Models of Circumstellar Maser in Late-Type Variable Stars

The database of observations of H₂O maser variability in a sample of late-type variable stars (oxygen-rich Miras and semiregulars) is analyzed. Some regularities of the H₂O variability are traced: in most of the stars studied, the H₂O flux peaks soon after visual light maxima with a phase delay Δ_ϕ ranging between 0.1 and 0.3 P. The models considered involve the effects of pulsation-induced shock waves: direct impact of a shock on the masering layer in the circumstellar envelope or amplification of the radio continuum, produced by the postshock ionized gas near light maxima, by pumped H₂O molecules. This revised version was published online in September 2006 with corrections to the Cover Date.     

Distribution of Kolmogorov-Sinaï Entropy in Self-Consistent Models of Barred Galaxies

The properties of chaos in 2D self-consistent models of barred galaxies are investigated using Kolmogorov-Sinai entropy h_KS. These models are constructed with Schwarzschild's method which combines orbits as elementary building blocks. Most models are dominated by chaos near the 2/3 of the length of the bar and close to corotation. These locations correspond to regions where star forming HII regions are observed because gas clouds could shock, shrink and fragment such that star formation could be ignited. The model the most similar to N-body models shows a peak of h_KS between the corners of the rectangular-like x₁ orbits and the maximum extension points of the Lagrangian orbits. This emphasizes the role of Lagrangian orbits in the morphology of bars. Most models essentially contain 'semi-chaotic' orbits confined inside the corotation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Martian shock and magnetic pile-up boundary positions and shapes determined from the Phobos 2 and Mars Global Surveyor data sets

A great many Martian bow shock and magnetic pile-up boundary crossings have been identified in the Phobos 2 and Mars Global Surveyor, MGS, data. From these observations the positions and shapes of the bow shock and magnetic pile-up boundary, MPB, have been derived and modelled, using curve-fitting techniques. The models thus derived separately from the Phobos 2 and MGS data sets do not differ drastically, despite the different time and space data coverages. The purpose of the paper is therefore to show the results obtained from the mixing of the Phobos 2 and MGS data bases and to compare the derived bow shock and MPB models with the ones obtained previously. The underlying objective was to see whether it was possible to determine improved bow shock and MPB models or not. The answer is definitely yes, and particularly for the MPB, thanks to the complementary nature of the observations. The boundaries crossed close to the subsolar direction or mostly far downstream by Phobos 2 indeed allow a better coverage of the Martian space environment to be considered. Nevertheless, in order to reduce the domination of the overabundant MGS data set and/or the crossings that are close to Mars (x>−4 R_M, i.e. x>−13 562 km) weighting factors have been introduced.     

Observations of shocked H2 and [FeII] line profiles in orion bullet wakes

New observations of H₂ velocity profiles in the Orion bullet wakes are extremely difficult to reconcile with existing steady-state shock models. We have observed [FeII] 1.644µm velocity profiles of selected bullets and H₂ 1-0 S(1) 2.122µm velocity profiles for a series of positions along and across the corresponding bow-shock wakes. Integrated [FeII] velocity profiles of the brightest bullets are consistent with theoretical bow shock predictions. Observations of broad, singly-peaked H₂ 1-0 S(1) profiles in the most clearly resolved bullet wakes challenge our understanding of molecular shocks. It may be necessary to model the effects of instabilities and turbulence in the Orion bullet wakes in order to fit our observations.     

Diagnosing the conditions in molecular outflow sources: New developments in shock wave models with non-equilibrium chemistry

The shock waves associated with molecular outflows may be of continuous (C) type or jump (J) type, depending on conditions in the preshock gas, notably the degree of ionization. Intermediate situations also exist, in which a J-discontinuity terminates or is embedded in a C-type flow. We consider the results of recent modelling of several important cases where shock waves will comprise both C and J components, namely: (1) in the evolution of a planar J into a planar C type shock wave, prior to the attainment of a stationary state; (2) at shock speeds exceeding the maximum value for a planar C type shock, when the cooling flow encounters a sonic point; (3) in a curved bowshock, when the shock speed at the apex exceeds the maximum value for a C type shock while the bow wings remain of C type. We show that proper allowance for the departure of the chemistry from equilibrium, particularly the dissociation/reformation of H₂, is crucial for an accurate treatment of the C to J transition. All the possible modes of shock propagation need to be considered when interpreting observations of molecular outflow sources. An important diagnostic tool in this context is the H₂ excitation diagram, which plots the logarithm of the column densities of the H₂ rotational levels, divided by the statistical weights, against their excitation energies. There can be large differences between the dynamical and physical conditions implied by J type shocks (with and without a precursor), C type shocks, and bowshocks which best fit the observed excitation diagram. We discuss, by means of examples, the use of the excitation diagram, in conjunction with our sophisticated shock model, to constrain conditions in shocks propagating in molecular outflows.     

