The scale size of chondrule formation regions: Constraints imposed by chondrule cooling rates

Abstract— Meteoritic data strongly suggest that most chondrules reached maximum temperatures in a range of 1650–2000 K and cooled at relatively slow rates of 100–1000 K/h, implying a persistence of external energy supply. The presence of fine‐grained rims around chondrules in most unequilibrated chondrites also indicates that a significant quantity of micron‐sized dust was present in chondrule formation regions. Here, we assume that the persistent external energy source needed to explain chondrule cooling rates consists primarily of radiation from surrounding heated chondrules, fine dust, and gas after the formation event. Using an approximate one‐dimensional numerical model for the outward diffusion of thermal radiation from such a system, the scale sizes of formation regions required to yield acceptable cooling rates are determined for a range of possible chondrule, dust, and gas parameters. Results show that the inferred scale sizes depend sensitively on the number densities of micron‐sized dust and on their adopted optical properties. In the absence of dust, scale sizes > 1000 km are required for plausible maximum chondrule number densities and heated gas parameters. In the presence of dust with mass densities comparable to those of the chondrules and with absorptivities and emissivities of ～0.01 calculated for Mie spheres with a pure mineral composition, scale sizes as small as ～100 km are possible. If dust absorptivities and emissivities approach unity (as may occur for particles with more realistic shapes and compositions), then scale sizes as small as ×10 km are possible. Considering all uncertainties in model parameters, it is concluded that small scale sizes (10–100 km) for chondrule formation regions are allowed by the experimentally inferred cooling rates.     

Recovering 3D particle size distributions from 2D sections

We discuss different ways to convert observed, apparent particle size distributions from 2D sections (thin sections, SEM maps on planar surfaces, etc.) into true 3D particle size distributions. We give a simple, flexible, and practical method to do this; show which of these techniques gives the most faithful conversions; and provide (online) short computer codes to calculate both 2D‐3D recoveries and simulations of 2D observations by random sectioning. The most important systematic bias of 2D sectioning, from the standpoint of most chondrite studies, is an overestimate of the abundance of the larger particles. We show that fairly good recoveries can be achieved from observed size distributions containing 100–300 individual measurements of apparent particle diameter.     

Quantifying the error of 2D bulk chondrule analyses using a computer model to simulate chondrules (SIMCHON)

Bulk chondrule compositions are important to many questions in cosmochemistry, however, the number of available bulk chondrule data sets is still small. A main reason for this is the difficulties of determining bulk chondrule compositions. A commonly used technique is to obtain 2D bulk chondrule compositions from meteorite sections. This technique has an error that we quantify here for the first time using a mathematical model of a chondrule called SIMCHON. The theoretically calculated errors are compared to errors that we determined from serial sectioning of eight Efremovka chondrules. The errors obtained from both approaches are in excellent agreement, proving that our mathematical model produces reliable errors that can be assigned to 2D bulk chondrule compositions. These errors allow a much better interpretation of 2D bulk chondrule data. We provide a table that contains typical errors for 2D bulk compositions of porphyritic chondrules. The errors are in the range of ±<1–30 relative‐%. This should be acceptable for many problems in cosmochemistry. The effect of a chemical layering inside chondrules and the occurrence of a rim around them, as well as the occurrence of opaque and other accessory phases have been studied. A spreadsheet is provided that enables the calculation of errors for any desired chondrule mineral composition. BO chondrules have a negligible error, but it is impossible to provide reasonable error estimates for BO chondrules with an igneous rim. Radial pyroxene chondrules have negligible errors.     

Impact-induced chondrule flattening in the Allende CV3 carbonaceous chondrite: Shock experiments

Abstract— We have carried out shock-recovery experiments on the Allende CV3 carbonaceous chondrite using a single-stage propellant gun and succeeded in reproducing oriented, flattened chondrules like those observed in some natural CV3 chondrites. The Allende samples were shocked at equilibrium pressures of 11 and 21 GPa, which are close to the highest values in shock stages S2 and S3, respectively (Stöffler et al., 1991). Chondrules are flattened nearly perpendicular to the compaction axis with mean aspect ratios of 1.34 and 1.62 at pressures of 11 and 21 GPa, respectively; thus, the degree of chondrule flattening is proportional to the shock intensity. The chondrule flattening and foliation are mainly due to collapse of pores in the matrix under shock pressure. High matrix abundance of CV3 chondrites could result in much apparent chondrule flattening relative to ordinary chondrites. Optical and electron microscope observations show that textural and mineralogical characteristics of chondrules and matrix in the shock-loaded samples are very similar to those observed in naturally shocked CV3 chondrites. Our results provide strong support for the interpretation that the chondrule flattening and foliation in CV3 chondrites were caused by shock-induced pressure due to hypervelocity impacts on the meteorite parent bodies.     

