Showing papers on "Shock wave published in 1999"

Jets in Gamma-Ray Bursts

Abstract: In the afterglows of several gamma-ray bursts (GRBs), rapid temporal decay, which is inconsistent with spherical (isotropic) blast-wave models, is observed. In particular, GRB 980519 had the most rapidly fading of the well-documented GRB afterglows, with t(sup -2.05 +/- 0.04) in optical as well as in X-rays. We show that such temporal decay is more consistent with the evolution of a jet after it slows down and spreads laterally, for which t(sup -P) decay is expected (where p is the index of the electron energy distribution). Such a beaming model would relax the energy requirements on some of the more extreme GRBs by a factor of several hundred. It is likely that a large fraction of the weak- (or no-) afterglow observations are also due to the common occurrence of beaming in GRBs and that their jets have already transitioned. to the spreading phase before the first afterglow observations were made. With this interpretation, a universal value of p approx. = 2.4 is consistent with all data.

Generation of Magnetic Fields in the Relativistic Shock of Gamma-Ray Burst Sources

Abstract: We show that the relativistic two-stream instability can naturally generate strong magnetic fields with 10-5-10-1 of the equipartition energy density, in the collisionless shocks of gamma-ray burst (GRB) sources. The generated fields are parallel to the shock front and fluctuate on the very short scale of the plasma skin depth. The synchrotron radiation emitted from the limb-brightened source image is linearly polarized in the radial direction relative to the source center. Although the net polarization vanishes under circular symmetry, GRB sources should exhibit polarization scintillations as their radio afterglow radiation gets scattered by the Galactic interstellar medium. Detection of polarization scintillations could therefore test the above mechanism for magnetic field generation.

The expulsion of stellar envelopes in core-collapse supernovae

Abstract: We examine the relation between presupernova stellar structure and the distribution of ejecta in core-collapse supernovae of Types Ib, Ic, and II, under the approximations of adiabatic, spherically symmetric flow. We develop a simple yet accurate analytical formula for the velocity of the initial forward shock that traverses the stellar envelope. For material that does not later experience a strong reverse shock, the entropy deposited by this forward shock persists into the final, freely expanding state. We demonstrate that the final density distribution can be approximated with simple models for the final pressure distribution, in a way that matches the results of simulations. Our results indicate that the distribution of density and radiation pressure in a star's ejecta depends on whether the outer envelope is radiative or convective, and if convective, on the composition structure of the star. Our models are most accurate for the high-velocity ejecta cast away from the periphery of a star. For stellar structures that limit to a common form in this region, the resulting ejecta limit to a common distribution at high velocities because the blast wave forgets its history as it approaches the stellar surface. We present formulae for the final density distribution of this material as a function of mass, for both radiative and efficiently convective envelopes. These formulae limit to the well-known planar, self-similar solutions for mass shells approaching the stellar surface. However, the assumption of adiabatic flow breaks down for shells of low optical depth, so this planar limit need not be attained. The event of shock emergence, which limits adiabatic flow, also produces a soft X-ray burst of radiation. Formulae are given for the observable properties of this burst and their dependence on the parameters of the explosion. Motivated by the relativistic expansion recently inferred by Kulkarni et al. for the synchrotron shell around SN 1998bw, we estimate the criterion for relativistic mass ejection and the rest mass of relativistic ejecta. We base our models for the entire ejecta distribution on the high-velocity solution, on our shock-velocity formula, and on realistic radiation pressure distributions. We also present simpler, but less flexible, analytical approximations for ejecta distributions. We survey the ejecta of the polytropic hydrogen envelopes of red supergiants. Our models will be useful for studies of the light curves and circumstellar or interstellar interactions of core-collapse supernovae, and of the birth of pulsar nebulae in their ejecta.

Observation of Ion-Acoustic Shocks in a Dusty Plasma

Abstract: Linear and nonlinear dust ion-acoustic waves are studied experimentally in a homogeneous unmagnetized dusty plasma. In the linear regime, the phase velocity of the wave increases and the wave suffers heavy damping with increasing dust density. An oscillatory ion-acoustic shock wave in usual Ar plasma transforms into a monotonic shock front when it travels through the dusty plasma column. The Korteweg--de Vries--Burgers equation is numerically integrated taking experimental parameters into account, and the results are compared with the experimental findings.

