Diffusive Shock Acceleration and Magnetic Field Amplification

Nonthermal radiation from supernova remnants (SNRs) provides observational evidence and constraints on the diffusive shock acceleration (DSA) hypothesis for the origins of Galactic cosmic rays (CRs). Recently it has been recognized that a variety of plasma wave-particle interactions operate at astrophysical shocks and the detailed outcomes of DSA are governed by their complex and nonlinear interrelationships. Here we calculate the energy spectra of CR protons and electrons accelerated at Type Ia SNRs, using time-dependent, DSA simulations with phenomenological models for magnetic field amplification due to CR streaming instabilities, Alf<TEX>$\acute{e}$</TEX>enic drift, and free escape boundary. We show that, if scattering centers drift with the Alf<TEX>$\acute{e}$</TEX>en speed in the amplified magnetic fields, the CR energy spectrum is steepened and the acceleration efficiency is significantly reduced at strong CR modified SNR shocks. Even with fast Afv<TEX>$\acute{e}$</TEX>nic drift, DSA can still be efficient enough to develop a substantial shock precursor due to CR pressure feedback and convert about 20-30% of the SN explosion energy into CRs. Since the high energy end of the CR proton spectrum is composed of the particles that are injected in the early stages, in order to predict nonthermal emissions, especially in X-ray and <TEX>${\gamma}-ray$</TEX> bands, it is important to follow the time dependent evolution of the shock dynamics, CR injection process, magnetic field amplification, and particle escape. Thus it is crucial to understand the details of these plasma interactions associated with collisionless shocks in successful modeling of nonlinear DSA.

Neutron star mergers (NSMs) eject energetic subrelativistic dynamical ejecta into circumbinary media. Analogous to supernovae and supernova remnants, the NSM dynamical ejecta are expected to produce nonthermal emission by electrons accelerated at a shock wave. In this paper, we present the expected radio and X-ray signals by this mechanism, taking into account nonlinear diffusive shock acceleration (DSA) and magnetic field amplification. We suggest that the NSM is unique as a DSA site, where the seed relativistic electrons are abundantly provided by the decays of r-process elements. The signal is predicted to peak at a few 100–1000 days after the merger, determined by the balance between the decrease of the number of seed electrons and the increase of the dissipated kinetic energy, due to the shock expansion. While the resulting flux can ideally reach the maximum flux expected from near-equipartition, the available kinetic energy dissipation rate of the NSM ejecta limits the detectability of such a signal. It is likely that the radio and X-ray emission are overwhelmed by other mechanisms (e.g., an off-axis jet) for an observer placed in a jet direction (i.e., for GW170817). However, for an off-axis observer, to be discovered once a number of NSMs are identified, the dynamical ejecta component is predicted to dominate the nonthermal emission. While the detection of this signal is challenging even with near-future facilities, this potentially provides a robust probe of the creation of r-process elements in NSMs.

The observed bimodality in radio luminosity in galaxy clusters is puzzling. We investigate the possibility that cosmic-ray (CR) streaming in the intra-cluster medium can 'switch off' hadronically induced radio and gamma-ray emission. For self-confined CRs, this depends on the source of MHD wave damping: if only non-linear Landau damping operates, then CRs stream on the slow Alfvenic timescale, but if turbulent wave damping operates, super-Alfvenic streaming is possible. As turbulence increases, it promotes outward streaming more than it enables inward turbulent advection. Curiously, the CR flux is independent of $\nabla f$ (as long as it is non-zero) and depends only on plasma parameters; this enables radio halos with flat inferred CR profiles to turn off. We perform 1D time-dependent calculations of a radio mini-halo (Perseus) and giant radio halo (Coma) and find that both diminish in radio luminosity by an order of magnitude in several hundred Myr, given plausible estimates for the magnetic field in the outskirts of the cluster. Due to the energy dependence of CR streaming, spectral curvature develops, and radio halos turn off more slowly at low frequencies -- properties consistent with observations. Similarly, CR streaming rapidly turns off gamma-ray emission at the high-energies probed by Cherenkov telescopes, but not at the low energies probed by Fermi. CR mediated wave-heating of the ICM is unaffected, as it is dominated by ~GeV CRs which stream Alfvenically.