Extent of chondrule melting: Evaluation of experimental textures,nominal grain size,and convolution index

Abstract— Dynamic crystallization experiments on the ordinary chondrite Queen Alexandra Range (QUE) 97008 document textural features that occur in partially melted chondrules with changes in the degree of partial melting and cooling rate. We carried out a matrix of experiments, at peak temperatures of 1250, 1350, 1370, and 1450 °C, and cooling rates of 1000, 100, and 10 °C/h, and quenched. All experimentally produced textures closely resemble textures of porphyritic chondrules. Because peak temperatures were well below the liquidi for typical chondrule compositions, the textural similarities support an incomplete melting origin for most porphyritic chondrules. Our experiments can be used to determine the extent of melting of natural chondrules by comparing textural relationships among the experimental results with those of natural chondrules. We used our experiments along with X‐ray computerized tomography scans of a Semarkona chondrule to evaluate two other methods that have been used previously to quantify the degree of melting: nominal grain size and convolution index. Proper applications of these methods can result in valid assessments of a chondrule's degree of melting, but only if accompanied by careful interpretation, as chondrule textures are controlled by more than just the extent of melting. Such measurements of single aspects of chondrule textures might be coupled with qualitative analysis of other textural aspects to accurately determine degree of melting.     

Cosmogenic and trapped noble gases in individual chondrules: Clues to chondrule formation

Abstract— We studied the elemental and isotopic abundances of noble gases (He, Ne, Ar in most cases, and Kr, Xe also in some cases) in individual chondrules separated from six ordinary, two enstatite, and two carbonaceous chondrites. Most chondrules show detectable amounts of trapped ²⁰Ne and ³⁶Ar, and the ratio (³⁶Ar/²⁰Ne)_t (from ordinary and carbonaceous chondrites) suggests that HL and Q are the two major trapped components. A different trend between (³⁶Ar/²⁰Ne)_t and trapped ³⁶Ar is observed for chondrules in enstatite chondrites indicating a different environment and/or mechanism for their formation compared to chondrules in ordinary and carbonaceous chondrites. We found that a chondrule from Dhajala chondrite (DH‐11) shows the presence of solar‐type noble gases, as suggested by the (³⁶Ar/²⁰Ne)_t ratio, Ne‐isotopic composition, and excess of ⁴He. Cosmic‐ray exposure (CRE) ages of most chondrules are similar to their host chondrites. A few chondrules show higher CRE age compared to their host, suggesting that some chondrules and/or precursors of chondrules have received cosmic ray irradiation before accreting to their parent body. Among these chondrules, DH‐11 (with solar trapped gases) and a chondrule from Murray chondrite (MRY‐1) also have lower values of (²¹Ne/²²Ne)_c, indicative of SCR contribution. However, such evidences are sporadic and indicate that chondrule formation event may have erased such excess irradiation records by solar wind and SCR in most chondrules. These results support the nebular environment for chondrule formation.     

The Euro3D data format: A common FITS data format for integral field spectrographs

As integral field spectrographs have become more common around the world and in Europe in particular, the need for a common data format has been recognized. Here, we present the Euro3D format that is adapted as a post‐instrumentalsignature‐removal format for all instruments within the Euro3D network. It follows the FITS standard, and includes several extensions, all of them being binary FITS tables. This article is intended to give a comprehensive overview, but does not attempt to serve as a full definition document. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Olivine dissolution in molten silicates: An experimental study with application to chondrule formation

Mg‐rich olivine is a ubiquitous phase in type I porphyritic chondrules in various classes of chondritic meteorites. The anhedral shape of olivine grains, their size distribution, as well as their poikilitic textures within low‐Ca pyroxene suggest that olivines suffer dissolution during chondrule formation. Owing to a set of high‐temperature experiments (1450–1540 °C) we determined the kinetics of resorption of forsterite in molten silicates, using for the first time X‐ray microtomography. Results indicate that forsterite dissolution in chondrule‐like melts is a very fast process with rates that range from ~5 μm min^?1 to ~22 μm min^?1. Forsterite dissolution strongly depends on the melt composition, with rates decreasing with increasing the magnesium and/or the silica content of the melt. An empirical model based on forsterite saturation and viscosity of the starting melt composition successfully reproduces the forsteritic olivine dissolution rates as a function of temperature and composition for both our experiments and those of the literature. Application of our results to chondrules could explain the textures of zoned type I chondrules during their formation by gas‐melt interaction. We show that the olivine/liquid ratio on one hand and the silica entrance from the gas phase (SiO_g) into the chondrule melt on the other hand, have counteracting effects on the Mg‐rich olivine dissolution behavior. Silica entrance would favor dissolution by maintaining disequilibrium between olivine and melt. Hence, this would explain the preferential dissolution of olivine as well as the preferential abundances of pyroxene at the margins of chondrules. Incipient dissolution would also occur in the silica‐poorer melt of chondrule core but should be followed by crystallization of new olivine (overgrowth and/or newly grown crystals). While explaining textures and grain size distributions of olivines, as well as the centripetal distribution of low‐Ca pyroxene in porphyritic chondrules, this scenario could also be consistent with the diverse chemical, isotopic, and thermal conditions recorded by olivines in a given chondrule.     