Predictions for the Very Early Afterglow and the Optical Flash

Abstract: According to the internal-external shocks model for gamma-ray bursts (GRBs), the GRB is produced by internal shocks within a relativistic flow while the afterglow is produced by external shocks with the interstellar medium. We explore the early afterglow emission. For short GRBs the peak of the afterglow will be delayed, typically by few dozens of seconds after the burst. For long GRBs the early afterglow emission will overlap the GRB signal. We calculate the expected spectrum and the light curves of the early afterglow in the optical, X-ray, and gamma-ray bands. These characteristics provide a way to discriminate between late internal shocks emission (part of the GRB) and the early afterglow signal. If such a delayed emission, with the characteristics of the early afterglow, is detected, it can be used to prove the internal shock scenario as producing the GRB, as well as to measure the initial Lorentz factor of the relativistic flow. The reverse shock, at its peak, contains energy which is comparable to that of the GRB itself but has a much lower temperature than that of the forward shock so it radiates at considerably lower frequencies. The reverse shock dominates the early optical emission, and an optical flash brighter than 15th magnitude is expected together with the forward shock peak at X-rays or gamma-rays. If this optical flash is not observed, strong limitations can be put on the baryonic contents of the relativistic shell deriving the GRBs, leading to a magnetically dominated energy density.

Dynamical Friction in a Gaseous Medium

Abstract: Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber Mp traveling at velocity V through a uniform gaseous medium of density ρ0 and sound speed cs. This drag force acts in the direction - and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (≡V/cs>1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion ( 1, but is less efficient when <1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal ρ∝r−2 halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.

Cracks Faster than the Shear Wave Speed

Abstract: Classical dynamic fracture theories predict the surface wave speed to be the limiting speed for propagation of in-plane cracks in homogeneous, linear elastic materials subjected to remote loading. This report presents experimental evidence to the contrary. Intersonic shear-dominated crack growth featuring shear shock waves was observed along weak planes in a brittle polyester resin under far-field asymmetric loading. When steady-state conditions were attained, the shear cracks propagated at speeds close to √2 times the material shear wave speed. These observations have similarities to shallow earthquake events where intersonic shear rupture speeds have been surmised.

A Super-Alfvénic Model of Dark Clouds

Abstract: Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfven waves, but the possibility that these motions are super-Alfvenic has not been ruled out. In this work we report the results of numerical experiments in two opposite regimes: A ~ 1 and A 1, where A is the initial Alfvenic Mach number—the ratio of the rms velocity to the Alfven speed. Our results show that models with A 1 are consistent with the observed properties of molecular clouds that we have tested (statistics of extinction measurements, distribution of integrated antenna temperature, Zeeman-splitting measurements of magnetic field strength, line width versus integrated antenna temperature of molecular emission-line spectra, statistical B-n relation, and scatter in that relation), while models withA ~ 1 have properties that are in conflict with the observations. We find that both the density and the magnetic field in molecular clouds may be very intermittent. The statistical distributions of the magnetic field and gas density are related by a power law, with an index that decreases with time in experiments with decaying turbulence. After about one dynamical time it stabilizes at B ∝ n0.4. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density field wins out, and also cores with a weak field can be generated by mass accretion along magnetic field lines.

A Simple Model of Nonlinear Diffusive Shock Acceleration

Abstract: We present a simple model of nonlinear diffusive shock acceleration (also called first-order Fermi shock acceleration) that determines the shock modification, spectrum, and efficiency of the process in the plane-wave, steady state approximation as a function of an arbitrary injection parameter, η. The model, which uses a three-power-law form for the accelerated particle spectrum and contains only simple algebraic equations, includes the essential elements of the full nonlinear model and has been tested against Monte Carlo and numerical kinetic shock models. We include both adiabatic and Alfven wave heating of the upstream precursor. The simplicity and ease of calculation make this model useful for studying the basic properties of nonlinear shock acceleration, as well as providing results accurate enough for many astrophysical applications. It is shown that the shock properties depend upon the shock speed u0 with respect to a critical value u ηp, which is a function of the injection rate η and maximum accelerated particle momentum pmax. For u0 MA0, or by rtot ≈ 1.5M in the opposite case (MS0 is the sonic Mach number and MA0 is the Alfven Mach number). If u0 > u, the shock, although still strong, becomes almost unmodified and accelerated particle production decreases inversely proportional to u0.