Behavior of the flare-produced coronal MHD wavefront and the occurrence of type II radio bursts

The propagation of the weak MHD fast-mode shock emitted into the corona by flares at their explosive phase is computer-simulated. It is shown as the result that the shock wave is refracted towards the low Alfvén velocity regions pre-existing in the corona, and the strength of the shock, which is otherwise weak, is drastically enhanced on encountering low- V _A regions due to the focussing effect by refraction and also due to the lowered propagation velocity of the shock in such regions. It is expected that electron acceleration takes place in such a drastic strengthening of the shock, leading to the local excitation of plasma waves and eventually to the occurrence of radio bursts at such locations. Such locations of shock strength enhancement, when computed by using HAO realistic models of coronal density and magnetic field of the day of certain type II burst events, actually coincide roughly with the observed positions of type II bursts. Peculiar configurations of type II burst sources as well as their occurrence even beyond the horizon of the responsible flare are explained consistently by the large scale refraction and the local enhancement of the shock due to the global and local distribution of Alfvén velocity in the corona. A unified interpretation is given for the occurrence of type II bursts and Moreton's wave phenomena, and also the relation of our MHD fast-mode disturbance with other flare-associated dynamical phenomena is discussed.     

Chemical evolution of the gas in C-type shocks in dark clouds

A magnetohydrodynamic model of a steady, transverse C-type shock in a dense molecular cloud is presented. A complete gas–grain chemical network is taken into account: the gas-phase chemistry, the adsorption of gas species on dust grains, various desorption mechanisms, the grain surface chemistry, the ion neutralization on dust grains, the sputtering of grain mantles. The population densities of energy levels of ions CI, CII and OI and molecules H₂, CO, H₂O are computed in parallel with the dynamical and chemical rate equations. The large velocity gradient approximation is used in the line radiative transfer calculations. The simulations consist of two steps: (i) modelling of the chemical and thermal evolution of a static molecular cloud and (ii) shock simulations. A comparison is made with the results of publicly available models of similar physical systems.The focus of the paper is on the chemical processing of gas material and ice mantles of dust grains by the shock. Sputtering of ice mantles takes place in the shock region close to the temperature peak of the neutral gas. At high shock speeds, molecules ejected from ice mantles are effectively destroyed in hot gas, and their survival time is low—of the order of dozens of years. After a passage of high-speed C-type shock, a zone of high abundance of atomic hydrogen appears in the cooling postshock gas that triggers formation of complex organic species such as methanol. It is shown that abundances of some complex organic molecules (COMs) in the postshock region can be much higher than in the preshock gas. These results are important for interpretation of observations of COMs in protostellar outflows.     

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.     

Terrestrial low-frequency bursts: Escape paths of radio waves through the bow shock

From the analysis of 119 low-frequency (LF) burst spectra observed onboard the Wind spacecraft, we propose an interpretation of the frequency-time characteristics including the low frequency cutoff of the LF burst spectra, and we use these characteristics to sound the bow shock structure at large tailward distances from Earth. When observed from within the solar wind, LF bursts appear to be made of two spectral components. The high frequency one is bursty and observed above twice the solar wind plasma frequency f_psw. The low frequency one is diffuse (ITKR) and its spectrum extends from about 2f_psw to a cutoff frequency f_c not much higher than f_psw; its onset time δt(f) increases as the frequency f decreases. For each of the 119 events observed from near the Lagrange point L1, the solar wind density variations were measured and the variations of the density jump across the shock calculated from plasma data all along a shock model over more than 2000R_E. But, except for a few events, neither the solar wind overdensities nor the shock density barrier can prevent waves with frequencies below f_c from reaching the spacecraft. Scattering on plasma density inhomogeneities was then introduced to account for the propagation of the LF burst waves in the magnetosheath, from near Earth to their escape point through the bow shock at a frequency-dependent distance |X_esc(f)| (GSE), and then in the solar wind to the spacecraft. In such media, at frequencies between 2f_psw and f_psw, the bulk speed of the scattered waves decreases rapidly as f decreases, and this accounts for the observed variations of the onset time δt(f). Angular scattering can also account for the observed cutoff at f_c if the distance |X_esc(f)| increases exponentially when f/f_psw decreases. As the shock model we used meets that requirement, we consider that this model is valid, which implies that the bow shock still exists beyond 1000R_E from the Earth. The observed decrease of the average spectral intensity of the LF burst between about 1.5f_psw and 2f_psw can also be explained by the scattering in the solar wind if we take into account the angular distribution of the rays when they leave the bow shock.     

