Star formation induced by supersonic turbulence in interstellar molecular cloud

We studied fragmentation process of the interstellar molecular cloud which is predominated by supersonic turbulence with special regard to collisions of turbulent gas elements and formation of a shock-compressed layer by receding shock waves. The propagation of the shock waves and the evolution of the compressed layer are followed by one-dimensional gas dynamical simulation until self-gravity becomes significant, taking account of the effects of thermal properties of the molecular gas and magnetic fields. It is shown that the efficient cooling by CO molecules and its sensitive dependence on gas density make the shock-compressed layer so cold and dense that the layer becomes gravitationally unstable and breaks into fragments even if the gas elements are gravitationally stable prior to the collision. The mass of the unstable fragment is estimated to be about two solar masses or less, irrespective of the presence of the magnetic field. The stars formed by collisions of supersonic turbulent gas elements accelerate the surrounding gas in T Tauri stage and replenish the turbulent energy to maintain the mechanical equilibrium of the molecular cloud.     

Explosion-triggered star formation in the central region of the Galaxy

The role of shock waves generated by explosions in the nucleus of a galaxy and propagating through the surrounding gas, on the efficiency of star formation in this region, is investigated. It is found that if the gas in the shock-compressed layer follows polytropic changes in the density and temperature, a very wide range of masses of the fragments can be formed. Calculation shows that under suitable physical conditions a burst of star formation is actually realized.     

Nonisothermal Wave Motions in the HII Regions

The propagation of the linear and nonlinear waves in the HII regions is considered. The relaxation processes to the temperature and ionization fraction are taken into account. It is shown, that the essential damping of the waves takes place. The motion at long wavelengths is not isothermal and the velocity perturbations should be accompanied with the noticeable temperature variations. Instability of the traveling waves in the partially ionized hydrogen is possible. This effect may be important in the gas layer between ionization and shock fronts. It is found out, that the nonlinear waves can be generated by the ionization-shock front. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Morávka meteorite fall: 2. Interpretation of infrasonic and seismic data

Abstract— The sound production from the Morávka fireball has been examined in detail making use of infrasound and seismic data. A detailed analysis of the production and propagation of sonic waves during the atmospheric entry of the Morávka meteoroid demonstrates that the acoustic energy was produced both by the hypersonic flight of the meteoroid (producing a cylindrical blast wave) and by individual fragmentation events of the meteoroid, which acted as small explosions (producing quasispherical shock waves). The deviation of the ray normals for the fragmentation events was found to be as much as 30° beyond that expected from a purely cylindrical line source blast. The main fragmentation of the bolide was confined to heights above 30 km with a possible maximum in acoustic energy production near 38 km. Seismic stations recorded both the direct arrival of the airwaves (the strongest signal) as well as air‐coupled P‐waves and Rayleigh waves (earlier signals). In addition, deep underground stations detected the seismic signature of the fireball. The seismic data alone permit reconstruction of the fireball trajectory to a precision on the order of a few degrees. The velocity of the meteoroid is much less well‐determined by these seismic data. The more distant infrasonic station detected 3 distinct signals from the fireball, identified as a thermospheric return, a stratospheric return, and an unusual mode propagating through the stratosphere horizontally and then leaking to the receiver.     

Jump relations across a shock in non-ideal gas flow

Generalized forms of jump relations are obtained for one dimensional shock waves propagating in a non-ideal gas which reduce to Rankine-Hugoniot conditions for shocks in idea gas when non-idealness parameter becomes zero. The equation of state for non-ideal gas is considered as given by Landau and Lifshitz. The jump relations for pressure, density, temperature, particle velocity, and change in entropy across the shock are derived in terms of upstream Mach number. Finally, the useful forms of the shock jump relations for weak and strong shocks, respectively, are obtained in terms of the non-idealness parameter. It is observed that the shock waves may arise in flow of real fluids where upstream Mach number is less than unity.     

