Laboratory Simulations of Supernova Shockwave Propagation

Supernovae launch spherical shocks into the circumstellar medium (CSM). These shocks have high Mach numbers and may be radiative. We have created similar shocks in the laboratory by focusing laser pulses onto the tip of a solid pin surrounded by ambient gas; ablated material from the pin rapidly expands and launches a shock through the surrounding gas. Laser pulses were typically 5 ns in duration with ablative energies ranging from 1–150 J. Shocks in ambient gas pressures of ~1 kPa were observed at spatial scales of up to 5 cm using optical cameras with schlieren. Emission spectroscopy data were obtained to infer electron temperatures (< 10 eV). In this experiment we have observed a new phenomena; at the edge of the radiatively heated gas ahead of the shock, a second shock forms. The two expanding shocks are simultaneously visible for a time, until the original shock stalls from running into the heated gas. The second shock remains visible and continues to expand. A minimum condition for the formation of the second shock is that the original shock is super-critical, i.e., the temperature distribution ahead of the original shock has an inflexion point. In a non-radiative control experiment the second shock does not form. We hypothesize that a second shock could form in the astrophysical case, possibly in radiative supernova remnants such as SN1993J, or in shock-CSM interaction.     

Evolution and decay of acceleration waves in perfectly conducting inviscid radiative magnetogasdynamics

The paper examines the evolutionary behaviour of acceleration waves in a perfectly conducting inviscid radiating gas permeated by a transverse magnetic field. Solution of the problem in the characteristic plane has been determined. It is shown that a linear solution in the characteristic plane exhibits nonlinear behaviour in the physical plane. Transport equation governing the behaviour of acceleration waves has been derived. The effect of radiative heat transfer under the influence of magnetic field on the formation of shock wave with generalized geometry is analyzed. The critical amplitude of the initial disturbance has been obtained such that the initial amplitude of any compressive wave greater than the critical one always terminates into shock wave. Critical time, when the compressive wave will grow into a shock wave, has been determined. Also, it is assessed as to how the radiative heat transfer in the presence of magnetic field affects the shock formation.     

Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.     

On the manifestation of Richtmyer-Meshkov instability in an inhomogeneous interstellar medium with radiative cooling

We numerically simulate the evolution of the plane two-dimensional deformations of a contact discontinuity that is impulsively accelerated by a shock wave. We take into account the effects of radiative cooling and perturbation scale lengths on the dynamics and shape of the forming density inhomogeneities. For moderately intense shocks in a stellar wind and for strong shocks from a supernova, we show that the radiative cooling processes do not affect significantly the growth rate of the initial perturbations and the total mass of the forming condensations. However, the density of the matter compressed by the transmitted shock wave increases dramatically. At the same time, the contribution from long-wavelength perturbations to the deformation of the contact surface decreases significantly. In the case of shock propagation from a supernova, the initial conditions have been found to be a factor that can affect the morphology of the shocked interstellar medium.     

Oscillations of magnetohydrodynamic shock waves on the surfaces of T Tauri stars

This work treats the matter deceleration in a magnetohydrodynamic radiative shock wave at the surface of a star. The problem is relevant to classical T Tauri stars where infalling matter is channelled along the star's magnetic field and stopped in the dense layers of photosphere. A significant new aspect of this work is that the magnetic field has an arbitrary angle with respect to the normal to the star's surface. We consider the limit where the magnetic field at the surface of the star is not very strong in the sense that the inflow is super-Alfvénic. In this limit, the initial deceleration and heating of plasma (at the entrance to the cooling zone) occurs in a fast magnetohydrodynamic shock wave. To calculate the intensity of radiative losses we use 'real' and 'power-law' radiative functions. We determine the stability/instability of the radiative shock wave as a function of parameters of the incoming flow: velocity, strength of the magnetic field, and its inclination to the surface of the star. In a number of simulation runs with the 'real' radiative function, we find a simple criterion for stability of the radiative shock wave. For a wide range of parameters, the periods of oscillation of the shock wave are of the order of  0.02–0.2 s  .     

