Parallel Shocks Research Articles

STIS optical spectroscopy of the lobes of CRL 618

Context. Many proto-planetary nebulae show collimated structures sometimes showing multiple outflows.Aims. We present the results of new optical spectroscopic observations (both medium (with a dispersion of 0.56 A pixel-1 ) and low (2.73 and 4.92 A pixel-1 for the G430L and G750L gratings) spectral resolution) of the lobes of the proto-planetary nebula CRL 618 obtained with the Space Telescope Imaging Spectrograph on board of the Hubble Space Telescope. Methods. We analyse the density structure and the excitation conditions of the lobes of CRL 618. The spectra obtained at medium spectral resolution (~50 km s-1 ) allow us to quote the fraction of unscattered (intrinsic) Hα emission. We have also obtained de-reddened emission line ratios of several features from the low spectral resolution spectra.Results. We find that most of the analysed line ratios are reproduced by planar shocks moving through a dense medium (with pre-shock densities ~104 cm-3 ) with shock velocities from 30 to 40 km s-1 (except the [O III]/Hβ line ratios which require shock velocities of 80 to 90 km s-1 ). We find that the [S II]-weighted ionization fraction ranges from 0.015 to 0.06. The total densities derived from the electron density and the ionization fraction are ~105 to 106 cm-3 . Conclusions. We conclude that the spectra of the lobes of CRL 618 can be margially reproduced by steady plane–parallel shock models for shock velocities which are significantly lower than the velocities at which the jet moves outwards (~200 km s-1 ). These results are consistent with the predictions of a jet with a variable ejection velocity. The mirror-symmetry, the luminosity asymmetry between both lobes and the ejection velocity variability suggest that its central source may host a binary system.

ENERGY SPECTRUM OF ENERGETIC PARTICLES ACCELERATED BY SHOCK WAVES: FROM FOCUSED TRANSPORT TO DIFFUSIVE ACCELERATION

The focused transport equation (FTE) includes all the necessary physics for modeling the shock acceleration of energetic particles with a unified description of first-order Fermi acceleration, shock drift acceleration, and shock surfing acceleration. It can treat the acceleration and transport of particles with an anisotropic distribution. In this study, the energy spectrum of pickup ions accelerated at shocks of various obliquities is investigated based on the FTE. We solve the FTE by using a stochastic approach. The shock acceleration leads to a two-component energy spectrum. The low-energy component of the spectrum is made up of particles that interact with shock one to a few times. For these particles, the pitch angle distribution is highly anisotropic, and the energy spectrum is variable depending on the momentum and pitch angle of injected particles. At high energies, the spectrum approaches a power law consistent with the standard diffusive shock acceleration (DSA) theory. For a parallel shock, the highenergy component of the power-law spectrum, with the spectral index being the same as the prediction of DSA theory, starts just a few times the injection speed. For an oblique or quasi-perpendicular shock, the high-energy component of the spectrum exhibits a double power-law distribution: a harder power-law spectrum followed by another power-law spectrum with a slope the same as the spectral index of DSA. The shock acceleration will eventually go into the DSA regime at higher energies even if the anisotropy is not small. The intensity of the energy spectrum given by the FTE, in the high-energy range where particles get efficient acceleration in the DSA regime, is different from that given by the standard DSA theory for the same injection source. We define the injection efficiency η as the ratio between them. For a parallel shock, the injection efficiency is less than 1, but for an oblique shock or a quasi-perpendicular shock it could be greater.

One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamics

Extending investigations of Barker, Humpherys, Lafitte, Rudd, and Zumbrun for compressible gas dynamics and Freistühler and Trakhinin for compressible magnetohydrodynamics, we study by a combination of asymptotic ODE estimates and numerical Evans function computations the one-dimensional stability of parallel isentropic magnetohydrodynamic shock layers over the full range of physical parameters (shock amplitude, strength of imposed magnetic field, viscosity, magnetic permeability, and electrical resistivity) for a γ-law gas with γ ∈ [ 1 , 3 ] . Other γ-values may be treated similarly, but were not checked numerically. Depending on magnetic field strength, these shocks may be of fast Lax, intermediate (overcompressive), or slow Lax type; however, the shock layer is independent of magnetic field, consisting of a purely gas-dynamical profile. In each case, our results indicate stability. Interesting features of the analysis are the need to renormalize the Evans function in order to pass continuously across parameter values where the shock changes type or toward the large-amplitude limit at frequency λ = 0 and the systematic use of winding number computations on Riemann surfaces.

