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1.
The problem of explosion along a line in a gas cloud in the presence of transverse magnetic field has been considered. Similarity solutions of the adiabatic motion of a gas behind an infinitely strong cylindrical shock wave propagating into an infinitely conducting medium at rest is obtained. Shock radius varies exponentially with time and density is inversely proportional to fourth power of shock radius just ahead of the shock front.  相似文献   

2.
The dynamical evolution of a relativistic explosion in a homogeneous medium is studied by means of a time-dependent, hydrodynamic code. When the expanding velocity of the shock front reduces to the sound velocity in the relativistic fluid, the reverse shock wave propagating inward through the expanding material is generated. The radius of the turning point of the reverse shock wave is proportional to the explosion energy and hardly depends on the mass of the explosion products. In the case of the non-relativistic explosion, the reverse shock wave is generated just after the free expansion stage. The radius of the turning point of the reverse shock wave is proportional to the mass of the explosion products and little depends on the explosion energy. In both cases of the non-relativistic and relativistic explosion, the reverse shock wave is strong in a spherical explosion and weak in a cylindrical one. The plane symmetric explosion does not generate the reverse shock wave.  相似文献   

3.
An approximate analytical solution for self-similar flow behind a spherically-symmetric magnetogasdynamic strong shock wave is investigated using the method of Laumbach and Probstein (1969). The total energy of flow is taken to be dependent on the shock radius obeying a power law. The shock is propagating into a perfect gas at rest with non-uniform density and magnetic field.  相似文献   

4.
Exarhos  G.  Moussas  X. 《Solar physics》1999,187(1):145-155
In this work we study the temporal variation of the heliospheric termination shock radius using in-ecliptic combined measurements from different spacecraft at 1 AU near the Earth. The results show that the radius of the heliospheric termination shock varies in time with a period of 11 years. During some 11-year time periods the shock radius anti-correlates with the solar cycle activity, specifically with the sunspot number. The average radius is approximately 115 AU with minimum value 80 AU and maximum value 150 AU. These values are the upper limits since we do not take into account the charge exchange effects of solar wind with the interstellar neutrals. We also compare the results with those from other spacecraft (Helios 1 and Voyager 2). We find that Helios 1 measurements give almost the same result as the one obtained from measurements at 1 AU while Voyager 2 measurements give a heliospheric termination shock radius approximately 15 AU lower.  相似文献   

5.
We presume the re-brightening of SN 1006 in AD 1016 as recorded in the ancient Chinese literature to be true and the re-brightening was caused by the encounter either of photons or the shock wave from the SN outburst with the circumstellar thin envelope mate- rials. Based on these considerations, and combining the observational results on the optical proper motion of the N-W limb and the radio observations of the other parts of the supernova remnant G327.6 14.5, we re-determine the distance to SN 1006. For the photon-encounter model, the average radius of the envelope material would be 10ly; and for the shock wave- encounter model, the radius would be about 1 ly. We then set up four equations to solve for the distance of the SN, the initial shock speed, the expansion index for two different parts of the supernova remnant, and the real original radius of the thin envelope nebula. It is indicated that only the case of photon-encounter will lead to a reasonable result. We derived a distance of 5074ly (1.56kpc), an original shock expansion velocity of 0.071c, an expansion index of 0.72 for the N-W limb of the SNR, and 0.76 for the other parts . We deem that the SNR evolution is still in the stage of reverse shock.  相似文献   

6.
Recently, a soft blackbody component was observed in the early X-ray afterglow of GRB 060218, which was interpreted as shock breakout from the thick wind of the progenitor Wolf–Rayet (WR) star of the underlying Type Ic supernova 2006aj. In this paper, we present a simple model for computing the characteristic quantities (including energy, temperature and time duration) for the transient event from the shock breakout in Type Ibc supernovae produced by the core-collapse of WR stars surrounded by dense winds. In contrast to the case of a star without a strong wind, the shock breakout occurs in the wind region rather than inside the star, caused by the large optical depth in the wind. We find that, for the case of a WR star with a dense wind, the total energy of the radiation generated by the supernova shock breakout is larger than that in the case of the same star without a wind by a factor of >10. The temperature can be either hotter or colder, depending on the wind parameters. The time duration is larger caused by the increase in the effective radius of the star due to the presence of a thick wind. Then, we apply the model to GRB 060218/SN 2006aj. We show that, to explain both the temperature and the total energy of the blackbody component observed in GRB 060218 by the shock breakout, the progenitor WR star has to have an unrealistically large core radius (the radius at optical depth of 20), larger than 100 R⊙. In spite of this disappointing result, our model is expected to have important applications to the observations on Type Ibc supernovae in which the detection of shock breakout will provide important clues to the progenitors of Type Ibc supernovae.  相似文献   