Supernova remnants (SNRs) are believed to be the source of Galactic cosmic rays (CRs). SNR shocks accelerate CR protons and electrons which reveal key insights into the non-thermal physics by means of their synchrotron and γ-ray emission. The remnant SN 1006 is an ideal particle acceleration laboratory because it is observed across all electromagnetic wavelengths from radio to γ-rays. We perform 3D magnetohydrodynamics (MHD) simulations where we include CR protons and follow the CR electron spectrum. By matching the observed morphology and non-thermal spectrum of SN 1006 in radio, X-rays, and γ-rays, we gain new insight into CR electron acceleration and magnetic field amplification. (1) We show that a mixed leptonic–hadronic model is responsible for the γ-ray radiation: while leptonic inverse-Compton emission and hadronic pion-decay emission contribute equally at GeV energies observed by Fermi, TeV energies observed by imaging air Cherenkov telescopes are hadronically dominated. (2) We show that quasi-parallel acceleration (i.e. when the shock propagates at a narrow angle to the upstream magnetic field) is preferred for CR electrons and that the electron acceleration efficiency of radio-emitting GeV electrons at quasi-perpendicular shocks is suppressed at least by a factor ten. This precludes extrapolation of current 1D plasma particle-in-cell simulations of shock acceleration to realistic SNR conditions. (3) To match the radial emission profiles and the γ-ray spectrum, we require a volume-filling, turbulently amplified magnetic field and that the Bell-amplified magnetic field is damped in the immediate post-shock region. Our work connects microscale plasma physics simulations to the scale of SNRs.

The interstellar medium and ejecta of supernova are not always completely ionized. Such partially ionized plasmas are though to be unsuitable for cosmic ray acceleration. In order to study shock structures of collisionless shocks in partially ionized plasmas, we perform two-dimensional hybrid simulations. We find that large density fluctuations and large magnetic fields fluctuations are generated both in the upstream and downstream regions for high Alfven Mach number shocks. For the shock velocity vs = 1333 km/s = 57 vA, the strong turbulence is generated in the downstream region by the upstream density fluctuations and the downstream magnetic field is amplified over 30 times the initial upstream magnetic field. Observed shock structures suggest that diffusive shock acceleration can operate at perpendicular shocks propagating into partially ionized plasmas in real three-dimensional systems.

The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical E −2 spectrum predicted by the standard diffusive shock acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The γ-ray “probes” of the acceleration spectra of CRs on the spot, inside the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the combination of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface, and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two “polar caps” of a spherical shock where the local magnetic field is within ≃45° to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at an expanding shock surface with an arbitrary energy dependence of particle diffusivity κ. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where κ cancels out.

Collisionless shocks with low sonic Mach numbers, , 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-β (≈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 , a sufficient fraction of incoming protons is 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 , 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.

It is largely accepted that Galactic cosmic rays, which pervade the interstellar medium, originate by means of shock waves in supernova remnants. Cosmic rays activate the rich chemistry that is observed in a molecular cloud and they also regulate its collapse timescale, determining the efficiency of star and planet formation, but they cannot penetrate up to the densest part of a molecular cloud, where the formation of stars is expected, because of energy loss processes and magnetic field deflections. Recently, observations towards young protostellar systems showed a surprisingly high value of the ionisation rate, the main indicator of the presence of cosmic rays in molecular cloud. Synchrotron emission, the typical feature of relativistic electrons, has been also detected towards the bow shock of a T Tauri star. Nevertheless, the origin of these signatures peculiar to accelerated particles is still puzzling. Here we show that particle acceleration can be driven by shock waves occurring in protostars through the diffusive shock acceleration mechanism. We find that shocks in protostellar jets and on the protostellar surface can be strong accelerators of thermal particles, which can be easily boosted up to relativistic energies. Our results demonstrate the possibility of accelerating particles during the early phase of a proto-Solar-like system and can be used as the argument to support available observations. The existence of an internal source of energetic particles can have a strong and unforeseen impact over the stellar and planet formation process as well as on the formation of pre-biotic molecules. Finally, I will discuss the challenges for current and future telescopes such as ALMA, SKA, and CTA.

