates strong proton cyclotron and mirror modes. The electron temperature anisotropy induced by field amplification exceeds the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance and allows for efficient entropy production. For our reference run, the postshock electron temperature exceeds the adiabatic expectation by , resulting in an electron-to-proton temperature ratio of . We find that the electron heating efficiency displays only a weak dependence on mass ratio (less than drop, as we increase the mass ratio from up to ). We develop an analytical model of electron irreversible heating and show that it is in excellent agreement with our simulation results.

The case for electron re-acceleration at galaxy cluster shocks

On the largest scales, the Universe consists of voids and filaments making up the cosmic web. Galaxy clusters are located at the knots in this web, at the intersection of filaments. Clusters grow through accretion from these large-scale filaments and by mergers with other clusters and groups. In a growing number of galaxy clusters, elongated Mpc-size radio sources have been found, so-called radio relics. These relics are thought to trace relativistic electrons in the intracluster plasma accelerated by low-Mach number collisionless shocks generated by cluster-cluster merger events. A long-standing problem is how low-Mach number shocks can accelerate electrons so efficiently to explain the observed radio relics. Here we report on the discovery of a direct connection between a radio relic and a radio galaxy in the merging galaxy cluster Abell 3411-3412. This discovery indicates that fossil relativistic electrons from active galactic nuclei are re-accelerated at cluster shocks. It also implies that radio galaxies play an important role in governing the non-thermal component of the intracluster medium in merging clusters.

Electron and proton acceleration efficiency by merger shocks in galaxy clusters

Radio relics in galaxy clusters are associated with powerful shocks that (re) accelerate relativistic electrons. It is widely believed that the acceleration proceeds via diffusive shock acceleration. In the framework of thermal leakage, the ratio of the energy in relativistic electrons to the energy in relativistic protons should be smaller than K-e/p similar to 10(-2). The relativistic protons interact with the thermal gas to produce gamma-rays in hadronic interactions. Combining observations of radio relics with upper limits from gamma-ray observatories can constrain the ratio K-e/p. In this work, we selected 10 galaxy clusters that contain double radio relics, and derive new upper limits from the stacking of gamma-ray observations by Fermi. We modelled the propagation of shocks using a semi-analytical model, where we assumed a simple geometry for shocks and that cosmic ray protons are trapped in the intracluster medium. Our analysis shows that diffusive shock acceleration has difficulties in matching simultaneously the observed radio emission and the constraints imposed by Fermi, unless the magnetic field in relics is unrealistically large (>> 10 mu G). In all investigated cases (also including realistic variations of our basic model and the effect of re-acceleration), the mean emission of the sample is of the order of the stacking limit by Fermi, or larger. These findings put tension on the commonly adopted model for the powering of radio relics, and imply that the relative acceleration efficiency of electrons and protons is at odds with predictions of diffusive shock acceleration, requiring K-e/p >= 10 - 10(-2).

NON-THERMAL ELECTRON ACCELERATION IN LOW MACH NUMBER COLLISIONLESS SHOCKS. II. FIREHOSE-MEDIATED FERMI ACCELERATION AND ITS DEPENDENCE ON PRE-SHOCK CONDITIONS

Electron acceleration to non-thermal energies is known to occur in low Mach number (M<5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves, that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (>20) at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

A CRITICAL SHOCK MACH NUMBER FOR PARTICLE ACCELERATION IN THE ABSENCE OF PRE-EXISTING COSMIC RAYS: $M=\sqrt{5}$

It is shown that, under some generic assumptions, shocks cannot accelerate particles unless the overall shock Mach number exceeds a critical value M > sqrt(5). The reason is that for M <= sqrt(5) the work done to compress the flow in a particle precursor requires more enthalpy flux than the system can sustain. This lower limit applies to situations without significant magnetic field pressure. In case that the magnetic field pressure dominates the pressure in the unshocked medium, i.e. for low plasma beta, the resistivity of the magnetic field makes it even more difficult to fulfil the energetic requirements for the formation of shock with an accelerated particle precursor and associated compression of the upstream plasma. We illustrate the effects of magnetic fields for the extreme situation of a purely perpendicular magnetic field configuration with plasma beta = 0, which gives a minimum Mach number of M = 5/2. The situation becomes more complex, if we incorporate the effects of pre-existing cosmic rays, indicating that the additional degree of freedom allows for less strict Mach number limits on acceleration. We discuss the implications of this result for low Mach number shock acceleration as found in solar system shocks, and shocks in clusters of galaxies.