E3D,the Euro3D visualization tool II: Mosaics,VIMOS data and large IFUs of the future

In this paper, we describe the capabilities of E3D, the Euro3D visualization tool, to handle and display data created by large Integral Field Units (IFUs) and by mosaics consisting of multiple pointings. The reliability of the software has been tested with real data, originating from the PMAS instrument in mosaic mode and from the VIMOS instrument, which features the largest IFU currently available. The capabilities and limitations of the current software are examined in view of future large IFUs, which will produce extremely large datasets. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shock-wave heating model for chondrule formation: Hydrodynamic simulation of molten droplets exposed to gas flows

Millimeter-sized, spherical silicate grains abundant in chondritic meteorites, which are called as chondrules, are considered to be a strong evidence of the melting event of the dust particles in the protoplanetary disk. One of the most plausible scenarios is that the chondrule precursor dust particles are heated and melt in the high-velocity gas flow (shock-wave heating model). We developed the non-linear, time-dependent, and three-dimensional hydrodynamic simulation code for analyzing the dynamics of molten droplets exposed to the gas flow. We confirmed that our simulation results showed a good agreement in a linear regime with the linear solution analytically derived by Sekyia et al. [Sekyia, M., Uesugi, M., Nakamoto, T., 2003. Prog. Theor. Phys. 109, 717-728]. We found that the non-linear terms in the hydrodynamical equations neglected by Sekiya et al. [Sekiya, M., Uesugi, M., Nakamoto, T., 2003. Prog. Theor. Phys. 109, 717-728] can cause the cavitation by producing negative pressure in the droplets. We discussed that the fragmentation through the cavitation is a new mechanism to determine the upper limit of chondrule sizes. We also succeeded to reproduce the fragmentation of droplets when the gas ram pressure is stronger than the effect of the surface tension. Finally, we compared the deformation of droplets in the shock-wave heating with the measured data of chondrules and suggested the importance of other effects to deform droplets, for example, the rotation of droplets. We believe that our new code is a very powerful tool to investigate the hydrodynamics of molten droplets in the framework of the shock-wave heating model and has many potentials to be applied to various problems.     

2D/3D Dust Continuum Radiative Transfer Codes to Analyze and Predict VLTI Observations

Radiative Transfer (RT) codes with image capability are a fundamental tool for preparing interferometric observations and for interpreting visibility data. In view of the upcoming VLTI facilities, we present the first comparison of images/visibilities coming from two 3D codes that use completely different techniques to solve the problem of self-consistent continuum RT. In addition, we focus on the astrophysical case of a disk distorted by tidal interaction with by-passing stars or internal planets and investigate for which parameters the distortion can be best detected in the mid-infrared using the mid-infrared interferometric device MIDI. This revised version was published online in July 2006 with corrections to the Cover Date.     

Orbit classification in arbitrary 2D and 3D potentials

A method of classifying generic orbits in arbitrary 2D and 3D potentials is presented. It is based on the concept of spectral dynamics introduced by Binney &38; Spergel that uses the Fourier transform of the time series of each coordinate. The method is tested using a number of potentials previously studied in the literature and is shown to distinguish correctly between regular and irregular orbits, to identify the various families of regular orbits (boxes, loops, tubes, boxlets, etc.), and to recognize the second-rank resonances that bifurcate from them. The method returns the position of the potential centre and, for 2D potentials, the orientation of the principal axes as well, should this be unknown. A further advantage of the method is that it has been encoded in a FORTRAN program that does not require user intervention, except for 'fine tuning' of search parameters that define the numerical limits of the code. The automatic character makes the program suitable for classifying large numbers of orbits.     

A methodology to construct a reduced chemical scheme for 2D-3D photochemical models: Application to Saturn

We present a methodology to build a reduced chemical scheme adapted to the study of hydrocarbons in the atmospheres of giant planets and Titan. As an example, we have built a reduced chemical scheme, containing only 25 compounds and 46 reactions (including photolysis), which is well adapted to compute the abundance of the main hydrocarbons observed so far in the atmosphere of Saturn (CH₃, CH₄, C₂H₂, C₂H₄, C₂H₆, CH₃C₂H, C₃H₈ and C₄H₂). This scheme gives similar results, within the error bars of the model, as a 1D photochemical model using an initial chemical scheme containing 90 compounds and more than 600 reactions. As a consequence, such a methodology can be used to build a reduced scheme well adapted to future 2D (or 3D) photochemical models and GCMs.     