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.     

Revision and recalibration of existing shock classifications for quartzose rocks using low‐shock pressure (2.5–20 GPa) recovery experiments and mesoscale numerical modeling

A combination of shock recovery experiments and numerical modeling of shock deformation in the low‐shock pressure range from 2.5 to 20 GPa for two dry sandstone types of different porosity, a completely water‐saturated sandstone, and a well‐indurated quartzite provides new insights into strongly heterogeneous distribution of different shock features. (1) For nonporous quartzo‐feldspathic rocks, the traditional classification scheme (Stöffler 1984 ) is suitable with slight changes in pressure calibration. (2) For water‐saturated quartzose rocks, a cataclastic texture (microbreccia) seems to be typical for the shock pressure range up to 20 GPa. This microbreccia does not show formation of PDFs but diaplectic quartz glass/SiO₂ melt is formed at 20 GPa (~1 vol%). (3) For porous quartzose rocks, the following sequence of shock features is observed with progressive increase in shock pressure (1) crushing of pores, (2) intense fracturing of quartz grains, and (3) increasing formation of diaplectic quartz glass/SiO₂ melt replacing fracturing. The formation of diaplectic quartz glass/SiO₂ melt, together with SiO₂ high‐pressure phases, is a continuous process that strongly depends on porosity. This experimental observation is confirmed by our concomitant numerical modeling. Recalibration of the shock classification scheme results in a porosity versus shock pressure diagram illustrating distinct boundaries for the different shock stages.     

Electron heating in superhigh mach number shocks

Fluid and MHD models, as well as direct extrapolation of the Earth's bow shock measurements in the high Mach number (HMN) range (3M _F 12) to the superhigh Mach number (SHMN) range (M _F >30–40) predict that the downstream electron pressurep _e2 is only a negligible fraction of the Rankine-Hugoniot downstream pressurep ₂, i.e.,p _e2/p₂(M _F ² )^–1. However, the interpretation of X-ray supernovae emissions, due to SHMN shock heating requiresp _e2/p₂0(1). Following Alfvén we have used plasma physics experimental-theoretical data combined with magnetospheric observations to probe the physics of the SHMN shocks. It is shown below that inclusion of proper plasma physics considerations in the interaction of the reflected and transmitted ions and the electrons at the foot of the shock leads to the surprising result that electron heating can dominate in the SHNM range. A stationary model of the shock structure is derived and shown to be the result of extrapolation of the high Mach number shock physics with incorporation of collective interactions at the foot.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Computation of Jupiter interior models from gravitational inversion theory

A method for deriving a planetary interior model which exactly satisfies a set of N gravitational constraints is implemented. For Jupiter, recent spacecraft measurements provide the mass, radius at a standard pressure level, rotation law, multipole moments of the internal mass distribution, and constraints on the internal composition and temperature distribution. By appropriate iterations, interior models are found which exactly satisfy these constraints. The models are assumed to have constant chemical composition and constant specific entropy in the hydrogenic envelope. The derived pressure-density relation in the outer envelope depends sensitively on the observational uncertainty in the mass multipole moment J₄. Models are not forced to fit the more indirectly derived constraints, which are instead used as consistency checks. For a helium mass fraction in the envelope (Y) equal to 0.20, the inferred pressure at a mass density ≈ 0.2 g/cm³ is about a factor of 2 higher than would be indicated by experimental hydrogen shock compression data in the relevant pressure range of 10⁵ to 10⁶ bar. The inferred pressure distribution is in much better agreement with the shock data for a nominal Y = 0.30 ± 0.05. This value of Y is interpreted in terms of an enhancement in the envelope, by a factor of order 5 over solar abundance, of species primarily consisting of CH₄, NH₃, and possibly H₂O. The same method is applied to Saturn, but existing uncertainties in Saturn's gravitational parameters are still too large to allow useful conclusions about the composition of its envelope.     