SLOW SHOCKS AND CONDUCTION FRONTS FROM PETSCHEK RECONNECTION OF SKEWED MAGNETIC FIELDS: TWO-FLUID EFFECTS

In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not perfectly anti-parallel, i.e. they are skewed, magnetic energy is first converted to bulk kinetic energy and then thermalized in slow magnetosonic shocks. We show that the latter resemble parallel shocks or hydrodynamic shocks for all skew angles except those very near the anti-parallel limit. As for parallel shocks, the structures of reconnection-driven slow shocks are best studied using two-fluid equations in which ions and electrons have independent temperature. Time-dependent solutions of these equations can be used to predict and understand the shocks from reconnection of skewed magnetic fields. The results differ from those found using a single-fluid model such as magnetohydrodynamics. In the two-fluid model electrons are heated indirectly and thus carry a heat flux always well below the free-streaming limit. The viscous stress of the ions is, however, typically near the fluid-treatable limit. We find that for a wide range of skew angles and small plasma beta an electron conduction front extends ahead of the slow shock but remains within the outflow jet. In such cases conduction will play a more limited role in driving chromospheric evaporation than has been predicted based on single-fluid, anti-parallel models.

Structure of cosmic ray-modified perpendicular shocks

Kinetic diffusion of cosmic rays ahead of perpendicular shocks induces charge non-neutrality, which is mostly, yet not completely, screened by the bulk plasma via polarization drift current. Hydrodynamic shear instabilities as well as modified Buneman instability of the polarization current generate the turbulence necessary for a Fermi-type acceleration. Thus, similar to the case of parallel shocks, in perpendicular shocks the diffusing cosmic rays generate unstable plasma currents that in turn excite turbulence. This allows a self-consistent evolution of a shock-cosmic rays system. In the kinetic regime of the modified Buneman instability, electrons may be heated in the cosmic ray precursor.

APERIODIC MAGNETIC TURBULENCE PRODUCED BY RELATIVISTIC ION BEAMS

Magnetic-field generation by a relativistic ion beam propagating through an electron-ion plasma along a homogeneous magnetic field is investigated with 2.5D high-resolution particle-in-cell (PIC) simulations. The studies test predictions of a strong amplification of short-wavelength modes of magnetic turbulence upstream of nonrelativistic and relativistic parallel shocks associated with supernova remnants, jets of active galactic nuclei, and gamma-ray bursts. We find good agreement in the properties of the turbulence observed in our simulations compared with the dispersion relation calculated for linear waves with arbitrary orientation of ${\vec k}$. Depending on the parameters, the backreaction on the ion beam leads to filamentation of the ambient plasma and the beam, which in turn influences the properties of the magnetic turbulence. For mildly- and ultra-relativistic beams, the instability saturates at field amplitudes a few times larger than the homogeneous magnetic field strength. This result matches our recent studies of nonrelativistically drifting, hot cosmic-ray particles upstream of supernova-remnant shocks which indicated only a moderate magnetic-field amplification by nonresonant instabilities. We also demonstrate that the aperiodic turbulence generated by the beam can provide efficient particle scattering with a rate compatible with Bohm diffusion. Representing the ion beam as a constant external current, i.e. excluding a backreaction of the magnetic turbulence on the beam, we observe non-resonant parallel modes with wavelength and growth rate as predicted by analytic calculations. In this unrealistic setup the magnetic field is amplified to amplitudes far exceeding the homogeneous field, as observed in recent MHD and PIC simulations.

Hybrid simulations of stellar wind interaction with close-in extrasolar planets

A large fraction of exoplanets orbit their host stars on distances much smaller than any planet in the Solar System. This opens up for the possibility of qualitatively new kinds of stellar wind interaction. The understanding of these interactions may be important both for future detection methods and for mass loss estimates. In this work we investigate such close-in stellar wind interaction using primarily hybrid simulations. These describe plasmas by modeling electrons as a fluid and ions as particles. Two scenarios of stellar wind interaction with unmagnetized, Earth-sized, close-in exoplanets in orbit around a Sun-like star are investigated: 1.) interaction with an extremely hydrodynamically expanding atmosphere, and 2.) quasiparallel stellar wind interaction. In the expanding ionosphere study we can see how the bow shock, magnetic draping and ion composition boundary are pushed upstream, increasing the size of the interaction region. In the process it creates a significant wake behind the planet, largely void of electromagnetic fields and dominated only by the expanding ionosphere. An attempt is also made to analytically estimate the standoff distance and compare these estimates with simulations. In the quasiparallel interaction study we observe how generic features of quasiperpendicular interaction are modified. The dayside bow shock surface is replaced by a vaguely defined parallel shock that destroys the strict division between magnetosheath and stellar wind. The stellar wind also penetrates deeper into the ionosphere.