A fast 2D image reconstruction algorithm from 1D data for the Gaia mission

A fast 2-dimensional image reconstruction method is presented, which takes as input 1-dimensional data acquired from scans across a central source in different orientations. The resultant reconstructed images do not show artefacts due to non-uniform coverage in the orientations of the scans across the central source, and are successful in avoiding a high background due to contamination of the flux from the central source across the reconstructed image. Due to the weighting scheme employed this method is also naturally robust to hot pixels. This method was developed specifically with Gaia data in mind, but should be useful in combining data with mismatched resolutions in different directions.     

Fast computation of 2D transfer functions from adaptive optics data

The use of atmospheric transfer functions is common in image reconstruction techniques such as speckle interferometry to calibrate the Fourier amplitudes of the reconstructed images. Thus, an accurate model is needed to ensure proper photometry in the reconstruction. The situation complicates when adaptive optics (AO) are used during data acquisition. I propose a novel technique to derive two‐dimensional transfer functions from data collected using AO simultaneously with the observations. The technique is capable to compute the relevant transfer functions within a short time for the prevailing atmospheric conditions and AO performance during data acquisition (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Few projections astrotomography: radio astronomical approach to 3D reconstruction

We develop a radio astronomical approach to 3D‐reconstruction in few projections tomography. It is based on the 2‐CLEAN DSA method which consists of two clean algorithms by using a synthesized beam. In complex cases two extreme solutions are used for the analysis of the image structure. These solutions determine the limits of permissible energy redistribution on the image among the components of small and large scales. Two variants of 3D‐reconstruction proceeding from a set of two‐dimensional projections (3D_2D) and from a set of one‐dimensional ones (3D_1D) are considered. It is shown that the quality of 3D_2D‐reconstruction should be similar to the quality of 2D_1D‐reconstruction if the same number of equally spaced scans is used. But a doubled number of projections is required for 3D_1D‐reconstruction. We have simulated 3D‐reconstruction of an optically thin emitting object. The present technique is a component of astrotomography and it has good prospects for a wide range of remote sensing. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D stellar reddening map from 2MASS photometry: An improved version

An improved version of the 3D stellar reddening map in a space with a radius of 1200 pc around the Sun and within 600 pc of the Galactic midplane is presented. As in the previous 2010 and 2012 versions of the map, photometry with an accuracy better than 0.05 ^m in the J and Ks bands for more than 70 million stars from the 2MASS catalogue is used in the new version. However, the data reduction technique is considerably more complicated. As before, an analysis of the distribution of stars near the main-sequence turnoff on the (J ? Ks)?Ks diagram, where they form a distribution maximum, provides a basis for the method. The shift of this maximum, i.e., the mode (J ? Ks), along (J ? Ks) and Ks, given the spatial variations of the mean dereddened color (J ? Ks)₀ of these stars, is interpreted as a growth of the reddening with increasing distance. The main distinction of the new method is that instead of the fixed mean absolute magnitude, dereddened color, distance, and reddening for each cell, the individual values of these quantities are calculated for each star by iterations when solving the system of equations relating them. This has allowed one to increase the random accuracy of the map to 0.01 ^m and its spatial resolution to 20 pc in coordinates and distance and to 1° in longitude and latitude. Comparison with other reddening estimates for the same spatial cells and Gaia DR1 TGAS stars shows that the constructed map is one of the best maps for the space under consideration. Its systematic errors have been estimated to be σ(E(J ? Ks)) = 0.025 ^m , or σ(E(B ? V)) = 0.04 ^m . The main purpose of the map is to analyze the characteristics of Galactic structures, clouds, and cloud complexes. For this purpose, the reddening map within each spatial cell has also been computed by analyzing the reddening along each line of sight.     

Some special restricted four-body problems—II. From Caledonia to Copenhagen

Special analytical solutions are determined for restricted, coplanar, four-body equal mass problems, including the Caledonian problem, where the masses M_i = M for i = 1,2,3,4. Most of these solutions are shown to reduce to the Lagrange solutions of the Copenhagen problem of three bodies by reducing two of the masses (m_i = m for i = 1,2) in the four-body equal mass problem to zero while maintaining their equality of mass. In so doing, families of special solutions to the four-body problem are shown to exist for any value of the mass ratio μ = m/M.     

From inflation to Friedmann regime inR 2 cosmology

A cosmological model describing the different stages of the universe, i.e.: inflation, radiation dominated period and matter dominated (Friedmann-like) period is shown. The model consists of the usual gravitational lagrangian with a R ² term, and, for the matter content, the lagrangian of a massive conformally coupled scalar field. The effect of backreaction is evaluated by means of an extremum condition on the entropy at each time. The differential equation, obtained when the lowest quantum order is considered, describes all the periods of evolution of the universe. For a range of values of, inflation is unstable and the universe can reach the following regime.