Laboratory Observation of Secondary Shock Formation Ahead of a Strongly Radiative Blast Wave

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.     

Petrogenesis of Allan Hills 84001: Constraints from impact‐melted feldspathic and silica glasses

Abstract— Compositional and textural relationships of shock‐melted glasses in the Allan Hills (ALH) 84001 meteorite have been examined by optical microscopy, electron microprobe analysis, and compositional mapping. The feldspathic and silica glasses exhibit features which constrain the relative timing of shock events and carbonate deposition in ALH 84001. The feldspathic glasses are stoichiometric and have compositions plausibly described as forming from igneous plagioclase (An_27–39Ab_58–68Or_3–7) or sanidine (Or₅₁Ab₄₆An₃), or from a mixture of these phases (mixed‐feldspar glasses). These observations argue against prior interpretations of feldspathic glasses as unflowed maskelynite, hydrothermal precipitates or alteration products, or shock melts that have undergone alkali volatilization. Carbonate was deposited around previously formed mixed‐feldspar glass clasts, suggesting that carbonate deposition occurred after the shock event that formed the granular bands (crushed zones) in this meteorite. SiO₂‐rich glasses appear to be silica remobilized during shock, with little addition of other material. A petrogenetic history of ALH 84001 consistent with the observations of feldspathic and silica glasses is (1) igneous crystallization and cumulate formation; (2) a pre‐carbonate shock event that formed the granular bands (crushed zones) and sheared chromites, and melted igneous plagioclase and sanidine to form mixed‐feldspar glasses; (3) carbonate and silica deposition in the granular bands (veining of plagioclase glasses by SiO₂ and deposition of carbonate around mixed‐feldspar and plagioclase glass clasts); (4) a post‐carbonate shock event that resulted in invasion of carbonate by feldspathic melts, shock faulting and decarbonation of carbonate, high‐temperature mobilization of silica melts, and minor dissolution of orthopyroxene by silica melts.     

Experimental investigation of shock metamorphic effects in a metapelitic granulite: The importance of shock impedance contrast between components

Shock recovery experiments were performed at 12.5, 25, 34, 40, and 56 GPa at 25 °C, and at 18 and 25 GPa at 400 °C, on a high‐grade, migmatitic, garnet‐cordierite metapelite from the Etivé aureole, Scotland. Objectives for this study were to (1) characterize shock effects in a complex polymineralic rock with a significant proportion of hydrous ferromagnesian minerals, both as a function of variable shock pressure and preshock temperature, and (2) to explore the effects of shock impedance contrast between component minerals on the respective abundances and distribution of these features. At any shock pressure, the order of decreasing intensity of shock metamorphic effects in component phases is: cordierite (Crd)→biotite (Bt)→plagioclase (Pl)→K‐feldspar (Kfs)→quartz (Qtz)→garnet (Grt)→orthopyroxene (Opx). Samples shocked to pressures below 40 GPa (25 °C) were typically characterized by marked heterogeneous distribution of shock effects on both intragranular and intergranular scales. Shock heterogeneity is mainly attributed to shock impedance contrast between contiguous phases, and manifests as shock amplification locally where shock impedance contrast is greatest, and shock suppression where impedance contrast is least. The heterogeneous distribution of shock metamorphic effects in both experiments and natural rocks is a signature of extreme disequilibrium at the submillimeter scale. The heterogeneous distribution of shock metamorphic effects mitigates against the use of shock effects in minerals exclusively as regional shock pressure barometers, and ought to be augmented by additional constraints on shock pressure from numerical models.     

Propagation of impact‐induced shock waves in porous sandstone using mesoscale modeling