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)

Solar wind proton reflection and injection to the ACR regime at the parallel termination shock

Our recent kinetic model for the parallel solar wind termination shock describes the ion shock transit under the influence of a decelerating electrostatic potential and the turbulent wave-particle interaction with electrostatic plasma waves. Due to this diffusive interaction, a certain number of ions are reflected at the shock. These ions propagate with a bulk velocity comparable to the bulk velocity of the incoming solar wind backwards into the inner heliosphere. They undergo strong pitch-angle diffusion as they interact with the interplanetary Alfvturbulence similar to freshly ionized pick-up ions (PUIs). Their distribution function is hence isotropized to a shell in velocity space. Since their velocity magnitude in the wind frame is higher (about two times) than the estimated PUI velocity, part of the reflected and isotropized ions can directly enter an acceleration pro- cess (diffusive or stochastic, respectively) without the neces- sity of a pre-acceleration. This means that an additional self- initialized seed population for the injection into the anoma- lous cosmic ray (ACR) acceleration is shown to appear due to shock reflected solar wind ions.

PARTICLE ACCELERATION IN RELATIVISTIC MAGNETIZED COLLISIONLESS PAIR SHOCKS: DEPENDENCE OF SHOCK ACCELERATION ON MAGNETIC OBLIQUITY

We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to "subluminal" shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For increasing magnetic inclination in the subluminal range, the high-energy tail accounts for an increasing fraction of particles (from ~1% to ~2%) and energy (from ~4% to ~12%). The spectral index of the power law increases with angle from -2.8+-0.1 to -2.3+-0.1. Particle energization is driven by the Diffusive Shock Acceleration process for nearly parallel shocks, and switches to Shock-Drift Acceleration for larger subluminal inclinations. For "superluminal" shocks, the downstream particle spectrum does not show any significant suprathermal tail. As seen from the upstream frame, efficient acceleration in relativistic (Lorentz factor gamma0 > 5) magnetized (sigma > 0.03) flows exists only for a very small range of magnetic inclination angles (< 34/gamma0 degrees), so relativistic astrophysical pair shocks have to be either nearly parallel or weakly magnetized to generate nonthermal particles. These findings place constraints on the models of AGN jets, Pulsar Wind Nebulae and Gamma Ray Bursts that invoke particle acceleration in relativistic magnetized shocks. (Abridged)

Modified jump conditions for anisotropic temperature plasmas at parallel shocks

Aims. We reinvestigate the parallel pressure-anisotropic MHD shock with an emphasis on the downstream stability of the plasma with respect to the firehose instability. Methods. Aiming to close the underdetermined jump conditions, we take advantage of a kinetic model of the shock transit, based on the Boltzman-Vlasow equation with CGL invariants. In addition, we show that we need to consider plasma waves as an additional component of the system. Results. The system of jump conditions and the kinetic model reduces to a relatively simple form. At first glance, about all parallel magnetosonic shocks must be considerd unstable, at least with respect to plasma-wave generation caused by the firehose instability. In a similar way to this fundamental instability, the system will be also unstable when considering other plasma instabilities.

Dynamical feedback of self-generated magnetic fields in cosmic ray modified shocks

We present a semi-analytical kinetic calculation of the process of non-linear diffusive shock acceleration (NLDSA) which includes the magnetic field amplification due to cosmic ray induced streaming instability, the dynamical reaction of the amplified magnetic field and the possible effects of turbulent heating. The approach is specialized to parallel shock waves, and the parameters we chose are the ones appropriate to forward shocks in supernova remnants. Our calculation allows us to show that the net effect of the amplified magnetic field is to enhance the maximum momentum of accelerated particles while reducing the concavity of the spectra, with respect to the standard predictions of NLDSA. This is mainly due to the dynamical reaction of the amplified field on the shock, which notably reduces the modification of the shock precursor. The total compression factors which are obtained for parameters typical of supernova remnants are Rtot∼ 7–10, in good agreement with the values inferred from observations. The strength of the magnetic field produced through excitation of streaming instability is found in good agreement with the values inferred for several remnants if the thickness of the X-ray rims is interpreted as due to severe synchrotron losses of high-energy electrons. We also discuss the relative role of turbulent heating and magnetic dynamical reaction in driving the reduction of the precursor modification.