Cylindrical and Spherical Pistons as Drivers of MHD Shocks

We consider an expanding three-dimensional (3-D) piston as a driver of an MHD shock wave. It is assumed that the source-region surface accelerates over a certain time interval to achieve a particular maximum velocity. Such an expansion creates a large-amplitude wave in the ambient plasma. Owing to the nonlinear evolution of the wavefront, its profile steepens and after a certain time and distance a discontinuity forms, marking the onset of the shock formation. We investigate how the formation time and distance depend on the acceleration phase duration, the maximum expansion velocity (defining also acceleration), the Alfvén velocity (defining also Mach number), and the initial size of the piston. The model differs from the 1-D case, since in the 3-D evolution, a decrease of the wave amplitude with distance must be taken into account. We present basic results, focusing on the timing of the shock formation in the low- and high-plasma-beta environment. We find that the shock-formation time and the shock-formation distance are (1) approximately proportional to the acceleration phase duration; (2) shorter for a higher expansion velocity; (3) larger in a higher Alfvén speed environment; (4) only weakly dependent on the initial source size; (5) shorter for a stronger acceleration; and (6) shorter for a larger Alfvén Mach number of the source surface expansion. To create a shock causing a high-frequency type II burst and the Moreton wave, the source region expansion should, according to our results, achieve a velocity on the order of 1000 km?s^?1 within a few minutes, in a low Alfvén velocity environment.     

Formation of coronal MHD shock waves – II. The Pressure Pulse Mechanism

The ignition of coronal shock waves by flares is investigated. It is assumed that an explosive expansion of the source region caused by impulsive heating generates a fast-mode MHD blast wave which subsequently transforms into a shock wave. The solutions of 1-D MHD equations for the flaring region and for the external region are matched at their boundary. The obtained results show under what conditions flares can ignite shock waves that excite the metric type II bursts. The heat input rate per unit mass has to be sufficiently high and the preflare value of the plasma parameter in the flaring region has to be larger than ₀ ^crit. The critical values depend on the flare dimensions and impulsiveness. Larger and more impulsive flares are more effective in generating type II bursts. Shock waves of a higher Mach number require a higher preflare value of and a more powerful heating per unit mass. The results demonstrate why only a small fraction of flares is associated with type II bursts and why the association rate increases with the flare importance.     

The hydrogen emission spectrum of a shock wave in a stellar atmosphere

Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M₁?10 and unperturbed gas densities σ₁=10^?10 g cm^?3, the Doppler shift is approximately one third of the shock velocity U₁. The FWHM of the emission-line profile δ _? is related to the shock velocity by δ _? ≈ k _? U₁, where k _? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.     

Hydrodynamics of Supernova Evolution in the Winds of Massive Stars

Core-Collapse supernovae arise from stars greater than 8 M_⊙. These stars lose a considerable amount of mass during their lifetime, which accumulates around the star forming wind-blown bubbles. Upon the death of the star in a spectacular explosion, the resulting SN shock wave will interact with this modified medium. We study the evolution of the shock wave, and investigate the properties of this interaction. We concentrate on the evolution of the SN shock wave in the medium around a 35 solar mass star. We discuss the hydrodynamics of the resulting interaction, the formation and growth of instabilities, and deviations from sphericity.     

Design of jet-driven, radiative-blast-wave experiments for 10 kJ class lasers

We discuss the design of jet-driven, radiative-blast-wave experiments for a 10 kJ class pulsed laser facility. The astrophysical motivation is the fact that jets from Young Stellar Objects are typically radiative and that the resulting radiative bow shocks produce complex structure that is difficult to predict. To drive a radiative bow shock, the jet velocity must exceed the threshold for strong radiative effects. Using a 10 kJ class laser, it is possible to produce such a jet that can drive a radiative bow shock in gas that is dense enough to permit diagnosis by x-ray radiography. We describe the design and simulations of such experiments. The basic approach is to shock the jet material and then accelerate it through a collimating hole and into a Xe ambient medium. We identify issues that must be addressed through experimentation or further simulations in order to field successful experiments.     