Generation and propagation of shock waves by meteorite impact is significantly affected by material properties such as porosity, water content, and strength. The objective of this work was to quantify processes related to the shock‐induced compaction of pore space by numerical modeling, and compare the results with data obtained in the framework of the Multidisciplinary Experimental and Modeling Impact Research Network (MEMIN) impact experiments. We use mesoscale models resolving the collapse of individual pores to validate macroscopic (homogenized) approaches describing the bulk behavior of porous and water‐saturated materials in large‐scale models of crater formation, and to quantify localized shock amplification as a result of pore space crushing. We carried out a suite of numerical models of planar shock wave propagation through a well‐defined area (the “sample”) of porous and/or water‐saturated material. The porous sample is either represented by a homogeneous unit where porosity is treated as a state variable (macroscale model) and water content by an equation of state for mixed material (ANEOS) or by a defined number of individually resolved pores (mesoscale model). We varied porosity and water content and measured thermodynamic parameters such as shock wave velocity and particle velocity on meso‐ and macroscales in separate simulations. The mesoscale models provide additional data on the heterogeneous distribution of peak shock pressures as a consequence of the complex superposition of reflecting rarefaction waves and shock waves originating from the crushing of pores. We quantify the bulk effect of porosity, the reduction in shock pressure, in terms of Hugoniot data as a function of porosity, water content, and strength of a quartzite matrix. We find a good agreement between meso‐, macroscale models and Hugoniot data from shock experiments. We also propose a combination of a porosity compaction model (ε–α model) that was previously only used for porous materials and the ANEOS for water‐saturated quartzite (all pore space is filled with water) to describe the behavior of partially water‐saturated material during shock compression. Localized amplification of shock pressures results from pore collapse and can reach as much as four times the average shock pressure in the porous sample. This may explain the often observed localized high shock pressure phases next to more or less unshocked grains in impactites and meteorites.     

The Effect of the Heliospheric Current Sheet on Interplanetary Shocks

Using 180 interplanetary (IP) shock events associated with coronal mass ejections (CMEs) during 1997 – 2005, we investigate the influence of the heliospheric current sheet (HCS) upon the propagation and geoeffectiveness of IP shocks. Our preliminary results are: (1) The majority of CME-driving IP shocks occurred near the HCS. (2) The numbers of shock events and related geomagnetic storms observed when the Earth and the solar source are located on the same side of the HCS, represented by f _SS and f _SG, respectively, are obviously higher than those when the Earth and the solar source are located on the opposite sides of the HCS, denoted by f _OS and f _OG, with f _SS/f _OS=126/54, f _SG/f _OG = 91/36. (3) Parameter jumps across the shock fronts for the same-side events are also higher than those for the opposite-side events, and the stronger shocks (Δ V ≥ 200 km s⁻¹) are mainly attributed to be same-side events, with f _SSh/f _OSh = 28/15, where f _SSh and f _OSh are numbers of stronger shocks which belong to same-side events and opposite-side events, respectively. (4) The level of the geomagnetic disturbances is higher for the same-side events than for the opposite-side events. The ratio of the number of intense magnetic storms (Dst < −100) triggered by same-side events to those triggered by opposite-side events is 25/10. (5) We propose an empirical model to predict the arrival time of the shock at the Earth, whose accuracy is comparable to that of other prevailing models. These results show that the HCS is an important physical structure, which probably plays an important role in the propagation of interplanetary shocks and their geoeffectiveness.     

High‐pressure phases in shock‐induced melt veins of the Umbarger L6 chondrite: Constraints of shock pressure

Abstract— We report a previously undocumented set of high‐pressure minerals in shock‐induced melt veins of the Umbarger L6 chondrite. High‐pressure minerals were identified with transmission electron microscopy (TEM) using selected area electron diffraction and energy‐dispersive X‐ray spectroscopy. Ringwoodite (Fa₃₀), akimotoite (En₁₁Fs₈₉), and augite (En₄₂Wo₃₃Fs₂₅) were found in the silicate matrix of the melt vein, representing the crystallization from a silicate melt during the shock pulse. Ringwoodite (Fa₂₇) and hollandite‐structured plagioclase were also found as polycrystalline aggregates in the melt vein, representing solid state transformation or melting with subsequent crystallization of entrained host rock fragments in the vein. In addition, Fe₂SiO₄‐spinel (Fa₆₆‐Fa₉₉) and stishovite crystallized from a FeO‐SiO₂‐rich zone in the melt vein, which formed by shock melting of FeO‐SiO₂‐rich material that had been altered and metasomatized before shock. Based on the pressure stabilities of the high‐pressure minerals, ringwoodite, akimotoite, and Ca‐clinopyroxene, the melt vein crystallized at approximately 18 GPa. The Fe₂SiO₄‐spinel + stishovite assemblage in the FeO‐SiO₂‐rich melts is consistent with crystallization of the melt vein matrix at the pressure up to 18 GPa. The crystallization pressure of ?18 GPa is much lower than the 45–90 GPa pressure one would conclude from the S6 shock effects in melt veins (Stöffler et al. 1991) and somewhat less than the 25–30 GPa inferred from S5 shock effects (Schmitt 2000) found in the bulk rock.