Electron-Ion Temperature Equilibration in Collisionless Shocks: The Supernova Remnant-Solar Wind Connection

Collisionless shocks are loosely defined as shocks where the transition between pre-and post-shock states happens on a length scale much shorter than the collisional mean free path. In the absence of collision to enforce thermal equilibrium post-shock, electrons and ions need not have the same temperatures. While the acceleration of electrons for injection into shock acceleration processes to produce cosmic rays has received considerable attention, the related problem of the shock heating of quasi-thermal electrons has been relatively neglected. In this paper we review that state of our knowledge of electron heating in astrophysical shocks, mainly associated with supernova remnants (SNRs), shocks in the solar wind associated with the terrestrial and Saturnian bowshocks, and galaxy cluster shocks. The solar wind and SNR samples indicate that the ratio of electron temperature to ion temperature declines with increasing shock speed or Alfvenic Mach number. We discuss the extent to which such behavior can be understood via cosmic ray-generated waves in a shock precursor, which then subsequently damp by heating electrons. Finally, we speculate that a similar mechanism may be at work for both solar wind and SNR shocks.

Magnetic field amplification by shocks in galaxy clusters: application to radio relics

Merger shocks induce turbulence in the intra-cluster medium (ICM), and, under some circumstances, accelerate electrons to relativistic velocities to form so-called radio relics. Relics are mostly found at the periphery of galaxy clusters and appear to have magnetic fields at the microGauss level. Here we investigate the possible origins of these magnetic fields. Turbulence produced by the shock itself cannot explain the magnitude of these fields. However, we argue that if the turbulent pressure support in the ICM upstream of the merger shock is of the order of 10 to 30 percent of the total pressure on scales of a few times 100 kpc, then vorticity generated by compressive and baroclinic effects across the shock discontinuity can lead to a sufficient amplification of the magnetic field. Compressional amplification can explain the large polarisation of the radio emission more easily than dynamo turbulent amplification. Finally, clumping of the ICM is shown to have a negligible effect on magnetic field amplification.

RELATIVISTIC ELECTRON SHOCK DRIFT ACCELERATION IN LOW MACH NUMBER GALAXY CLUSTER SHOCKS

An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters such as CIZA J2242.8+5301 which has well defined radio relics.

CANGAROO-III SEARCH FOR TeV GAMMA RAYS FROM TWO CLUSTERS OF GALAXIES

Because accretion and merger shocks in clusters of galaxies may accelerate particles to high energies, clusters are candidate sites for the origin of ultra-high-energy (UHE) cosmic rays. A prediction was presented for gamma-ray emission from a cluster of galaxies at a detectable level with the current generation of imaging atmospheric Cherenkov telescopes. The gamma-ray emission was produced via inverse Compton upscattering of cosmic microwave background photons by electron–positron pairs generated by collisions of UHE cosmic rays in the cluster. We observed two clusters of galaxies, Abell 3667 and Abell 4038, searching for very high energy gamma-ray emission with the CANGAROO-III atmospheric Cherenkov telescope system in 2006. The analysis showed no significant excess around these clusters, yielding upper limits on the gamma-ray emission. From a comparison of the upper limit for the northwest radio relic region of Abell 3667 with a model prediction, we derive a lower limit for the magnetic field of the region of ∼0.1 μG. This shows the potential of gamma-ray observations in studies of the cluster environment. We also discuss the flux upper limit from cluster center regions using a model of gamma-ray emission from neutral pions produced in hadronic collisions of cosmic-ray protons with the intracluster medium. The derived upper limit of the cosmic-ray energy density within this framework is an order of magnitude higher than that of our Galaxy.

ACCRETION SHOCKS IN CLUSTERS OF GALAXIES AND THEIR SZ SIGNATURE FROM COSMOLOGICAL SIMULATIONS

Cold dark matter (CDM) hierarchical structure formation models predict the existence of large-scale accretion shocks between the virial and turnaround radii of clusters of galaxies. Kocsis et al. (2005) suggest that the Sunyaev-Zel'dovich (SZ) signal associated with such shocks might be observable with the next generation radio interferometer, ALMA. We study the three--dimensional distribution of accretion shocks around individual clusters of galaxies drawn from adaptive mesh refinement (AMR) and smoothed particle hydrodynamics (SPH) simulations of LCDM (dark energy dominated CDM) models. In relaxed clusters, we find two distinct sets of shocks. One set ("virial shocks"), with Mach numbers of 2.5-4, is located at radii 0.9-1.3 Rvir, where Rvir is the spherical infall estimate of the virial radius, covering about 40-50% of the total surface area around clusters at these radii. Another set of stronger shocks ("external shocks") is located farther out, at about 3 Rvir, with large Mach numbers (~100), covering about 40-60% of the surface area. We simulate SZ surface brightness maps of relaxed massive galaxy clusters drawn from high resolution AMR runs, and conclude that ALMA should be capable of detecting the virial shocks in massive clusters of galaxies. More simulations are needed to improve estimates of astrophysical noise and to determine optimal observational strategies.