7.
Self-similar flows of a perfect gas behind the cylindrical shock wave propagating exponentially in an atmosphere whose density varies inversely as the fourth power of shock radius are investigated. The effects of radiation flux has also been taken into consideration. The total energy of the wave is constant.  相似文献   

8.
A self-similar solution to Sedov’s problem of a strong explosion in a homogeneous medium is generalized to the case of relativistic-particle generation in a supernova remnant; the particles are accelerated by Fermi’s mechanism at the shock front and in the perturbed post-shock region. Self-similarity takes place if the thickness of the prefront is small compared to its radius and if the pressure ratio of the relativistic and nonrelativistic components at the shock front is kept constant. In the presence of relativistic particles, the time dependence of the shock-front radius remains the same as that in their absence, but the plasma parameters in the inner perturbed region change appreciably. The shell of the matter raked up by the explosion is denser and thinner than that in the nonrelativistic case, the relativistic-particle pressure in the central region remains finite, and the nonrelativistic-gas pressure at the explosion center approaches zero. The influence of relativistic particles on the transition to the radiative phase of expansion of the supernova remnant and on its dynamics is studied. It is shown that relativistic particles can decrease several-fold the remnant radius at which the transition to the radiative phase occurs.  相似文献   

9.
We have previously reported the experimental discovery of a second shock forming ahead of a radiative shock propagating in Xe. The initial shock is spherical, radiative, with a high Mach number, and it sends a supersonic radiative heat wave far ahead of itself. The heat wave rapidly slows to a transonic regime and when its Mach number drops to two with respect to the downstream plasma, the heat wave drives a second shock ahead of itself to satisfy mass and momentum conservation in the heat wave reference frame. We now show experimental data from a range of mixtures of Xe and N2, gradually changing the properties of the initial shock and the environment into which the shock moves and radiates (the radiative conductivity and the heat capacity). We have successfully observed second shock formation over the entire range from 100% Xe mass fraction to 100% N2. The formation radius of the second shock as a function of Xe mass fraction is consistent with an analytical estimate.  相似文献   

10.
Abstract— Over the last few decades, rapid improvement of computer capabilities has allowed impact cratering to be modeled with increasing complexity and realism, and has paved the way for a new era of numerical modeling of the impact process, including full, three‐dimensional (3D) simulations. When properly benchmarked and validated against observation, computer models offer a powerful tool for understanding the mechanics of impact crater formation. This work presents results from the first phase of a project to benchmark and validate shock codes. A variety of 2D and 3D codes were used in this study, from commercial products like AUTODYN, to codes developed within the scientific community like SOVA, SPH, ZEUS‐MP, iSALE, and codes developed at U.S. National Laboratories like CTH, SAGE/RAGE, and ALE3D. Benchmark calculations of shock wave propagation in aluminum‐on‐aluminum impacts were performed to examine the agreement between codes for simple idealized problems. The benchmark simulations show that variability in code results is to be expected due to differences in the underlying solution algorithm of each code, artificial stability parameters, spatial and temporal resolution, and material models. Overall, the inter‐code variability in peak shock pressure as a function of distance is around 10 to 20%. In general, if the impactor is resolved by at least 20 cells across its radius, the underestimation of peak shock pressure due to spatial resolution is less than 10%. In addition to the benchmark tests, three validation tests were performed to examine the ability of the codes to reproduce the time evolution of crater radius and depth observed in vertical laboratory impacts in water and two well‐characterized aluminum alloys. Results from these calculations are in good agreement with experiments. There appears to be a general tendency of shock physics codes to underestimate the radius of the forming crater. Overall, the discrepancy between the model and experiment results is between 10 and 20%, similar to the inter‐code variability.  相似文献   

