Hydrocode modeling of oblique impacts: The fate of the projectile

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 sin^3/2 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.     

A numerical assessment of simple airblast models of impact airbursts

Asteroids and comets 10–100 m in size that collide with Earth disrupt dramatically in the atmosphere with an explosive transfer of energy, caused by extreme air drag. Such airbursts produce a strong blastwave that radiates from the meteoroid's trajectory and can cause damage on the surface. An established technique for predicting airburst blastwave damage is to treat the airburst as a static source of energy and to extrapolate empirical results of nuclear explosion tests using an energy‐based scaling approach. Here we compare this approach to two more complex models using the iSALE shock physics code. We consider a moving‐source airburst model where the meteoroid's energy is partitioned as two‐thirds internal energy and one‐third kinetic energy at the burst altitude, and a model in which energy is deposited into the atmosphere along the meteoroid's trajectory based on the pancake model of meteoroid disruption. To justify use of the pancake model, we show that it provides a good fit to the inferred energy release of the 2013 Chelyabinsk fireball. Predicted overpressures from all three models are broadly consistent at radial distances from ground zero that exceed three times the burst height. At smaller radial distances, the moving‐source model predicts overpressures two times greater than the static‐source model, whereas the cylindrical line‐source model based on the pancake model predicts overpressures two times lower than the static‐source model. Given other uncertainties associated with airblast damage predictions, the static‐source approach provides an adequate approximation of the azimuthally averaged airblast for probabilistic hazard assessment.     

Experimental ejection angles for oblique impacts: Implications for the subsurface flow‐field

Abstract— A simple analytical solution for subsurface particle motions during impact cratering is useful for tracking the evolution of the transient crater shape at late times. A specific example of such an analytical solution is Maxwell's Z‐Model, which is based on a point‐source assumption. Here, the parameters for this model are constrained using measured ejection angles from both vertical and oblique experimental impacts at the NASA Ames Vertical Gun Range. Data from experiments reveal that impacts at angles as high as 45° to the target's surface generate subsurface flow‐fields that are significantly different from those created by vertical impacts. The initial momentum of the projectile induces a subsurface momentum‐driven flow‐field that evolves in three dimensions of space and in time to an excavation flow‐field during both vertical and oblique impacts. A single, stationary point‐source model (specifically Maxwell's Z‐Model), however, is found inadequate to explain this detailed evolution of the subsurface flow‐field during oblique impacts. Because 45° is the most likely impact angle on planetary surfaces, a new analytical model based on a migrating point‐source could prove quite useful. Such a model must address the effects of the subsurface flow‐field evolution on crater excavation, ejecta deposition, and transient crater morphometry.     

The Seismic Efficiency of Space Body Impacts

The numerical analysis of the propagation of shock waves initiated by either a space body striking the Earth’s surface, or underground explosions, allows us to compare the energies required to attain the same amplitudes of shock waves at impacts and explosions. Proceeding from this and based on the data of seismic efficiency of underground explosions, the authors have estimated the fraction of the kinetic energy of a space body transformed into the energy of seismic disturbances when the body strikes the Earth. This fraction is about 10^–3, which is an order of magnitude more than the most common estimates. Space bodies decelerating and collapsing in the atmosphere also generate seismic waves in the ground due to the impact of the air-shock wave on the Earth’s surface. In this case, the seismic efficiency is considerably lower, according to the calculations, it is about 10^–5.     

彗木相撞的可压缩分层流体模型

提出一个彗木相撞的修正了的线性模型．在这个模型中,将木星大气视为一个转动的、分层的、可压缩和无粘滞的流体层．结果表明,虽然大部分撞击能量仍然转换成内波能量,但不能忽视可压缩效应．     

On the overtaking interaction of typical shock waves in the solar wind flow

The interaction of traveling fast solar shock waves with other fast shock waves generated previously is considered in terms of magnetohydrodynamics for various solar wind parameters. The shocks are not piston ones and move freely in the flow. The magnetic structure in the interplanetary magnetic field emerging after the shock interaction is shown to correspond to the well-known magnetic configuration commonly observed on spacecraft or the classical Hundhausen R model. A head-on collision of solar shock waves with the boundary of a magnetic cloud is considered. It is pointed out that a slow shockwave refracted into the magnetic cloud can appear at an oblique collision of the shock with the cloud boundary. The results clarify our understanding of the available spacecraft data.     

Heterogeneous chemical processes as a source of persistent meteor trains

Abstract— Observations of long‐lasting persistent trains following the entry of some meteoroids into the Earth's atmosphere are suggested to arise in part from the interaction between meteoroid components and the atmosphere and in the heterogeneous recombination reaction of atmospheric O atoms with NO. The latter occurs on the surfaces of dust left by the explosive fragmentation of larger meteoroids. A strong role is attributed to reactions of troilite (FeS), a meteorite component, with the atmosphere at elevated temperatures. The suggestions made in this paper complement previous work that suggested that long‐lived emissions results from a variety of species made in the shock of larger meteoroids.     