Interaction of a thin shock with turbulence. I. Effect on shock structure: Analytic model

A two-dimensional magnetohydrodynamical model describing the interaction of thin shock waves with turbulence is developed by adopting a multiscale perturbation analysis. The interaction is found to be governed by a two-dimensional inviscid Burgers’ equation that includes “perturbation terms.” Initially prescribed perturbation profiles are explored with numerical simulations to show how the shock front is modified by turbulence. Our numerical simulations show that magnetic field perturbations play a very important role in modifying the structure of perpendicular and parallel shocks. While turbulence can balance the nonlinear steepening of a shock wave at some regions, it can also help to create a larger jump in physical quantities such as the magnetic field at other regions. The plasma medium in these regions can therefore experience a higher compression, which will result in a downstream state that differs from the usual Rankine–Hugoniot state.

Self-initialised Fermi-1 acceleration by pitch-angle re-scattering of solar wind ions reflected from the parallel termination shock

In a recent kinetic calculation a rather high amount of reflected ions was shown to occur at the solar wind ter- mination shock under a parallel magnetic field orientation. The fate of these reflected ions is analysed within the scope of this paper. In the inner heliosphere their further trans- port is expected to be mainly influenced by pitch-angle scat- tering similar to the process governing pick-up ions (PUIs). This diffusive scattering isotropises the ions on a shell-like distribution in the comoving upstream solar wind reference frame. The resulting distribution is calculated and the re- sult is applied on our earlier kinetic model. The isotropised ions, when again convected into the shock, tend to attenu- ate the shock a little and lead to an additional energetic tail population in the downstream distribution function. A con- sistent incorporation of the reflected ions into the model is iteratively possible. It turns out that a part of the reflected and isotropised ions offer properties which allow for the ac- celeration to the anomalous cosmic ray (ACR) regime as an additional contribution to the injection by pick-up ions (i.e. we propose a self-injection mechanism to the Fermi-1 accel- eration process).

Shock Acceleration of Solar Energetic Protons: The First 10 Minutes

Proton acceleration at a parallel coronal shock is modeled with self-consistent Alfvén wave excitation and shock transmission. 18-50 keV seed protons at 0.1% of plasma proton density are accelerated in 10 minutes to a power-law intensity spectrum rolling over at 300 MeV by a 2500 km s−1 shock traveling outward from 3.5 r☉, for typical coronal conditions and low ambient wave intensities. Interaction of high-energy protons of large pitch angles with Alfvén waves amplified by low-energy protons of small pitch angles is key to rapid acceleration. Shock acceleration is not significantly retarded by sunward streaming protons interacting with downstream waves. There is no significant second-order Fermi acceleration.

WAVE TRANSMISSION AND HARD PARTICLE SPECTRA FROM PARALLEL SHOCKS

I review recent results concerning the effects that relativistic parallel shocks can have on the particle-scattering turbulence, and how these effects, in turn, can change the shock's particle acceleration properties. I discuss the possibility of increased compression ratio due to this kind of turbulence transmission, and consider the effects of additional compression on the energy spectrum of the accelerated particles. Emphasis is put on the possibility of producing spectral indices that are significantly harder than what is usually expected from the first-order Fermi mechanism, but required by some observations. Finally, I discuss the physical requirements — and their plausibility in real astronomical objects — of this mechanism to have notable effects.

Ion reflections from the parallel MHD termination shock and a possible injection mechanism into the Fermi-1 acceleration

Context. The analysis with our recently developed kinetic solar wind termination shock model for a parallel magnetic field orientation has shown several interesting features of the ion distribution function at the downstream side of the magnetohydrodynamic shock. Among these results, it turned out that a certain amount of ions are provided with a velocity backwards into the shock transition layer by turbulent interaction.

