NUMERICAL STUDIES OF COSMIC RAY ACCELERATION AT COSMIC SHOCKS

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 <TEX>$\ge$</TEX> 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 <TEX>$10^{-4} - 10^{-3}$</TEX> 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 <TEX>${\~}50\%$</TEX> in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks (<TEX>$M_s {\le} 5$</TEX>), 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.

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.

A numerical scheme that incorporates a injection model into a combined gasdynamics and cosmic-ray (CR) diffusion-convection code has been developed. The hydro/CR code can follow in a very cost-effective way the evolution of CR-modified planar quasi-parallel shocks by adopting subzone shock tracking and multilevel adaptive mesh refinement techniques. An additional conservative quantity, S = Pg/ργg−1, is introduced to follow the adiabatic compression accurately in the precursor region, especially in front of strong, highly modified shocks. The thermal leakage injection model is based on the nonlinear 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 the upstream region according to a velocity-dependent transparency function that controls the fraction of leaking particles. This function is determined by a single parameter, , which should depend on the strength of postshock wave turbulence but is modeled as a constant parameter in our simulations. We have studied CR injection and acceleration efficiencies during the evolution of CR-modified planar shocks for a wide range of initial shock Mach numbers, M0, assuming a Bohm-like diffusion coefficient. For expected values of the injection process is very efficient when the subshock is strong, leading to fast and significant modification of the shock structure. As the CR pressure increases, the subshock weakens and the injection rate decreases accordingly so that the subshock does not disappear. Although some fraction of the particles injected early in the evolution continue to be accelerated to ever higher energies, the postshock CR pressure reaches an approximate time-asymptotic value because of a balance between fresh injection/acceleration and advection/diffusion of the CR particles away from the shock. In the strong shock limit of M0 30, the injection and acceleration processes are largely independent of the initial shock Mach number for a given , while they are sensitively dependent on M0 for M0 < 30. We conclude that the injection rates in strong parallel shocks are sufficient to lead to rapid nonlinear modifications to the shock structures and that self-consistent injection and time-dependent simulations are crucial to understanding the nonlinear evolution of CR-modified shocks.

We discuss new methods to integrate the cosmic ray (CR) evolution equations\ncoupled to magneto-hydrodynamics (MHD) on an unstructured moving mesh, as\nrealised in the massively parallel AREPO code for cosmological simulations. We\naccount for diffusive shock acceleration of CRs at resolved shocks and at\nsupernova remnants in the interstellar medium (ISM), and follow the advective\nCR transport within the magnetised plasma, as well as anisotropic diffusive\ntransport of CRs along the local magnetic field. CR losses are included in\nterms of Coulomb and hadronic interactions with the thermal plasma. We\ndemonstrate the accuracy of our formalism for CR acceleration at shocks through\nsimulations of plane-parallel shock tubes that are compared to newly derived\nexact solutions of the Riemann shock tube problem with CR acceleration. We find\nthat the increased compressibility of the post-shock plasma due to the produced\nCRs decreases the shock speed. However, CR acceleration at spherically\nexpanding blast waves does not significantly break the self-similarity of the\nSedov-Taylor solution; the resulting modifications can be approximated by a\nsuitably adjusted, but constant adiabatic index. In first applications of the\nnew CR formalism to simulations of isolated galaxies and cosmic structure\nformation, we find that CRs add an important pressure component to the ISM that\nincreases the vertical scale height of disk galaxies, and thus reduces the star\nformation rate. Strong external structure formation shocks inject CRs into the\ngas, but the relative pressure of this component decreases towards halo centres\nas adiabatic compression favours the thermal over the CR pressure.\n

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.