Gamma-ray burst afterglow: Polarization and analytic light curves

Abstract: Gamma-ray burst afterglow polarization is discussed. We find an observable, up to ~10%, polarization, if the magnetic field coherence length grows at about the speed of light after the field is generated at the shock front. Detection of a polarized afterglow would show that collisionless ultrarelativistic shocks can generate strong large-scale magnetic fields and confirm the synchrotron afterglow model. Nondetection, at the ~1% level, would imply that either the synchrotron emission model is incorrect or that strong magnetic fields, after they are generated in the shock, somehow manage to stay undissipated at "microscopic," skin depth, scales. Analytic light curves of synchrotron emission from an ultrarelativistic self-similar blast wave are obtained for an arbitrary electron distribution function, taking into account the effects of synchrotron cooling. The peak synchrotron flux and the flux at frequencies much smaller than the peak frequency are insensitive to the details of the electron distribution function; hence, their observational determination would provide strong constraints on blast-wave parameters.

GRB 990123: reverse and internal shock flashes and late afterglow behaviour

Abstract: The prompt (t≲0.16 d) light curve and initial 9th-magnitude optical flash from GRB 990123 can be attributed to a reverse external shock, or possibly to internal shocks. We discuss the time decay laws and spectral slopes expected under various dynamical regimes, and the constraints imposed on the model by the observations, arguing that they provide strongly suggestive evidence for features beyond those in the simple standard model. The longer term afterglow behaviour is discussed in the context of the forward shock, and it is argued that, if the steepening after 3 d is due to a jet geometry, this is likely to be a result of jet-edge effects, rather than sideways expansion.

Images and spectra from the interior of a relativistic fireball

Abstract: The power-law decay of gamma-ray burst (GRB) afterglow can be well described by synchrotron emission from a relativistic spherical blast wave, driven by an expanding fireball. We calculate the spectrum and the light curve expected from an adiabatic blast wave which is described by the Blandford-McKee self-similar solution. These calculations include emission from the whole blast wave and not just from the shock front. We provide numerical corrections that can be used to modify simple analytic estimates of such emission. We find that the expected light curve and spectra are flat near the peak. This rules out the interpretation of the sharp optical peak observed in GRB 970508 as the peak of the light curve. We also calculate the observed image of an afterglow. This image could be resolved in future VLBI observations, and its structure could influence microlensing and scintillation. The observed image is ringlike: brighter near the edge and dimmer at the center. The image depends on the observed frequency. The contrast between the edge and the center increases and the ring becomes narrower at higher frequencies.

Bubble dynamics, shock waves and sonoluminescence

Abstract: Sound and light emission by bubbles is studied experimentally. Single bubbles kept in a bubble trap and single lasergenerated bubbles are investigated using ultrafast and highspeed photography in c...

Blunt-Body Wave Drag Reduction Using Focused Energy Deposition

Abstract: A parametric computational study of energy deposition upstream of generic two-dimensional and axisymmetric blunt bodies at Mach numbers of 6.5 and 10 is performed utilizing a full Navier-Stokes computational fluid dynamics code. The energy deposition modifies the upstream shock structure and results in large wave drag reduction and very high power effectiveness. Specifically, drag is reduced to values as low as 30% of baseline drag (no energy deposited into flow) and power effectiveness ratios (ratio of thrust power saved to power deposited into the flow) of up to 33 are obtained. The fluid dynamic and thermodynamic bases of the observed drag reduction are examined

Ultra-high-energy cosmic ray acceleration by relativistic blast waves

Abstract: We consider the acceleration of charged particles at the ultrarelativistic shocks, with Lorentz factors Γs≫1 relative to the upstream medium, arising in relativistic fireball models of gamma-ray bursts (GRBs). We show that for Fermi-type shock acceleration, particles initially isotropic in the upstream medium can gain a factor of order Γs2 in energy in the first shock-crossing cycle, but that the energy gain factor for subsequent shock-crossing cycles is only of order 2, because for realistic deflection processes particles do not have time to become isotropic upstream before recrossing the shock. We evaluate the maximum energy attainable and the efficiency of this process, and show that for a GRB fireball expanding into a typical interstellar medium, these exclude the production of ultra-high-energy cosmic rays (UHECRs), with energies in the range 1018.5--1020.5 eV, by the blast wave. However, we propose that in the context of neutron-star binaries as the progenitors of GRBs, relativistic ions from the pulsar-wind bubbles produced by these systems could be accelerated by the blast wave. We show that if the known binary pulsars are typical, the maximum energy, efficiency, and spectrum in this case can account for the observed population of UHECRs.

