Shock Precursor Research Articles

Particle transport and heating in the microturbulent precursor of relativistic shocks

Collisionless relativistic shocks have been the focus of intense theoretical and numerical investigations in recent years. The acceleration of particles, the generation of electromagnetic microturbulence and the building up of a shock front are three interrelated essential ingredients of a relativistic collisionless shock wave. In this paper we investigate two issues of importance in this context: (1) the transport of suprathermal particles in the excited microturbulence upstream of the shock and its consequences regarding particle acceleration; (2) the preheating of incoming background electrons as they cross the shock precursor and experience relativistic oscillations in the microturbulent electric fields. We place emphasis on the importance of the motion of the electromagnetic disturbances relatively to the background plasma and to the shock front. This investigation is carried out for the two major instabilities involved in the precursor of relativistic shocks, the filamentation instability and the oblique two stream instability. Finally, we use our results to discuss the maximal acceleration at the external shock of a gamma-ray burst; we find in particular a maximal synchrotron photon energy of the order of a few GeV.

DIFFUSIVE SHOCK ACCELERATION WITH MAGNETIC FIELD AMPLIFICATION AND ALFVÉNIC DRIFT

We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfv<TEX>$\acute{e}$</TEX>nic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is <TEX>${\xi}$</TEX> > <TEX>$2{\times}10^{-4}$</TEX>, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be amplified up to a factor of 20 via CR streaming instability in the upstream region. If scattering centers drift with Alfv<TEX>$\acute{e}$</TEX>n speed in the amplified magnetic field, the CR energy spectrum can be steepened significantly and the acceleration efficiency is reduced. Nonlinear DSA with self-consistent MFA and Alfv<TEX>$\acute{e}$</TEX>nic drift predicts that the postshock CR pressure saturates roughly at ~10 % of the shock ram pressure for strong shocks with a sonic Mach number ranging <TEX>$20{\leq}M_s{\leq}100$</TEX>. Since the amplified magnetic field follows the flow modification in the precursor, the low energy end of the particle spectrum is softened much more than the high energy end. As a result, the concave curvature in the energy spectra does not disappear entirely even with the help of Alfv<TEX>$\acute{e}$</TEX>nic drift. For shocks with a moderate Alfv<TEX>$\acute{e}$</TEX>n Mach number (<TEX>$M_A$</TEX> < 10), the accelerated CR spectrum can become as steep as <TEX>$E^{-2.1}$</TEX> - <TEX>$E^{-2.3}$</TEX>, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.

THE COUPLED EVOLUTION OF ELECTRONS AND IONS IN CORONAL MASS EJECTION-DRIVEN SHOCKS

We present simulations of coronal mass ejections (CMEs) performed with a new two-temperature coronal model developed at the University of Michigan, which is able to address the coupled thermodynamics of the electron and proton populations in the context of a single fluid. This model employs heat conduction for electrons, constant adiabatic index (γ = 5/3), and includes Alfven wave pressure to accelerate the solar wind. The Wang-Sheeley-Arge empirical model is used to determine the Alfven wave pressure necessary to produce the observed bimodal solar wind speed. The Alfven waves are dissipated as they propagate from the Sun and heat protons on open magnetic field lines to temperatures above 2 MK. The model is driven by empirical boundary conditions that includes GONG magnetogram data to calculate the coronal field, and STEREO/EUVI observations to specify the density and temperature at the coronal boundary by the Differential Emission Measure Tomography method. With this model, we simulate the propagation of fast CMEs and study the thermodynamics of CME-driven shocks. Since the thermal speed of the electrons greatly exceeds the speed of the CME, only protons are directly heated by the shock. Coulomb collisions low in the corona couple the protons and electrons allowing heat exchange between the two species. However, the coupling is so brief that the electrons never achieve more than 10% of the maximum temperature of the protons. We find that heat is able to conduct on open magnetic field lines and rapidly propagates ahead of the CME to form a shock precursor of hot electrons.