Chondrule formation by the ablation of small planetesimals

Abstract— Numerous models have been proposed to explain the formation of chondrules, but none can be reconciled with the highly diverse properties of these objects. Here the formation of chondrules by the surface melting and ablation of small planetesimals in nebula shock waves is investigated using a numerical model. It is shown that bodies between ～1 mm and 500 m in diameter would have produced molten droplets by ablation during gas drag in nebula shocks stronger than ～2.0 Mach. The properties of chondrules produced by ablation are estimated by comparison with meteorite fusion crusts and through consideration of the environment within the bow shock envelope of ablating planetesimals. It is suggested that most ablation chondrules will have broadly chondritic compositions with depletions in siderophile and chalcophile elements and relatively high volatile contents and textures that are mainly porphyritic. The formation of chondrules by ablation of planetesimals in shock waves was probably most important at a late stage in nebula history and occurred at the same time as chondrules formed by the melting of dust particles. The high abundance of dust particles relative to larger bodies at all stages of accretion implies that only a proportion of chondrules may have been formed by ablation and that genetic groups of chondrules with very different origins may coexist in meteorites.     

Dynamics of shock waves in a contracting cloud

The contraction of an interstellar cloud is followed. The results indicates that there are shock waves appear during contraction. In order to study the effect of shock waves, two models have been studied. The post-shock temperature for the two models are, respectively, 3006 K and 2984 K. The density increases by more than three orders of magnitude. The gas is generally cooled by atoms, molecules, and grains. The dominant cooling process changes according to the chemical composition and the temperature of the gas. The thermal equilibrium depends on the existing physical conditions.     

The structure of a shock front in atomic hydrogen

A shock wave passing through a stellar atmosphere disturbs the gas, and the consequent adjustment of the fluid is a redistribution of the shock's kinetic energy among the various degrees of freedom. This paper deals with the effects of the Lyman continuum on the shock front. The shock heated gas is cooled principally by ionizing collisions of ground state atoms. This process is followed by a large quasi-isothermal region in which radiative recombinations occur. A final cycle of processes consisting of ionization, photo-recombinations to upper-level and collisional de-excitation, gives way to a sequence of statistical balances as each degree of freedom in the fluid attains equilibrium. Our calculations show that to a great extent, the shock structure is separated into successive regions of internal and radiative relaxation by an intermediate layer of ionized gas appearing at high shock speeds. Numerical results are presented for a range of shock speeds typifying a cepheid atmosphere.Radiation field and gas motions in shock waves are coupled, but the gas reacts little to the radiation it produces. Only the Lyman continuum has an appreciable effect on the shock structure. The principal escape of energy from the shock wave is through continuum radiation produced in recombinations to upper levels; thus the continuum emission in the red is stronger than an equivalent black body. Lyman photons are trapped in the shock while 20–30% of the shock's kinetic energy escapes to the Balmer and Paschen continua after the Lyman continuum is in equilibrium. The post- and pre-shock lines, as well as the post-shock continuum above the Lyman constitute the only observable spectra which emanate from the shock wave. The shock structure is perturbed only by the radiation which is not observed, and its absence tends to distort the emission profile from a Planck distribution.This work was originally started at Smithsonian Observatory and was completed at City College New York under contract with NASA Institute for Space Studies, New York.     

Plane relativistic shock waves at the edge of a gas

Similarity solutions for propagation of plane relativistic shock waves through a medium of decreasing nucleon density and approaching the edge of the gas as well as for the subsequent motion of the gas after the shock front arrives at the vacuous boundary are studied in this paper. The medium in the pre-disturbed stage is assumed cold and in the disturbed stage its equation of state is taken as that of a photonic gas.     

Problems on gravitational collapse of interstellar gas clouds

The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation)-even in the case of spherical symmetry- at times smaller than the free-fall timet _ff, provided the initial data of the Cauchy problem be discontinuous within a sphere of radius (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical timest _cr<t _ff (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves.     

Grain destruction in interstellar shock waves

Interstellar shock waves can erode and destroy grains present in the shocked gas, primarily as the result of sputtering and grain-grain collisions. Uncertainties in current estimates of sputtering yields are reviewed. Results are presented for the simple case of sputtering of fast grains being stopped in cold gas. An upper limit is derived for sputtering of refractory grains in C-type MHD shocks: shock speedsv _s 50 km s^–1 are required for return of more than 30% of the silicate to the gas phase. Sputtering can also be important for removing molecular ice mantles from grains in two-fluid MHD shock waves in molecular gas. Recent estimates of refractory grain lifetimes against destruction in shock waves are summarized, and the implications of these short lifetimes are discussed.     