Similarity solution for the propagation of shock waves with varying energy in non-uniform medium

A model of self-similar propagation of shock waves driven by a flare energy release in a non-uniform atmosphere has been considered. The total energy content of the model is assumed to be increased with time within the inner expanding surface and shock front. Finally the variation of velocity, pressure, density, and energy of the model have been discussed. The gas is assumed to be grey and opaque.     

“Comet‐tail” ejecta streaks: A predicted cratering landform unique to Titan

Abstract— A model for an impact ejecta landform peculiar to Saturn's moon Titan is presented. Expansion of the ejecta plume from moderate‐sized craters is constrained by Titan's thick atmosphere. Much of the plume is collimated along the incoming bolide's trajectory, as was observed for plumes from impacts on Jupiter of P/Shoemaker‐Levy‐9, but is retained as a linear, diagonal ejecta cloud, unlike on Venus where the plume “blows out.” On Titan, the blowout is suppressed because the vertically‐extended atmosphere requires a long wake to reach the vacuum of space, and the modest impact velocities mean plume expansion along the wake is slow enough to allow the wake to close off. Beyond the immediate ejecta blanket around the crater, distal ejecta is released into the atmosphere from an oblique line source: this material is winnowed by the zonal wind field to form streaks, with coarse radar‐bright particles transported less far than fine radar‐dark material. Thus, the ejecta form two distinct streaks faintly reminiscent of dual comet tails, a sharply W‐E radar‐dark one, and a less swept and sometimes comma‐shaped radar‐bright one.     

On nonadiabatic waves in the photospheres of cool stars

The coupled set of equations of hydrodynamics and radiative transfer is derived for small disturbances in a plane, grey atmosphere. Only radiative transfer is taken into account in the energy equation; dynamical effects of radiation are ignored. A mean stationary radiative flux through the photosphere is taken into account. The radiative transfer equation is used by assuming the Eddington approximation, moreover, an exponential height profile of the temperature and an analytical opacity formula are supposed. For this model we obtained an asymptotic solution for plane nonadiabatic acoustic waves and radiation waves. The approach provides a detailed discussion of the interaction of nonadiabatic p‐modes and radiation waves in a realistic model of the photosphere of a solar‐like star.     

Roles of Fast-Cyclotron and Alfvén-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave–particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfvén waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. In this paper, we assume that i) low-frequency Alfvén and fast waves, emanating from the solar surface, have the same spectral shape and the same amplitude of power spectral density (PSD); ii) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; iii) kinetic wave–particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha–proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfvén-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfvén-cyclotron wave at the same wave propagation angle θ, particularly at 80^°<θ<90^°. When Alfvén-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by a differential speed and a temperature anisotropy of alpha particles via the self-consistently evolving wave–particle interaction. Therefore, fast-cyclotron waves, as a result of linear mode coupling, constitute a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.     

MHD shock interactions in coronal structures

We consider the magnetohydrodynamic (MHD) interactions of solar coronal fast shock waves of flare and/or nonflare origin with the boundaries of coronal streamers and coronal holes. Boundaries are treated as MHD tangential discontinuities (TD). Different parameters of the observed corona are used in the investigation. The general case of the oblique interaction is studied.It is shown that a solar fast shock wave must be refracted usually as a fast shock wave inside the coronal streamer. For the special case of the velocity shear across TD, a slow shock wave is generated. On the contrary, the shock wave refracted inside the coronal hole is indeed a slow shock wave.The significance of different effects due to the interaction of fast and slow shock waves on the coronal magnetic field is noticed, especially at the time of a coronal mass ejection (CME). It is also shown, that an oblique fast MHD coronal shock wave may trigger an instability at the boundary of a streamer considered as a TD. It might have a relation with the observed process of abrupt disappearance of the streamer's boundary in the solar corona.On leave from the Academy of Sciences, Central Astronomical Observatory Pulkovo, 196140, St. Petersburg, Russia.     

The effect of impact obliquity on shock heating in planetesimal collisions

Collisions between planetesimals in the early solar system were a common and fundamental process. Most collisions occurred at an oblique incidence angle, yet the influence of impact angle on heating in collisions is not fully understood. We have conducted a series of shock physics simulations to quantify oblique heating processes, and find that both impact angle and target curvature are important in quantifying the amount of heating in a collision. We find an expression to estimate the heating in an oblique collision compared to that in a vertical incidence collision. We have used this expression to quantify heating in the Rhealsilvia‐forming impact on Vesta, and find that there is slightly more heating in a 45° impact than in a vertical impact. Finally, we apply these results to Monte Carlo simulations of collisional processes in the early solar system, and determine the overall effect of impact obliquity from the range of impacts that occurred on a meteorite parent body. For those bodies that survived 100 Myr without disruption, it is not necessary to account for the natural variation in impact angle, as the amount of heating was well approximated by a fixed impact angle of 45°. However, for disruptive impacts, this natural variation in impact angle should be accounted for, as around a quarter of bodies were globally heated by at least 100 K in a variable‐angle model, an order of magnitude higher than under an assumption of a fixed angle of 45°.     