An experimental investigation of screech noise generation

Abstract: The screech noise generation process from supersonic underexpanded jets, issuing from a sonic nozzle at pressure ratios of 2.4 and 3.3 (fully expanded Mach number, Mj = 1.19 and 1.42), was investigated experimentally. The extremely detailed data provide a fresh, new look at the screech generation mechanism. Spark schlieren visualization at different phases of the screech cycle clearly shows the convection of the organized turbulent structures over a train of shock waves. The potential pressure field (hydrodynamic fluctuations) associated with the organized structures is fairly intense and extends outside the shear layer. The time evolution of the near-field pressure fluctuations was obtained from phase-averaged microphone measurements. Phase-matched combined views of schlieren photographs and pressure fluctuations show the sound generation process. The individual compression and rarefaction parts of the sound waves are found to be generated from similar hydrodynamic fluctuations. A partial interference between the upstream-propagating sound waves and the downstream-propagating hydrodynamic waves is found to be present along the jet boundary. The partial interference manifests itself as a standing wave in the root-mean-square pressure fluctuation data. The standing wavelength is found to be close to, but somewhat different from, the shock spacing. An outcome of the interference is a curious 'pause and go' motion of the sound waves along the jet periphery. Interestingly, a length scale identical to the standing wavelength is found to be present inside the jet shear layer. The coherent fluctuations and the convective velocity of the organized vortices are found to be modulated periodically, and the periodicity is found to match with the standing wavelength distance rather than the shock spacing. The reason for the appearance of this additional length scale, different from the shock spacing, could not be explained. Nevertheless, it is demonstrated that an exact screech frequency formula can be derived from the simple standing wave relationship. The exact relationship shows that the correct spacing between the sources, for a point source model similar to that of Powell (1953), should be a standing wavelength (not the shock spacing).

Melt Production in Oblique Impacts

Abstract: Hydrocode modeling is a fundamental tool for the study of melt production in planetary impact events. Until recently, however, numerical modeling of impacts for melt production studies has been limited to vertical impacts. We present the first results of the investigation of melt production in oblique impacts. Simulations were carried out using Sandia's three-dimensional hydrocode CTH, coupled to the SESAME equation of state. While keeping other impact parameters constant, the calculations span impact angles (measured from the surface) from 90° (vertical impact) to 15°. The results show that impact angle affects the strength and distribution of the shock wave generated in the impact. As a result, both the isobaric core and the regions of melting in the target appear asymmetric and concentrated in the downrange, shallower portion of the target. The use of a pressure-decay power law (which describes pressure as function of linear distance from the impact point) to reconstruct the region of melting and vaporization is therefore complicated by the asymmetry of the shock wave. As an analog to the pressure decay versus distance from the impact point, we used a “volumetric pressure decay,” where the pressure decay is modeled as a function of volume of target material shocked at or above the given shock pressure. We find that the volumetric pressure decay exponent is almost constant for impact angles from 90° to 30°, dropping by about a factor of two for a 15° impact. In the range of shock pressures at which most materials of geologic interest melt or begin to vaporize, we find that the volume of impact melt decreases by at most 20% for impacts from 90° down to 45°. Below 45°, however, the amount of melt in the target decreases rapidly with impact angle. Compared to the vertical case, the reduction in volume of melt is about 50% for impacts at 30° and more than 90% for a 15° impact. These estimates do not include possible melting due to shear heating, which can contribute to the amount of melt production especially in very oblique impacts. Studies of melt production in vertical impacts suggest an energy scaling law in agreement with the point source limit. An energy scaling law, however, does not seem to hold for oblique impacts, even when the impact velocity is substituted by its vertical component. However, we find that for impact angles between about 30° and 90° (a range that includes 75% of impact events on planetary surfaces) the volume of melt is directly proportional to the volume of the transient crater generated by the impact.

Black holes, shock waves, and causality in the AdS/CFT correspondence

Abstract: We find the expectation value of the energy-momentum tensor in the CFT corresponding to a moving black hole in AdS. Boosting the black hole to the speed of light, keeping the total energy fixed, yields a gravitational shock wave in AdS. The analogous procedure on the field theory side leads to ``light cone'' states, i.e., states with energy-momentum tensor localized on the light cone. The correspondence between the gravitational shock wave and these light cone states provides a useful tool for testing causality. We show, in several examples, how the CFT reproduces the causal relations in AdS.

Sound generation by shock–vortex interactions

Abstract: Two-dimensional, unsteady, compressible flow fields produced by the interactions between a single vortex or a pair of vortices and a shock wave are simulated numerically. The Navier–Stokes equations are solved by a finite difference method. The sixth-order-accurate compact Pade scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The detailed mechanics of the flow fields at an early stage of the interactions and the basic nature of the near-field sound generated by the interactions are studied. The results for both a single vortex and a pair of vortices suggest that the generation and the nature of sounds are closely related to the generation of reflected shock waves. The flow field differs significantly when the pair of vortices moves in the same direction as the shock wave than when opposite to it.