A kinetic description of the dissipative quasi-parallel solar wind termination shock

Context. As a special case of astrophysical MHD shock waves, the solar wind termination shock is typically treated using the MHD jump conditions as they have been determined by Rankine and Hugoniot. A kinetic analysis becomes necessary for both a more detailed view of the governing processes and a deeper understanding of the plasma behaviour. Aims. In the case of a parallel shock, only an electric field can be considered as the main process decelerating the solar wind ions. This field leads to a strong acceleration for the electrons due to the other sign of their charge and the much lower mass of the electrons than of the ions. This situation enforces a two-stream instability, which is considered to be compensated by wave-particle interactions with electrostatic plasma waves. Methods. The kinetic approach leads to an equation in Fokker-Planck form, which can be solved by using It¯ o’s calculus for stochastic differential equations. Results. These two processes (electric field and wave-particle interaction) yield a decelerated subsonic solar wind on the downstream side of the termination shock, showing some new features in the ion distribution function, such as a double-hump structure and a comparatively large number of reflected ions. Within these considerations, we estimate of the spatial size of the shock region.

Observational 2D model of H2emission from a bow shock in the Orion Molecular Cloud

Aims. We present a new method for reproducing high spatial resolution observations of bow shocks by using 1D plane parallel shock models. As an example we analyse one bow shock located in the Orion Molecular Cloud (OMC1). Methods. We use high spatial resolution near-infrared observations of H2 rovibrational emission to constrain shock models. These observations have been made at the ESO-VLT using a combination of the NACO adaptive optics system and infrared camera array and the Fabry-Perot interferometer. Three rovibrational H2 lines have been observed: v = 1− 0S (1) at 2.12µm, v = 1− 0S (0) at 2.23µm and v = 2− 1S (1) at 2.25µm. The spatial resolution is 0. �� 15 ∼ 70 AU. We analyse a single bow shock located in our field, featuring a very well defined morphology and high brightness. Results. One dimensional shock models are combined to estimate the physical properties of pre-shock density, shock velocity and transverse magnetic field strength along the bow shock. We find that the pre-shock density is constant at ∼5 × 10 5 cm −3 and shock velocities lie between ∼35 km s −1 in the wings of the shock and ∼50 km s −1 at the apex. We also find that the transverse magnetic field is stronger at the apex and weaker further down the wings varying between ∼2 and 4 mGauss. Predictions of shock velocity and magnetic field strength agree with previous independent observations.

Assessment of shock effects on amphibole water contents and hydrogen isotope compositions: 1. Amphibolite experiments

Kaersutitic amphiboles found within a subset of the Martian meteorites have low water contents and variably heavy hydrogen isotope compositions. In order to assess if impact shock-induced devolatilization and hydrogen isotope fractionation were determining factors in these water and isotopic characteristics of the Martian kaersutites, we conducted impact shock experiments on samples of Gore Mountain amphibolite in the Ames Vertical Gun Range (AVGR). A parallel shock experiment conducted on an anorthosite sample indicated that contamination of shocked samples by the AVGR hydrogen propellant was unlikely. Petrographic study of the experimental amphibolite shock products indicates that only ∼ 10% of the shock products experienced levels of damage equivalent to those found in the most highly shocked kaersutite-bearing Martian meteorites (30–35 GPa). Ion microprobe studies of highly shocked hornblende from the amphibolite exhibited elevated water contents (ΔH 2O ∼ 0.1 wt.%) and enriched hydrogen isotope compositions (Δ D ∼ + 10‰) relative to unshocked hornblende. Water and hydrogen isotope analyses of tens of milligrams of unshocked, moderately shocked, and highly shocked hornblende samples by vacuum extraction/uranium reduction and isotope ratio mass spectrometry (IRMS), respectively, are largely consistent with analyses of single grains from the ion microprobe. The mechanisms thought to have produced the excess water in most of the shocked hornblendes are shock-induced reduction of hornblende Fe and/or irreversible adsorption of hydrogen. Addition of the isotopically enriched Martian atmosphere to the Martian meteorite kaersutites via these mechanisms could explain their enriched and variable isotopic compositions. Alternatively, regrouping the water extraction and IRMS analyses on the basis of isotopic composition reveals a small, but consistent, degree of impact-induced devolatilization (∼ 0.1 wt.% H 2O) and H isotope enrichment (Δ D ∼ + 10‰). Extrapolating the shock signature of the regrouped data to grains that experienced Martian meteorite-like shock pressures suggests that shock-induced water losses and hydrogen isotope enrichments could approach 1 wt.% H 2O and Δ D = + 100‰, respectively. If these values are valid, then impact shock effects could explain a substantial fraction of the low water contents and variable hydrogen isotope compositions of the Martian meteorite kaersutites.