COLLISIONLESS SHOCKS IN A PARTIALLY IONIZED MEDIUM. I. NEUTRAL RETURN FLUX AND ITS EFFECTS ON ACCELERATION OF TEST PARTICLES

A collisionless shock may be strongly modified by the presence of neutral atoms through the processes of charge exchange between ions and neutrals and ionization of the latter. These two processes lead to exchange of energy and momentum between charged and neutral particles both upstream and downstream of the shock. In particular, neutrals that suffer a charge exchange downstream with shock-heated ions generate high velocity neutrals that have a finite probability of returning upstream. These neutrals might then deposit heat in the upstream plasma through ionization and charge exchange, thereby reducing the fluid Mach number. A consequence of this phenomenon, that we refer to as the "neutral return flux", is a reduction of the shock compression factor and the formation of a shock precursor upstream. The scale length of the precursor is determined by the ionization and charge exchange interaction lengths of fast neutrals moving towards upstream infinity. In the case of a shock propagating in the interstellar medium, the effects of ion-neutral interactions are especially important for shock velocities < 3000 km/s. Such propagation velocities are common among shocks associated with supernova remnants, the primary candidate sources for the acceleration of Galactic cosmic rays. We then investigate the effects of the return flux of neutrals on the spectrum of test-particles accelerated at the shock. We find that, for shocks slower than ~3000 km/s, the particle energy spectrum steepens appreciably with respect to the naive expectation for a strong shock, namely E^-2.

Gamma-ray emission from pulsar binaries

AbstractPulsar winds, containing charged particles, waves and a net (phase-averaged) magnetic field, are thought to fuel the high-energy emission from several gamma-ray binaries. They terminate where the ram pressure matches that of the surroundings - which, in binaries, is provided by the wind of the companion. Before termination, pulsed emission can be produced by inverse Compton scattering of photons from the companion by particles in the waves. After termination, both the bulk kinetic energy of the particles and the Poynting flux in the waves are dissipated into an energetic particle population embedded in the surviving phase-averaged magnetic field. Pulsed emission is no longer possible, but a substantial flux of unpulsed high-energy photons can be produced. I will present results showing that the physical conditions at the termination shock can be divided into two regimes: a high density one, where current sheets in the wind are first compressed by an MHD shock and subsequently dissipate by reconnection, and a low density one, where the wind can first convert into an electromagnetic wave in the shock precursor, which then damps and merges into the wind nebula. The shocks surrounding isolated pulsars fall into the low-density category, but those around pulsars in binary systems, may transit from one regime to the other according to binary phase. The implications of the shock-structure dichotomy for these objects will be discussed.

Generation of magnetized collisionless shocks by a novel, laser-driven magnetic piston

We present experiments on the Trident laser facility at Los Alamos National Laboratory which demonstrate key elements in the production of laser-driven, magnetized, laboratory-scaled astrophysical collisionless shocks. These include the creation of a novel magnetic piston to couple laser energy to a background plasma and the generation of a collisionless shock precursor. We also observe evidence of decoupling between a laser-driven fast ion population and a background plasma, in contrast to the coupling of laser-ablated slow ions with background ions through the magnetic piston. 2D hybrid simulations further support these developments and show the coupling of the slow to ambient ions, the formation of a magnetic and density compression pulses consistent with a collisionless shock, and the decoupling of the fast ions.

On the universality of nonthermal electron acceleration due to quasi-turbulent wakefields

Nonthermal acceleration of relativistic electrons in a wakefield induced by large amplitude light waves is discussed. It is considered that large amplitude light waves are excited as the precursor waves in the upstream of relativistic perpendicular shocks in the universe, and that the wakefield is excited by the light ponderomotive force. Thus, the wakefield acceleration is possible in the astrophysical circumstances. We model such shock environments in a laboratory plasma by substituting an intense laser pulse for the large amplitude light waves. By performing 2-D particle-in-cell simulations, we discuss the properties of the wakefield acceleration in various laser and plasma conditions. With the relativistic intensities of the laser pulses, the electrons are nonthermally accelerated by the wakefield. When the pulse length and the spot size are comparable to the electron inertial scale, the energy distribution functions of the electrons can be monoenergetic. On the other hand, when the pulse spatial scales are much larger than the electron inertial scale, which occurs in the case of the shock precursor light waves, the distribution functions are universally represented by power law spectra with an index of 2, independent of the laser intensity, the plasma density, and the laser pulse size.