A self-similar flow behind a spherical shock wave with thermal radiation,I

Similarity solutions, for one-dimensional unsteady flow of a perfect gas behind a spherical shock wave produced on account of a sudden explosion or driven out by an expanding piston including the effects of radiative cooling, are investigated. The shock ahead of the point of explosion or piston is propagating into a transparent medium at rest with non-uniform density. The total energy of the wave is assumed to be time dependent obeying a power law.     

Shock jump relations for a dusty gas atmosphere

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows.     

Studying Hydrodynamic Instability Using Shock-Tube Experiments

The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shock waves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.     

Shock acceleration of solar cosmic rays

We investigated the acceleration of solar cosmic rays (SCRs) by the shock waves produced by coronal mass ejections. We performed detailed numerical calculations of the SCR spectra produced during the shock propagation in the solar corona in terms of a model based on the diffusive transport equation using a realistic set of physical parameters for the corona. The resulting SCR energy spectrum N(ε) ∝ ε^?γ exp [? (ε/ε_max)^α] is shown to include a power-law portion with an index γ?2 that ends with an exponential tail with α ? 2.5 ? β, where β is the spectral index of the background Alfvén turbulence. The maximum SCR energy lies within the range ε_max = 1–300 MeV, depending on the shock velocity. Because of the steep spectrum of the SCRs, their backreaction on the shock structure is negligible. The decrease in the Alfvén Mach number of the shock due to the increase in the Alfvén velocity with heliocentric distance r causes the efficient SCR acceleration to terminate when the shock reaches a distance of r = 2–3R_⊙. Since the diffusive SCR propagation in this case is faster than the shock expansion, SCR particles intensively escape from the shock vicinity. A comparison of the calculated SCR fluxes expected near the Earth’s orbit with available experimental data indicates that the theory satisfactorily explains all of the main observed features.     

A model of the thermal processing of particles in solar nebula shocks: Application to the cooling rates of chondrules

Abstract— We present a model for the thermal processing of particles in shock waves typical of the solar nebula. This shock model improves on existing models in that the dissociation and recombination of H₂ and the evaporation of particles are accounted for in their effects on the mass, momentum and energy fluxes. Also, besides thermal exchange with the gas and gas‐drag heating, particles can be heated by absorbing the thermal radiation emitted by other particles. The flow of radiation is calculated using the equations of radiative transfer in a slab geometry. We compute the thermal histories of particles as they encounter and pass through the shock. We apply this shock model to the melting and cooling of chondrules in the solar nebula. We constrain the combinations of shock speed and gas density needed for chondrules to reach melting temperatures, and show that these are consistent with shock waves generated by gravitational instabilities in the protoplanetary disk. After their melting, cooling rates of chondrules in the range 10–1000 K h^?1 are naturally reproduced by the shock model. Chondrules are kept warm by the reservoir of hot shocked gas, which cools only as fast as the dust grains and chondrules themselves can radiate away the gas's energy. We predict a positive correlation between the concentration of chondrules in a region and the cooling rates of chondrules in that region. This correlation is supported by the unusually high frequency of (rapidly cooled) barred chondrules among compound chondrules, which must have collided preferentially in regions of high chondrule density. We discuss these and other compelling consistencies between the meteoritic record and the shock wave model of chondrule formation.     

The iodine‐xenon system in clasts and chondrules from ordinary chondrites: Implications for early solar system chronology

Abstract— We have studied the I‐Xe system in chondrules and clasts from ordinary chondrites. Cristobalite‐bearing clasts from Parnallee (LL3.6) closed to Xe loss 1–4 Ma after Bjurböle. Feline (a feldspar‐ and nepheline‐rich clast also from Parnallee) closed at 7.04 ± 0.15 Ma. Two out of three chondrules from Parnallee that yielded well‐defined initial I ratios gave ages identical to Bjurböle's within error. A clast from Barwell (L6) has a well‐defined initial I ratio corresponding to closure 3.62 ± 0.60 Ma before Bjurböle. Partial disturbance and complete obliteration of the I‐Xe system by shock are revealed in clasts from Julesburg (L3.6) and Quenggouk (H4), respectively. Partial disturbance by shock is capable of generating anomalously high initial I ratios. In some cases, these could be misinterpreted, yielding erroneous ages. A macrochondrule from Isoulane‐n‐Amahar contains concentrations of I similar to “ordinary” chondrules but, unlike most ordinary chondrules, contains no radiogenic ¹²⁹Xe. This requires resetting 50 Ma or more later than most chondrules. The earliest chondrule ages in the I‐Xe, Mn‐Cr, and Al‐Mg systems are in reasonable agreement. This, and the frequent lack of evidence for metamorphism capable of resetting the I‐Xe chronometer, leads us to conclude that (at least) the earliest chondrule I‐Xe ages represent formation. If so, chondrule formation took place at a time when sizeable parent bodies were present in the solar system.     