The amplification of primordial magnetic fields via a small-scale turbulent dynamo during structure formation might be able to explain the observed magnetic fields in galaxy clusters. The magnetization of more tenuous large-scale structures such as cosmic filaments is more uncertain, as it is challenging for numerical simulations to achieve the required dynamical range. In this work, we present magnetohydrodynamical cosmological simulations on large uniform grids to study the amplification of primordial seed fields in the intracluster medium (ICM) and in the warm–hot-intergalactic medium (WHIM). In the ICM, we confirm that turbulence caused by structure formation can produce a significant dynamo amplification, even if the amplification is smaller than what is reported in other papers. In the WHIM inside filaments, we do not observe significant dynamo amplification, even though we achieve Reynolds numbers of Re ∼ 200–300. The maximal amplification for large filaments is of the order of ∼100 for the magnetic energy, corresponding to a typical field of a few ∼nG starting from a primordial weak field of 10−10 G (comoving). In order to start a small-scale dynamo, we found that a minimum of ∼102 resolution elements across the virial radius of galaxy clusters was necessary. In filaments we could not find a minimum resolution to set off a dynamo. This stems from the inefficiency of supersonic motions in the WHIM in triggering solenoidal modes and small-scale twisting of magnetic field structures. Magnetic fields this small will make it hard to detect filaments in radio observations.

It is now well established that cosmic rays (CRs) are accelerated at collisionless shocks through diffusive shock acceleration. However, some key physical processes, such as thermal leakage injection, self-excitation and dissipation of waves, and resonant scatterings of particles by those waves are nonlinear and not fully understood yet. Hence it is not possible to make precise quantitative predictions for the particle spectrum accelerated at shocks from first principles. If the fraction of particles injected into the CR population is smaller than 10−4, the CR acceleration efficiency is low and so the test-particle solutions are justified. At moderately strong shocks (M0≳5) with higher injection fractions, the shock structure is significantly modified by nonlinear feedback of CRs. According to time-dependent kinetic simulations of CR modified shocks, the precursor and subshock transition approach a time-asymptotic state, and then evolve in an approximately self-similar fashion, depending only on the similarity variable, x/(ust). During this self-similar stage, the CR spectrum at the subshock maintains a characteristic form as it evolves: the sum of two power-laws with the slopes determined by the subshock and total compression ratios, along with an exponential cutoff at the highest accelerated momentum.

Shock waves propagating in collisionless heliospheric and astrophysical plasmas have been studied extensively over the decades. One prime motivation is to understand the nonthermal particle acceleration at shocks. Although the theory of diffusive shock acceleration (DSA) has long been the standard for cosmic-ray acceleration at shocks, plasma physical understanding of particle acceleration remains elusive. In this review, we discuss nonthermal electron acceleration mechanisms at quasi-perpendicular shocks, for which substantial progress has been made in recent years. The discussion presented in this review is restricted to the following three specific topics: The first is stochastic shock drift acceleration (SSDA), which is a relatively new mechanism for electron injection into DSA. The basic mechanism, related in-situ observations and kinetic simulations results, and how it is connected with DSA will be discussed. Second, we discuss shock surfing acceleration (SSA) at very high Mach number shocks relevant to young supernova remnants (SNRs). While the original proposal under the one-dimensional assumption is unrealistic, SSA has now been proven efficient by a fully three-dimensional kinetic simulation. We discuss the multidimensional nature of SSA and its role in electron injection. Finally, we discuss the current understanding of the magnetized Weibel-dominated shock. It is essentially a magnetized shock in which the reflected-gyrating ions dominate the formation of the shock structure but with a substantial magnetic field amplification by the ion-Weibel instability. Spontaneous magnetic reconnection of self-generated current sheets within the shock structure is an interesting consequence of Weibel-generated strong magnetic turbulence. Although the exact condition for active magnetic reconnection has not been clarified, we argue that high Mach number shocks with both Alfvén and sound Mach numbers exceeding 20–40 will likely behave as a Weibel-dominated shock. Despite a number of interesting recent findings, the relative roles of SSDA, SSA, and magnetic reconnection for electron acceleration at collisionless shocks and how the dominant particle acceleration mechanisms change depending on shock parameters remain to be answered.