A filamentation instability for streaming cosmic rays

We demonstrate that cosmic rays form filamentary structures in the precursors of supernova remnant shocks due to their self-generated magnetic fields. The cosmic-ray filamentation results in the growth of a long wavelength instability, and naturally couples the rapid non-linear amplification on small scales to larger length scales. Hybrid magnetohydrodynamics--particle simulations are performed to confirm the effect. The resulting large scale magnetic field may facilitate the scattering of high energy cosmic rays as required to accelerate protons beyond the knee in the cosmic-ray spectrum at supernova remnant shocks. Filamentation far upstream of the shock may also assist in the escape of cosmic rays from the accelerator.

Magnetic Fields in Cosmic Particle Acceleration Sources

We review here some magnetic phenomena in astrophysical particle accelerators associated with collisionless shocks in supernova remnants, radio galaxies and clusters of galaxies. A specific feature is that the accelerated particles can play an important role in magnetic field evolution in the objects. We discuss a number of CR-driven, magnetic field amplification processes that are likely to operate when diffusive shock acceleration (DSA) becomes efficient and nonlinear. The turbulent magnetic fields produced by these processes determine the maximum energies of accelerated particles and result in specific features in the observed photon radiation of the sources. Equally important, magnetic field amplification by the CR currents and pressure anisotropies may affect the shocked gas temperatures and compression, both in the shock precursor and in the downstream flow, if the shock is an efficient CR accelerator. Strong fluctuations of the magnetic field on scales above the radiation formation length in the shock vicinity result in intermittent structures observable in synchrotron emission images. Resonant and non-resonant CR streaming instabilities in the shock precursor can generate mesoscale magnetic fields with scale-sizes comparable to supernova remnants and even superbubbles. This opens the possibility that magnetic fields in the earliest galaxies were produced by the first generation Population III supernova remnants and by clustered supernovae in star forming regions.

EFFECTS OF NEUTRAL HYDROGEN ON COSMIC-RAY PRECURSORS IN SUPERNOVA REMNANT SHOCK WAVES

Many fast supernova remnant shocks show spectra dominated by Balmer lines. The H$\alpha$ profiles have a narrow component explained by direct excitations and a thermally Doppler broadened component due to atoms that undergo charge exchange in the post-shock region. However, the standard model does not take into account the cosmic-ray shock precursor, which compresses and accelerates plasma ahead of the shock. In strong precursors with sufficiently high densities, the processes of charge exchange, excitation and ionization will affect the widths of both narrow and broad line components. Moreover, the difference in velocity between the neutrals and the precursor plasma gives rise to frictional heating due to charge exchange and ionization in the precursor. In extreme cases, all neutrals can be ionized by the precursor. In this paper we compute the ion and electron heating for a wide range of shock parameters, along with the velocity distribution of the neutrals that reach the shock. Our calculations predict very large narrow component widths for some shocks with efficient acceleration, along with changes in the broad- to-narrow intensity ratio used as a diagnostic for the electron-ion temperature ratio. Balmer lines may therefore provide a unique diagnostic of precursor properties. We show that heating by neutrals in the precursor can account for the observed H$\alpha$ narrow component widths, and that the acceleration efficiency is modest in most Balmer line shocks observed thus far.

PARTIALLY COOLED SHOCKS: DETECTABLE PRECURSORS IN THE WARM/HOT INTERGALACTIC MEDIUM

I present computations of the integrated column densities produced in the post-shock cooling layers and in the radiative precursors of partially-cooled fast shocks as a function of the shock age. The results are applicable to the shock-heated warm/hot intergalactic medium (WHIM) which is expected to be a major baryonic reservoir, and contain a large fraction of the so-called "missing baryons". My computations indicate that readily observable amounts of intermediate and high ions, such as CIV, NV, and OVI are created in the precursors of young shocks, for which the shocked gas remains hot and difficult to observe. I suggest that such precursors may provide a way to identify and estimate the "missing" baryonic mass associated with the shocks. The absorption-line signatures predicted here may be used to construct ion-ratio diagrams, which will serve as diagnostics for the photoionized gas in the precursors. In my numerical models, the time-evolution of the shock structure, self-radiation, and associated metal-ion column densities are computed by a series of quasi-static models, each appropriate for a different shock age. The shock code used in this work calculates the nonequilibrium ionization and cooling, follows the radiative transfer of the shock self-radiation through the post-shock cooling layers, takes into account the resulting photoionization and heating rates, follows the dynamics of the cooling gas, and self-consistently computes the photoionization states in the precursor gas. I present a complete set of the age-dependent post-shock and precursor columns for all ionization states of the elements H, He, C, N, O, Ne, Mg, Si, S, and Fe, as functions of the shock velocity, gas metallicity, and magnetic field. I present my numerical results in convenient online tables.