A gas dynamic model of the rotating solar atmosphere

A model is presented of a solar atmosphere which is heated by the periodic passage of shock waves. The outer atmosphere rotates and is assumed not to affect the strength of the shock waves. This constant shock strength hypothesis is used as the basis of the model of the outer solar atmosphere. From the model it is concluded that the chromospheric temperature rise and flow Mach number are slightly affected by the rotation of the atmosphere.     

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.     

Effects of nonlinear Alfvén wave interaction on particle diffusive shock acceleration. The Earth’s bow shock

We investigate the role of nonlinear Alfvén-wave interaction in the diffusive shock acceleration of solar-wind ions at the Earth’s bow shock. Allowance for the nonlinear wave interaction through induced scattering and two-quanta absorption at plasma parameters β≲0.1 is shown to limit the Alfvén-wave amplitude δB to δB≲B, whereas the quasi-linear approach predicts the generation of waves with amplitudes much larger than the diffusive shock magnetic field strength B. The nonlinear interaction results in spectral wave energy transfer to lower frequencies, which yields a significant increase in the particle acceleration rate.     

Impact penetration of Europa's ice crust as a mechanism for formation of chaos terrain

Abstract— Ice thickness estimates and impactor dynamics indicate that some impacts must breach Europa's ice crust; and outcomes of impact experiments using ice‐over‐water targets range from simple craters to chaos‐like destroyed zones, depending on impact energy and ice competence. First‐order impacts‐into thick ice or at low impact energy‐produce craters. Second‐order impacts punch through the ice, making holes that resemble raft‐free chaos areas. Third‐order impacts‐into thinnest ice or at highest energy‐produce large irregular raft‐filled zones similar to platy chaos. Other evidence for an impact origin for chaos areas comes from the size‐frequency distribution of chaos+craters on Europa, which matches the impact production functions of Ganymede and Callisto; and from small craters around the large chaos area Thera Macula, which decrease in average size and density per unit area as a function of distance from Thera's center. There are no tiny chaos areas and no craters >50 km diameter. This suggests that small impactors never penetrate, whereas large ones (ÜberPenetrators: >2.5 km diameter at average impact velocity) always do. Existence of both craters and chaos areas in the size range 2–40 km diameter points to spatial/temporal variation in crust thickness. But in this size range, craters are progressively outnumbered by chaos areas at larger diameters, suggesting that probability of penetration increases with increasing scale of impact. If chaos areas do represent impact sites, then Europa's surface is older than previously thought. The recalculated resurfacing age is 480 (‐302/+960) Ma: greater than prior estimates, but still very young by solar system standards.     

Cratering on Titan: impact melt, ejecta, and the fate of surface organics

We conduct three-dimensional hydrodynamical simulations of hypervelocity impacts into the crust of Titan to determine the fraction of liquid water generated, under the reasonable assumption that the crust is largely water ice, and to track the fate of the organic-rich layer that is thought to overlie the ice over much of the surface. Impactors larger than a kilometer in diameter are only slightly affected by the atmosphere, while those well under that size are strongly decelerated and broken up before reaching the surface. Impact of a 2 km diameter icy projectile into the crust at velocities of 7 km per second or higher, and angles of impact between 30° and 45°, generate about 2-5% melt by volume within the crater. Our results for the amount of aqueous melt generated in impacts on Titan are broadly consistent with the analytic model developed by Thompson and Sagan (1992) although our numerical model allows us to more precisely quantify the fraction of melt, and fate of the organics, as a function of the impact parameters. While much of the organic surface layer is heavily shocked and ejected from the immediate region of the crater, a significant fraction located behind the oblique impact trajectory is only lightly shocked and is deposited in the liquid water at the crater base. Simple calculations suggest that the resulting aqueous organic phase may remain liquid for hundreds of years or longer, enough time for the synthesis of simple precursor molecules to the origin of life.     

Propagation of Alfvén waves in multi-layer solar atmosphere model

In this paper, we idealize the actual solar atmosphere as a multi-isothermal-layer system so as to obtain the energy transmittance of the linear Alfvén wave that propagates through such a system in presence of a uniform oblique magnetic filed. The results indicate that the two-layer model is essentially different to the three-layer one. In the two-layer model, the temperature jump acts as a high pass filter. In the three-layer model, resonant transfer will take place and the transmittance undergoes oscillation as the trigonometric function terms dominate its behavior. For actual solar atmosphere, the result reveals that the lower parts of solar atmosphere are more suitable for those Alfvén waves with period of seconds to transfer their energy.     

Similarity solution of the propagation of spherical shock waves in a magnetogasdynamic self-gravitating system

The self-similar model of propagation of spherical strong shock waves into non-uniform stellar atmosphere under self-gravitation and non-uniform magnetic field is investigated. The disturbances are headed by a shock surface of variable strength. Gas is assumed to be grey and opaque and the shock tobe transparent.