We present simulations of magnetized astrophysical shocks taking into account the interplay between the thermal plasma of the shock and supra-thermal particles. Such interaction is depicted by combining a grid-based magneto-hydrodynamics description of the thermal fluid with particle in cell techniques devoted to the dynamics of supra-thermal particles. This approach, which incorporates the use of adaptive mesh refinement features, is potentially a key to simulate astrophysical systems on spatial scales that are beyond the reach of pure particle-in-cell simulations. We consider in this study non-relativistic shocks with various Alfvenic Mach numbers and magnetic field obliquity. We recover all the features of both magnetic field amplification and particle acceleration from previous studies when the magnetic field is parallel to the normal to the shock. In contrast with previous particle-in-cell-hybrid simulations, we find that particle acceleration and magnetic field amplification also occur when the magnetic field is oblique to the normal to the shock but on larger timescales than in the parallel case. We show that in our simulations, the supra-thermal particles are experiencing acceleration thanks to a pre-heating process of the particle similar to a shock drift acceleration leading to the corrugation of the shock front. Such oscillations of the shock front and the magnetic field locally help the particles to enter the upstream region and to initiate a non-resonant streaming instability and finally to induce diffuse particle acceleration.

The cataclysmic explosions of massive stars as supernovae are one of the key ingredients of galaxy formation. However, their evolution is not well understood in the presence of magnetic fields or cosmic rays (CRs). We study the expansion of individual supernova remnants (SNRs) using our suite of 3D hydrodynamical (HD), magnetohydrodynamical (MHD) and CRMHD simulations generated using ramses. We explore multiple ambient densities, magnetic fields, and fractions of supernova energy deposited as CRs (χCR), accounting for CR anisotropic diffusion and streaming. All our runs have comparable evolutions until the end of the Sedov-Taylor phase. However, our CRMHD simulations experience an additional CR pressure-driven snowplough phase once the CR energy dominates inside the SNR. We present a model for the final momentum deposited by supernovae that captures this new phase: $p_{\rm SNR} = 2.87\times 10^{5} (\chi _{\text{CR}} + 1)^{4.82}\left(\frac{n}{\text{cm}^{-3}}\right)^{-0.196} M_{\odot }$ km s−1. Assuming a 10 per cent fraction of SN energy in CRs leads to a 50 per cent boost of the final momentum, with our model predicting even higher impacts at lower ambient densities. The anisotropic diffusion of CRs assuming an initially uniform magnetic field leads to extended gas and CR outflows escaping from the supernova poles. We also study a tangled initial configuration of the magnetic field, resulting instead in a quasi-isotropic diffusion of CRs and earlier momentum deposition. Finally, synthetic synchrotron observations of our simulations using the polaris code show that the local magnetic field configuration in the interstellar medium modifies the overall radio emission morphology and polarization.

Diffuse, extended radio emission in galaxy clusters, commonly referred to as radio halos, indicate the presence of high energy cosmic ray (CR) electrons and cluster-wide magnetic fields. We can predict from theory the expected surface brightness of a radio halo, given magnetic field and CR density profiles. Previous studies have shown that the nature of CR transport can radically effect the expected radio halo emission from clusters (Wiener et al. 2013). Reasonable levels of magnetohydrodynamic (MHD) wave damping can lead to significant CR streaming speeds. But a careful treatment of MHD waves in a high $\beta$ plasma, as expected in cluster environments, reveals damping rates may be enhanced by a factor of $\beta^{1/2}$. This leads to faster CR streaming and lower surface brightnesses than without this effect. In this work we re-examine the simplified, 1D Coma cluster simulations (with radial magnetic fields) of Wiener et al. (2013) and discuss observable consequences of this high $\beta$ damping. Future work is required to study this effect in more realistic simulations.

Origin of Galactic Cosmic Rays