THE RELATION BETWEEN POST-SHOCK TEMPERATURE, COSMIC-RAY PRESSURE, AND COSMIC-RAY ESCAPE FOR NON-RELATIVISTIC SHOCKS

Supernova remnants are thought to be the dominant source of Galactic cosmic rays. This requires that at least 5% of the available energy is transferred to cosmic rays, implying a high cosmic-ray pressure downstream of supernova remnant shocks. Recently, it has been shown that the downstream temperature in some remnants is low compared to the measured shock velocities, implying that additional pressure support by accelerated particles is present. Here we use a two-fluid thermodynamic approach to derive the relation between post-shock fractional cosmic-ray pressure and post-shock temperature, assuming no additional heating beyond adiabatic heating in the shock precursor and with all non-adiabatic heating occurring at the subshock. The derived relations show that a high fractional cosmic-ray pressure is only possible, if a substantial fraction of the incoming energy flux escapes from the system. Recently a shock velocity and a downstream proton temperature were measured for a shock in the supernova remnant RCW 86. We apply the two-fluid solutions to these measurements and find that the the downstream fractional cosmic-ray pressure is at least 50% with a cosmic-ray energy flux escape of at least 20%. In general, in order to have 5% of the supernova energy go into accelerating cosmic rays, on average the post-shock cosmic-ray pressure needs to be 30% for an effective cosmic-ray adiabatic index of 4/3.

RESOLVED SHOCK STRUCTURE OF THE BALMER-DOMINATED FILAMENTS IN TYCHO ’S SUPERNOVA REMNANT: COSMIC-RAY PRECURSOR?

We report on the results from H{\alpha} imaging observations of the eastern limb of Tycho's supernova remnant (SN1572) using the Wide Field Planetary Camera 2 on the Hubble Space Telescope. We resolve the detailed structure of the fast, collisionless shock wave into a delicate structure of nearly edge-on filaments. We find a gradual increase of H{\alpha} intensity just ahead of the shock front, which we interpret as emission from the thin (~1") shock precursor. We find that a significant amount of the H{\alpha} emission comes from the precursor and that this could affect the amount of temperature equilibration derived from the observed flux ratio of the broad and narrow H{\alpha} components. The observed H{\alpha} emission profiles are fit using simple precursor models, and we discuss the relevant parameters. We suggest that the precursor is likely due to cosmic rays and discuss the efficiency of cosmic-ray acceleration at this position.

TURBULENCE-INDUCED MAGNETIC FIELDS AND STRUCTURE OF COSMIC RAY MODIFIED SHOCKS

We propose a model for Diffusive Shock Acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray streaming instabilities; i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale cosmic ray streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to work are produced through the interactions of the pressure gradient of the cosmic ray precursor and density perturbations in the inflowing fluid. Our estimates show that this mechanism provides fast growth of magnetic field and is very generic. We argue that for supernovae shocks the mechanism is capable of generating upstream magnetic fields that are sufficiently strong for accelerating cosmic rays up to around 10^16 eV. No action of any other mechanism is necessary.

On electromagnetic instabilities at ultra-relativistic shock waves

(Abridged) This paper addresses the issue of magnetic field generation in a relativistic shock precursor through micro-instabilities. The level of magnetization of the upstream plasma turns out to be a crucial parameter, notably because the length scale of the shock precursor is limited by the Larmor rotation of the accelerated particles in the background magnetic field and by the speed of the shock wave. We discuss in detail and calculate the growth rates of the following beam plasma instabilities seeded by the accelerated and reflected particle populations: for an unmagnetized shock, the Weibel and filamentation instabilities, as well as the Cerenkov resonant longitudinal and oblique modes; for a magnetized shock, the Weibel instability and the resonant Cerenkov instabilities with the longitudinal electrostatic modes, as well as the Alfven, Whisler and extraordinary modes. All these instabilities are generated upstream, then they are transmitted downstream. The modes excited by Cerenkov resonant instabilities take on particular importance with respect to the magnetisation of the downstream medium since, being plasma eigenmodes, they have a longer lifetime than the Weibel modes. We discuss the main limitation of the wave growth associated with the length of the precursor and the magnetisation of the upstream medium for both oblique and parallel shock waves. We also characterize the proper conditions to obtain Fermi acceleration. We recover some results of most recent particle-in-cell simulations and conclude with some applications to astrophysical cases of interest, pulsar winds and gamma-ray burst external shock waves in particular. (Abridged)