Shock waves in the large-scale structure of the Universe

Cosmological shock waves are induced during hierarchical formation of large-scale structure in the universe. Like most astrophysical shocks, they are collisionless, since they form in the tenuous intergalactic medium through electromagnetic viscosities. The gravitational energy released during structure formation is transferred by these shocks to the intergalactic gas as heat, cosmic-rays, turbulence, and magnetic fields. Here we briefly described the properties and consequences of the shock waves in the context of the large-scale structure of the universe.     

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.     

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.     

A shock hodograph in collisionless plasma

In this paper, the shock hodograph (polar) for a collisionless transverse shock has been developed in the plane of the flow deflection angle and total pressure jump. The sonic point on the hodograph lies closer to the characteristic than to the point of maximum flow deflection for an attached shock. This hodograph is particularly useful in the analysis of three shock confluences and refraction of shock waves at gas interfaces. The first analysis is fully described in this paper. It is observed that the third shock wave is forward facing. It is pertinent to note that the limited region of supersonic flow also restricts the occurrences of three shock interactions.     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.     

The formation of shock waves in the recombination era of the universe

The formation and the evolution of shock waves in a two-component fluid during the recombination era of the Universe is studied. The fluid consists of photons and ionized hydrogen gas with interaction due to Thomson scattering. The analysis uses the expansion procedure in powers of the coordinates near the travelling wave front. Incorporating discontinuities in the first derivatives of the physical quantities, we are able to give the analytical solution which answers the questions as to when the discontinuities appear in the physical quantities themselves. Of the two possible waves (a radiation- and a matter-dominated wave) only the matter-dominated wave shows the shock phenomena. However, the shock is induced by the radiation due to Thomson scattering. Therefore, the time for the shock formation depends on the initial amplitude of the wave (as in usual shock phenomena) and on the collision frequency of the photons.     

Numerical simulation of slow shocks in the solar wind

The evolutionary state of slow forward shock waves is examined with the use of two MHD numerical codes. Our study is intended to be exploratory rather than a detailed parametric one. The first code is one-dimensional (with three components of velocity and magnetic field) which is used to follow a slow shock that propagates into a positive gradient of density versus distance. It is found that the slow shock evolves into an extraneous (intermediate) shock wave. The second code has a spherical, one-dimensional, planar geometry (with two velocity and magnetic field components) which is used to follow a spiral interplanetary magnetic field. It is found that a slow shock type perturbation can generate a forward slow shock; a fast forward shock is generated in the front of the slow shock; a contact discontinuity is formed behind the slow shock, and a compound nonlinear MHD wave is formed behind the contact discontinuity with a fast reverse shock formed further behind. Thus, we demonstrate that the evolution of a slow shock into (solely) a fast shock, as suggested by Whang (1987), is much more complicated.     

Propagation of cylindrical shock waves under the action of monochromatic radiation

A model of cylindrical shock waves is investigated under the action of monochromatic radiation into non-uniform stellar interiors with a constant intensity on a unit area. We have assumed that the radiation flux moves through the gas.     

Chondrule collisions in shock waves

Abstract— Detailed numerical models have shown that solar nebula shock waves would be able to thermally process chondrules in a way that is consistent with experimental constraints. However, it has recently been argued that the high relative velocities that would be generated between chondrules of different sizes immediately behind the shock front would lead to energetic collisions that would destroy the chondrules as they were processed rather than preserving them for incorporation into meteorite parent bodies. Here the outcome of these collisions is quantitatively explored using a simple analytic expression for the viscous dissipation of collisional energy in a liquid layer. It is shown that molten chondrules can survive collisions at velocities as high as a few hundred meters per second. It is also shown that the thermal evolution of chondrules in a given shock wave varies with chondrule size, which may allow chondrules of different textures to form in a given shock wave. While experiments are needed to further constrain the parameters used in this work, these calculations show that the expected outcomes from collisions behind shock waves are consistent with what is observed in meteorites.