Spherical expansion of the vapor plume into ambient gas: an analytical model

Abstract: A simplified model of plume expansion into ambient atmosphere is presented which is based on the laws of mass, momentum, and energy conservation. In the course of expansion, the energy is redistributed between the thermal and kinetic energies of the plume and (internal and external) shock waves (SW). The expansion is described by ordinary differential equations for the characteristic radii (contact surface, position of the SWs). The initial stage is similar to inertial expansion into vacuum, with radius R∝t. Internal SW propagates inwards from the contact surface. Later expansion follows a point-blast model with R∝t2/5. Here the homogenized plume is decelerated and heated because of the counter-pressure of the ambient gas, which forms external SW. At a certain distance from the target, the plume stops (and even contracts), while external SW weakens and detaches from the contact surface. Analytical formulas for the transitional stages of expansion are discussed, and theoretical predictions are compared with experimental results of laser ablation of steel and YBCO in Ar.

Synchrotron and Synchrotron Self-Compton Emission and the Blast-Wave Model of Gamma-Ray Bursts

Abstract: We investigate the dynamics and radiation from a relativistic blast wave that decelerates as it sweeps up ambient matter. The bulk kinetic energy of the blast-wave shell is converted into internal energy by the process of accreting external matter. If it takes the form of nonthermal electrons and magnetic fields, then this internal energy will be emitted as synchrotron and synchrotron self-Compton radiation. We perform analytic and numerical calculations for the deceleration and radiative processes and present time-resolved spectra throughout the evolution of the blast wave. We also examine the dependence of the burst spectra and light curves on various parameters describing the magnetic field and nonthermal electron distributions. We find that for bursts such as GRB 910503, GRB 910601, and GRB 910814, the spectral shapes of the prompt gamma-ray emission at the peaks in νFν strongly constrain the magnetic fields in these bursts to be well below (10-2) the equipartition values. These calculations are also considered in the context of the afterglow emission from the recently detected gamma-ray burst counterparts.

The role of ‘splashing’ in the collapse of a laser-generated cavity near a rigid boundary

Abstract: Vapour cavities in liquid flows have long been associated with cavitation damage to nearby solid surfaces and it is thought that the final stage of collapse, when a high- speed liquid jet threads the cavity, plays a vital role in this process. The present study investigates this aspect of the motion of laser-generated cavities in a quiescent liquid when the distance (or stand-off) of the point of inception from a rigid boundary is between 0.8 and 1.2 times the maximum radius of the cavity. Numerical simulations using a boundary integral method with an incompressible liquid impact model provide a framework for the interpretation of the experimental results. It is observed that, within the given interval of the stand-off parameter, the peak pressures measured on the boundary at the first collapse of a cavity attain a local minimum, while at the same time there is an increase in the duration of the pressure pulse. This contrasts with a monotonic increase in the peak pressures as the stand-off is reduced, when the cavity inception point is outside the stated interval. This phenomenon is shown to be due to a splash effect which follows the impact of the liquid jet. Three cases are chosen to typify the splash interaction with the free surface of the collapsing cavity: (i) surface reconnection around the liquid jet; (ii) splash impact at the base of the liquid jet; (iii) thin film splash. Hydrodynamic pressures generated following splash impact are found to be much greater than those produced by the jet impact. The combination of splash impact and the emission of shock waves, together with the subsequent re-expansion, drives the flow around the toroidal cavity producing a distinctive double pressure peak.

Measurement of shock structure and shock–vortex interaction in underexpanded jets using Rayleigh scattering