CONTEXT: Supernova Remnants (SNRs) are considered as the primary sources of galactic cosmic rays (CRs), where CRs are assumed to be accelerated by diffusive shock acceleration (DSA) mechanism. The SNR shocks expand in the complex ambient environment, particularly in the core-collapse scenarios as those SNRs evolve inside wind-blown bubbles created by the mass-loss of massive stars. Therefore, the evolution of core-collapse SNRs, as well as CRs acceleration is expected to be considerably different from SNR evolution in a uniform environment. AIM: The aim is to observe the influence of different ambient medium of core-collapse SNR shock on the particle spectra. Furthermore, the interactions of SNR shock with fluctuations in density within the wind-blown bubble generate several transmitted and reflected shocks. So, the impact of SNR shock interactions with different discontinuities, on particle spectra, and finally the effect on emission from the remnant are also the areas of focus. Methods. The hydrodynamic structures of wind-blown bubbles at pre-supernova stages formed by $20M_{\odot}$, $35M_{\odot}$, and $60M_{\odot}$ stars have been used to create the ambient environment for SNRs. Evolution of those stars through different stages from Zero Age Main Sequence (ZAMS) to the pre-supernova stage, results into formation of structurally different wind bubbles. Then, the transport equation for cosmic rays, and hydrodynamic equations have been solved simultaneously in 1-D spherical symmetry. RESULT: The modifications in particle spectra depend on the hydrodynamics and magnetic field structure of SNR ambient medium. We have obtained softer spectra with spectra index close to 2.5 originated during SNR interaction with hot wind bubble and further, magnetic field structure effectively influences the emission morphology of SNR as it governs the transportation of particles.

In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (Gaussian). The term ‘superdiffusive’ refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. Here we show a number of examples, both from laboratory and from astrophysical plasmas, where superdiffusive transport has been identified, with a focus on what could be the main influence of superdiffusion on fundamental processes like diffusive shock acceleration and heliospheric energetic particle propagation. For laboratory plasmas, superdiffusion appears to be due to the presence of electrostatic turbulence which creates long-range correlations and convoluted structures in perpendicular transport: this corresponds to a similar phenomenon in the propagation of solar energetic particles (SEPs) which leads to SEP dropouts. For the propagation of energetic particles accelerated at interplanetary shocks in the solar wind, parallel superdiffusion seems to be prevailing; this is based on a pitch-angle scattering process different from that envisaged by quasi-linear theory, and this emphasizes the importance of nonlinear interactions and trapping effects. In the case of supernova remnant shocks, parallel superdiffusion is possible at quasi-parallel shocks, as occurring in the interplanetary space, and perpendicular superdiffusion is possible at quasi-perpendicular shocks, as corresponding to Richardson diffusion: therefore, cosmic ray acceleration at supernova remnant shocks should be formulated in terms of superdiffusion. The possible relations among anomalous transport in laboratory, heliospheric, and astrophysical plasmas will be indicated.

We show here that highly polarized x-ray synchrotron radiation from young supernova remnants (SNRs) can be modeled within the framework of diffusive shock acceleration (DSA) and nonlinear magnetic turbulence generation. Cosmic ray acceleration by SNR shocks to very high energies requires efficient magnetic turbulence amplification in the shock precursor. As the strong turbulence generated by Bell's instability far upstream from the viscous subshock convects through the subshock, nonlinear dynamical effects on the large amplitude, compressible fluctuations produce a downstream layer filled with strong anisotropic turbulence with predominantly radial magnetic fields. The synchrotron radiation from shock accelerated electrons in the turbulent downstream layer has a high degree of polarization shown to be consistent with recent observations of young SNRs by the Imaging X-ray Polarimetry Explorer (IXPE) taking into account high-energy electron losses and line-of-sight integration in a spherical remnant. In the case of our model of Tycho's SNR, the measured x-ray radiation constrains the thickness of the energy containing interval and the amplitude of cosmic ray driven magnetic turbulence, as well as the maximal energy of accelerated protons. The preferential direction of the x-ray polarization depends sensitively on the SNR shock velocity and the ambient density. A fast shock in a region with high enough density is a favorable place to produce tangential polarization of synchrotron radiation, i.e., a dominantly radial magnetic field. A unique feature of our model is the sensitive dependence of the degree and direction of x-ray polarization on the spatial overlap between regions of amplified magnetic turbulence and TeV electron populations. While this overlap occurs on scales orders of magnitude below the resolution of IXPE, its polarization measurement allows testing of turbulent plasma processes on unprecedented scales.