11.
Self-similar unsteady flows with zero temperature gradient behind strong spherical shocks propagating in non-uniform perfect gas at rest are investigated. The total energy of the flow is assumed to be varying with the shock radius obeying a power law. Approximate solutions in a closed analytical form are obtained using the integral method. Also these solutions are shown to be useful to calculate easily and quickly the shock temperature, X-ray surface brightness and luminosity which are important in astrophysical problems. It is found that these approximate solutions are in close agreement with numerical solutions.  相似文献   

12.
In this paper self-similar solutions have been investigated for the propagation of axisymmetric radiative gasdynamic shocks caused by an explosion into an inhomogeneous ideal gas permeated by a current free azimuthal magnetic field. The effects of radiation flux and magnetic field together have been seen in the region of interest on the other flow variables. The total energy of the flow between the inner expanding surface and the shock is taken to be dependent on shock radius obeying a power law. The radiative pressure and energy have been neglected.  相似文献   

13.
The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n ext ∝  R − k , we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t ⊕ =  R /4(4− k ) γ2c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t co = 2 R /(5− k ) γc. We next study the evolution of the fireball by using the analytic solution of Blandford &38; McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p  = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k  = 2.  相似文献   

14.
The structure of collisionless shocks propagating parallel to the magnetic field is discussed in the case of a large ratio of plasma pressure to magnetic pressure. The theory makes use of the basic ideas of Kennel and Sagdeev and it is shown that their shock model is to be interpreted in terms of relaxation shocks. The calculations are based on a purely macroscopic set of equations including finite Larmor radius effects. The resulting shock structure is determined both in a quasilinear WKB-type approximation and through a direct numerical integration of the basic non-linear equations. The results from both methods agree fairly well, although the level of the turbulence is high. It is argued that strong parallel shocks have a double structure, where the main transition is followed by a broad relaxation wave. It is suggested that the magnetosheath should be considered as the relaxation zone of the Earth's bow shock.  相似文献   

15.
In the present paper self-similar solutions have been investigated for the propagation of piston driven, radiative gas-dynamic shocks into an inhomogeneous ideal gas permeated by a current free azimuthal magnetic field for spherical symmetry. The effects of radiation flux and magnetic field together have been seen in the region of interest on the other flow variables. The total energy of the flow between the piston and the shock is taken to be dependent on the shock radius obeying a power law. The radiative pressure and energy have been neglected. This problem is more general than the others done so far. The word piston implies some means to drive plasma radially onwards.  相似文献   

16.
We investigate the linear stability of a shocked accretion flow on to a black hole in the adiabatic limit. Our linear analyses and numerical calculations show that, despite the post-shock deceleration, the shock is generally unstable to non-axisymmetric perturbations. The simulation results of Molteni, Tóth & Kuznetsov can be well explained by our linear eigenmodes. The mechanism of this instability is confirmed to be based on the cycle of acoustic waves between the corotation radius and the shock. We obtain an analytical formula to calculate the oscillation period from the physical parameters of the flow. We argue that the quasi-periodic oscillation should be a common phenomenon in accretion flows with angular momentum.  相似文献   

17.
We show that it can be possible to obtain lower limits on the jet Lorentz factors in superluminal very high energy (VHE) -ray blazars (e.g. Mrk, 421) which are more restrict than that ones derived only from the observations of superluminal motion. To do that we need to define some parameters of the blazars (i.e. accretion disk luminosity, disk inner radius, or disk temperature at the inner radius) which can be fixed in some sources based on the optical-UV observations. Moreover the knowledge is required on: (a) the variability time scale of radiation emitted from the shock (blob) region; (b) the maximum energy of emitted -rays; (c) and the value of an apparent speed of the shock from measurements of superluminal motion in the source. Based on the available observations of Mrk 421 and QSO 1633+382 we put constraints on the jet Lorentz factor in these sources as a function of their disk inner radius.  相似文献   