Abstract: The density field of underexpanded supersonic free jets issuing from a choked circular nozzle was measured using a Rayleigh scattering-based technique. This reliable and nonintrusive technique is particularly suitable for high-speed flows and is fundamentally superior to the intrusive probes and particle-based techniques such as laser Doppler velocimetry. A continuous wave laser and photon counting electronics were employed for time and phase-averaged density measurements. The use of dust-free air for the entrained flow allowed measurements in the shear layer region. The free jets were produced in the plenum to ambient pressure ratio range of 1.88–5.75, which corresponded to a fully expanded Mach number range of 0.99⩽Mj⩽1.8. A comparative study of schlieren photographs and time-averaged density data provided insight into the shock-cell structures. The radial profiles obtained at various axial stations covering a downstream distance of 10 jet diameters show the development of the jet shear layer and the decay of the shock–cells. The supersonic free jets produced screech sound. A phase-averaged photon counting technique, using the screech tone as the trigger source, was used to measure the unsteady density variation. The phase-averaged density data show the evolution of the large-scale turbulent vortices that are found to be modulated periodically along the flow direction. A comparison with previously obtained data showing near-field pressure fluctuation and convective speed of the organized vortices reveals many interesting dynamics. All quantities show regular spatial modulation. The locations of local maxima in density fluctuations are found to coincide with the high convective speed and the antinode points in the near-field pressure fluctuation. Interestingly, the periodicity of modulation is found to be somewhat different from the shock spacing. Instead it shows that the standing wave system, known to exist in the near-field pressure fluctuation, extends into the jet shear layer. The standing wave is formed between the downstream moving Kelvin–Helmholtz instability waves and the upstream propagating part of sound waves. A detailed field measurement of the unsteady density fluctuation was conducted for the Mj=1.19 and 1.42 jets for which the near-field pressure fluctuation data were obtained previously. The phase-matched, combined plots of the density fluctuation present inside the jet flow, and the pressure fluctuation present just outside the jet boundary provide a charming insight into the shock–vortex interaction leading to the sound wave generation.

Particle acceleration and relativistic shocks

Abstract: Observations of both gamma-ray burst sources and certain classes of active galaxy indicate the presence of relativistic shock waves and require the production of high energy particles to explain their emission. In this paper we first review the basic theory of shock waves in relativistic hydrodynamics and magnetohydrodynamics, emphasizing the astrophysically interesting cases. This is followed by an overview of the theory of particle acceleration at such shocks. Whereas, for diffusive acceleration at non-relativistic shocks, it is the compression ratio which fixes the energetic particle spectrum uniquely, acceleration at relativistic shocks is more complicated. In the absence of scattering, particles are simply `compressed' as they pass through the shock front. This mechanism - called shock-drift acceleration - enhances the energy density in accelerated particles, but does so without changing the spectral index of upstream particles. Scattering due to MHD waves leads to multiple encounters between the particles and the shock front, producing an energetic particle population which depends on the properties of the shock front and the level and nature of particle scattering. We describe the method of matching the angular distributions of the upstream and downstream distributions at the shock front which leads to predictions of the spectral index. Numerical simulation of particle transport provides an alternative means of calculating spectral indices, and has recently been extended to cover ultra-relativistic shocks. We review these calculations and summarize the applications to the astrophysics of relativistic jets and fireball models of gamma-ray-bursts.

Two-Temperature Intracluster Medium in Merging Clusters of Galaxies

Abstract: We investigate the evolution of the intracluster medium during a cluster merger, explicitly considering the relaxation process between the ions and electrons using N-body and hydrodynamical simulations. When two subclusters collide, a bow shock is formed between the centers of the two substructures and propagates in both directions along the collision axis. The shock primarily heats the ions because the kinetic energy of an ion entering the shock is larger than that of an electron by the ratio of their masses. In the postshock region, the energy is transported from the ions to the electrons via Coulomb coupling. However, since the energy-exchange timescale depends on both the gas density and the temperature, the distribution of the electron temperature becomes more complex than that of the plasma mean temperature, especially in the expanding phase. After the collision of two subclusters, gas outflow occurs not only along the collision axis but also in its perpendicular direction. The gas originally located in the central parts of the subclusters moves in both the parallel and perpendicular directions. Since the equilibrium timescale of the gas along these directions is relatively short, the temperature difference between ions and electrons is larger in the directions tilted at angles of ±45° with respect to the collision axis. The electron temperature could be significantly lower than the plasma mean temperature, by at most ~50%. The significance of our results for the interpretation of X-ray observations is briefly discussed.

Ultrafast spectroscopy of shock waves in molecular materials

Abstract: ▪ Abstract Recent progress in combining the techniques of time-resolved molecular spectroscopy with shock compression science is reviewed. Shock wave spectroscopy probes the response of molecules to high-speed, large-amplitude mechanical transients and is an important way of studying physical chemical phenomena that involve large-amplitude displacements. A brief discussion of the continuum model for shock compression and a molecular model for the shock front is presented. Methods for generating and detecting shock effects are reviewed. Several applications of shock spectroscopy are reviewed, including high explosives, the nanoshock technique that uses ultrafast lasers, and shock compression of biological molecules.