Context. We revisit the study of shocks interacting with molecular clouds, incorporating coupled gas-dust dynamics. Aims. We study the effect of different parameters on the shock-cloud interaction, such as the dust-to-gas ratio or the Mach number of the impinging shock. By solving self-consistently for drag-coupled gas and dust evolutions, we can assess the frequently made assumption that the dust is locked to the dynamics of the gas so that dust observations would result in direct information on the gas distribution. Methods. We used a multi-fluid model where the dust is represented by grain-size specific pressureless fluids. The dust and gas interact through a drag force, and we used four dust species with weighted representative sizes between 1 and 500 nm. We use the open source code MPI-AMRVAC for a parametric study of the effect of the gas-dust ratio and the Mach number of the shock. By using the radiative transfer code SKIRT, we create synthetic millimeter wavelength maps to connect to observations. Results. We find that the presence of dust does not significantly affect the dynamics of the gas for realistic dust-gas ratios, and this is the case throughout the range of Mach numbers explored (1.5−10). For high Mach numbers, we find a significant discrepancy between the distribution of the dust and gas after the cloud-shock interaction with the larger dust species clearly lagging the heavily mixed and accelerated gas (re)distribution. Conclusions. We conclude that observational studies of dusty environments may need to account for clearly separated spatial distributions of dust and gas, especially those studies that are representative of molecular clouds that have been interacting with high Mach number shock fronts.

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.

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.

The suggestion that the shocks of supernova remnants (SNR’s) are cosmic ray acceleration sites dates back more than 40 years. While observations of nonthermal radio emission from SNR shells indicate the ubiquity of GeV cosmic ray production, there is still theoretical debate about whether SNR shocks accelerate particles up to the well-known “knee” in the primary cosmic ray spectrum at ∼3,000 TeV. Recent X-ray observations of SN1006 and other SNR’s may have provided the missing observational link between SNR shocks and high energy cosmic ray acceleration. We discuss these observations and their interpretation, and summarize our ongoing efforts to find evidence from X-ray observations of cosmic ray acceleration in the shells of other SNR’s.

The suggestion that the shocks of supernova remnants (SNR's) are cosmic ray acceleration sites dates back more than 40 years. While observations of nonthermal radio emission from SNR shells indicate the ubiquity of GeV cosmic ray production, there is still theoretical debate about whether SNR shocks accelerate particles up to the well-known “knee” in the primary cosmic ray spectrum at ~3,000 TeV. Recent X-ray observations of SN1006 and other SNR's may have provided the missing observational link between SNR shocks and high energy cosmic ray acceleration. We discuss these observations and their interpretation, and summarize our ongoing efforts to find evidence from X-ray observations of cosmic ray acceleration in the shells of other SNR's.

Diffusive shock acceleration (Fermi acceleration) of cosmic rays in a system containing two shock waves is investigated using test particle simulations and analysis of the diffusion convection equation. We assume that the cosmic ray acceleration timescale is much less than the approaching timescale of the two shocks. Low-energy cosmic rays are primarily accelerated as they interact with one of the two shocks. However, as they are energized, and their mean free path becomes comparable to the separation distance of the two shocks, they start to accelerate as they interact with both shocks. As a result, a double power-law-type spectrum for the cosmic ray distribution is produced. The numerical result is well explained by a model based on the diffusion convection equation, which accounts for the dependence of the diffusion coefficient on the cosmic ray energy. The break point of the spectrum can be estimated by considering transport of cosmic rays from one shock to the other.

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.