An exact similarity solution in radiation magneto-gas-dynamics for the flows behind a spherical shock wave

An exact similarity solution for a spherical magnetogasdynamic shock is obtained in the case when radiation energy, radiation pressure and radiative heat flux are important. The total energy of the shock wave increase with time. We have shown that due to the magnetic field the flow variables are considerably changed. Also, due to increases in radiation pressure number the radiation flux is increased.     

Initial Venus Express magnetic field observations of the Venus bow shock location at solar minimum

In this study, magnetic field measurements obtained by the Venus Express spacecraft are used to determine the bow shock position at solar minimum. The best fit of bow shock location from solar zenith angle 20-120° gives a terminator bow shock location of 2.14 R_V (1 R_V=6052 km) which is 1600 km closer to Venus than the 2.40 R_V determined during solar maximum conditions, a clear indication of the solar cycle variation of the Venus bow shock location. The best fit to the subsolar bow shock is 1.32 R_V, with the bow shock completely detached. Finally, a global bow shock model at solar minimum is constructed based on our best-fit empirical bow shock in the sunlit hemisphere and an asymptotic limit of the distant bow shock which is a Mach cone under typical Mach number of 5.5 at solar minimum. We also describe our approach to making the measurements and processing the data in a challenging magnetic cleanliness environment. An initial evaluation of the accuracy of measurements shows that the data are of a quality comparable to magnetic field measurements made onboard magnetically clean spacecraft.     

MHD Models and Laboratory Experiments of Jets

Jet research has long relied upon a combination of analytical, observational and numerical studies to elucidate the complex phenomena involved. One element missing from these studies (which other physical sciences utilize) is the controlled experimental investigation of such systems. With the advent of high-power lasers and fast Z-pinch machines it is now possible to experimentally studysimilar systems in a laboratory setting. Such investigations can contribute in two useful ways. They can be used for comparison with numerical simulations as a means to validate simulation codes. More importantly, however, such investigations can also be used to complement other jet research, leading to fundamentally new knowledge. In the first part of this article, we analyze the evolution of magnetized wide-angle winds in a collapsing environment. We track the ambient and wind mass separately and describe a physical mechanism by which an ionized central wind can entrain the ambient gas giving rise to internal shells of molecular material on short time scales. The formation of internal shells in molecular outflows has been found to be an important ingredient in describing the observations of convex spurs in P-V diagrams (Hubble wedges in M-V diagrams).In the second part, we present astrophysically relevant experiments in which supersonic jets are created using a conical wire array Z-pinch. The conically convergent flow generates a standing shock around the axis which collimates the flow into a Mach ～ 30 jet. The jet formation process is closely related to the work of Cantó et al. (1988) for hydrodynamic jet collimation. The influence of radiative cooling on collimation and stability is studied by varying the wire material (Al, Fe, and W).     

Radiatively driven winds from effective boundary layer around black holes

Matter accreting onto black holes suffers a standing or oscillating shock wave in much of the parameter space. The post-shock region is hot, puffed up and reprocesses soft photons from a Keplerian disc to produce the characteristic hard tail of the spectrum of accretion discs. The post-shock torus is also the base of the bipolar jets. We study the interaction of these jets with the hard photons emitted from the disc. We show that radiative force can accelerate outflows but the drag can limit the terminal speed. We introduce an equilibrium speed υ_eq as a function of distance, above which the flow will experience radiative deceleration.