18.
Abstract— Landsat TM, aerial photograph image analysis, and field mapping of Witwatersrand supergroup meta‐sedimentary strata in the collar of the Vredefort Dome reveals a highly heterogeneous internal structure involving folds, faults, fractures, and melt breccias that are interpreted as the product of shock deformation and central uplift formation during the 2.02 Ga Vredefort impact event. Broadly radially oriented symmetric and asymmetric folds with wavelengths ranging from tens of meters to kilometers and conjugate radial to oblique faults with strike‐slip displacements of, typically, tens to hundreds of meters accommodated tangential shortening of the collar of the dome that decreased from ?17% at a radius from the dome center of 21 km to <5% at a radius of 29 km. Ubiquitous shear fractures containing pseudotachylitic breccia, particularly in the metapelitic units, display local slip senses consistent with either tangential shortening or tangential extension; however, it is uncertain whether they formed at the same time as the larger faults or earlier, during the shock pulse. In addition to shatter cones, quartzite units show two fracture types—a cmspaced rhomboidal to orthogonal type that may be the product of shock‐induced deformation and later joints accomplishing tangential and radial extension. The occurrence of pseudotachylitic breccia within some of these later joints, and the presence of radial and tangential dikes of impact melt rock, confirm the impact timing of these features and are suggestive of late‐stage collapse of the central uplift.  相似文献   

19.
Interplanetary coronal mass ejections (ICMEs) and their subset, magnetic clouds (MCs), are important manifestations of solar activity which have substantial impact on the geomagnetic field. We re-analyze events already identified in Wind and Voyager 2 data and estimate changes of their geometry along the path from the Sun. The analysis is based on the thickness of the sheath between a shock and a particular ICME or MC which is proportional to the apparent curvature radius of ICMEs/MCs. We have found that this apparent radius of curvature increases with the Mach number and this effect is attributed to the larger deformation of the fast ICME/MC. Further, the relative sheath thickness that is proportional to the flux rope oblateness decreases with the magnetic field intensity inside the ICME/MC and increases with the heliospheric distance.  相似文献   

20.
Hydrocode modeling of oblique impacts: The fate of the projectile   总被引：1，自引：0，他引：1  
Abstract— All impacts are oblique to some degree. Only rarely do projectiles strike a planetary surface (near) vertically. The effects of an oblique impact event on the target are well known, producing craters that appear circular even for low impact angles (>15° with respect to the surface). However, we still have much to learn about the fate of the projectile, especially in oblique impact events. This work investigates the effect of angle of impact on the projectile. Sandia National Laboratories' three‐dimensional hydrocode CTH was used for a series of high‐resolution simulations (50 cells per projectile radius) with varying angle of impact. Simulations were carried out for impacts at 90, 60, 45, 30, and 15° from the horizontal, while keeping projectile size (5 km in radius), type (dunite), and impact velocity (20 km/s) constant. The three‐dimensional hydrocode simulations presented here show that in oblique impacts the distribution of shock pressure inside the projectile (and in the target as well) is highly complex, possessing only bilateral symmetry, even for a spherical projectile. Available experimental data suggest that only the vertical component of the impact velocity plays a role in an impact. If this were correct, simple theoretical considerations indicate that shock pressure, temperature, and energy would depend on sin2θ, where θ is the angle of impact (measured from the horizontal). However, our numerical simulations show that the mean shock pressure in the projectile is better fit by a sin θ dependence, whereas shock temperature and energy depend on sin3/2 θ. This demonstrates that in impact events the shock wave is the result of complex processes that cannot be described by simple empirical rules. The mass of shock melt or vapor in the projectile decreases drastically for low impact angles as a result of the weakening of the shock for decreasing impact angles. In particular, for asteroidal impacts the amount of projectile vaporized is always limited to a small fraction of the projectile mass. In cometary impacts, however, most of the projectile is vaporized even at low impact angles. In the oblique impact simulations a large fraction of the projectile material retains a net downrange motion. In agreement with experimental work, the simulations show that for low impact angles (30 and 15°), a downrange focusing of projectile material occurs, and a significant amount of it travels at velocities larger than the escape velocity of Earth.  相似文献   

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