SPECTRA OF MAGNETIC FLUCTUATIONS AND RELATIVISTIC PARTICLES PRODUCED BY A NONRESONANT WAVE INSTABILITY IN SUPERNOVA REMNANT SHOCKS

We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA) and the nonlinear feedback of particles and fields on the bulk flow are derived consistently. The shock structure depends critically on the efficiency of turbulence cascading. If cascading is suppressed, MFA is strong, the shock precursor is stratified, and the turbulence spectrum contains several discrete peaks. These peaks, as well as the amount of MFA, should influence synchrotron X-rays, allowing observational tests of cascading and other assumptions intrinsic to the nonlinear model of nonresonant wave growth.

An energetic‐particle‐mediated termination shock observed by Voyager 2

Voyager 2 crossed the solar wind termination shock several times during August 30 – September 1 of 2007. During the last forty days before the crossing intensities of energetic ions measured by the LECP instrument were increasing exponentially, and their spectrum showed clear evidence of unfolding at low energies. Plasma data featured a broad velocity precursor, where solar wind speed decreased from about 380 km/s far upstream to ∼300 km/s at the shock. By using plasma and energetic particle conservation laws we demonstrate that the speed decrease during Voyager 2's last ∼40 days in the solar wind could be plausibly produced by the back‐pressure of energetic ions with energies of a few MeV on the upstream plasma flow. These particles propagate diffusively upstream from the termination shock, producing a shock precursor that has a characteristic lengthscale of 0.35 AU, assuming the shock has not moved substantially during that time.

Cosmic ray spectrum produced by galactic supernova remnants

Cosmic ray acceleration by supernova shocks is considered. A new numerical code is used to describe the cosmic ray acceleration and shock wave evolution. The magnetohydrodynamic turbulence generation in the shock precursor by streaming instability of accelerated particles is taken into account. The cosmic ray spectrum produced by supernova explosion in uniform interstellar medium is simulated.

Acceleration of ultra-high energy cosmic rays by galaxy cluster accretion shocks

Acceleration of protons and nuclei by shock waves arising during accretion on galaxy clusters is considered. The generation of magnetohydrodynamic turbulence by streaming instability of accelerated particles in a shock precursor, cluster mass distribution, and particle energy loss upon interaction with cosmic microwave background and IR background radiation are taken into account. The contribution of these sources to the cosmic ray intensity observed at energies of 1017–1020 eV is calculated.

SELF-SIMILAR EVOLUTION OF COSMIC-RAY MODIFIED SHOCKS: THE COSMIC-RAY SPECTRUM

We use kinetic simulations of diffusive shock acceleration (DSA) to study the time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified shocks. Thermal leakage injection of low energy CRs and finite Alfv\'en wave propagation and dissipation are included. Bohm diffusion as well as the diffusion with the power-law momentum dependence are modeled. As long as the acceleration time scale to relativistic energies is much shorter than the dynamical evolution time scale of the shocks, the precursor and subshock transition approach the time-asymptotic state, which depends on the shock sonic and Alfv\'enic Mach numbers and the CR injection efficiency. For the diffusion models we employ, the shock precursor structure evolves in an approximately self-similar fashion, depending only on the similarity variable, x/(u_s t). During this self-similar stage, the CR distribution 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 with an exponential cutoff at the highest accelerated momentum, p_{max}(t). Based on the results of the DSA simulations spanning a range of Mach numbers, we suggest functional forms for the shock structure parameters, from which the aforementioned form of CR spectrum can be constructed. These analytic forms may represent approximate solutions to the DSA problem for astrophysical shocks during the self-similar evolutionary stage as well as during the steady-state stage if p_{max} is fixed.