Shock-Wave Heating Model for Chondrule Formation: Prevention of Isotopic Fractionation

Chondrules are considered to have much information on dust particles and processes in the solar nebula. It is naturally expected that protoplanetary disks observed in present star forming regions have similar dust particles and processes, so study of chondrule formation may provide us great information on the formation of the planetary systems. Evaporation during chondrule melting may have resulted in depletion of volatile elements in chondrules. However, no evidence for a large degree of heavy-isotope enrichment has been reported in chondrules. In order to meet this observed constraint, the rapid heating rate at temperatures below the silicate solidus is required to suppress the isotopic fractionation. We have developed a new shock-wave heating model taking into account the radiative transfer of the dust thermal continuum emission and the line emission of gas molecules and calculated the thermal history of chondrules. We have found that optically-thin shock waves for the thermal continuum emission from dust particles can meet the rapid heating constraint, because the dust thermal emission does not keep the dust particles high temperature for a long time in the pre-shock region and dust particles are abruptly heated by the gas drag heating in the post-shock region. We have also derived the upper limit of optical depth of the pre-shock region using the radiative diffusion approximation, above which the rapid heating constraint is not satisfied. It is about 1 - 10.Comment: 58 pages, including 5 tables and 15 figures, accepted for publication in The Astrophysical Journa

On elliptic curves with an isogeny of degree 7

We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\mathbf{Q}(\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the exceptions are exactly the curves with complex multiplication. As a by-product of one of the key steps in our proof, we determine exactly when there exist elliptic curves over an arbitrary field $k$ of characteristic not 7 with a $k$-rational isogeny of degree 7 and a specified Galois action on the kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in Version 1. Version 3 will appear in the American Journal of Mathematic

How well do we know the neutron structure function?

We present a detailed analysis of the uncertainty in the neutron F2n structure function extracted from inclusive deuteron and proton deep-inelastic scattering data. The analysis includes experimental uncertainties as well as uncertainties associated with the deuteron wave function, nuclear smearing, and nucleon off-shell corrections. Consistently accounting for the Q^2 dependence of the data and calculations, and restricting the nuclear corrections to microscopic models of the deuteron, we find significantly smaller uncertainty in the extracted F2n/F2p ratio than in previous analyses. In addition to yielding an improved extraction of the neutron structure function, this analysis also provides an important baseline that will allow future, model-independent extractions of neutron structure to be used to examine nuclear medium effects in the the deuteron.Comment: 5 pages, 6 figure

Directed Rh(I)-Catalyzed Asymmetric Hydroboration of Prochiral 1-Arylcycloprop-2-ene-1-carboxylic Acid Derivatives

This is the peer reviewed version of the following article: A. Edwards, M. Rubina, M. Rubin, Chem. Eur. J. 2018, 24, 1394., which has been published in final form at http://doi.org/10.1002/chem.201704443. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A full account on rhodium-catalyzed asymmetric, directed hydroboration of functionalized prochiral cyclopropenes affording enantiomerically enriched cyclopropylboronates is reported. The scope and limitations of two alternate directing groups, ester and carboxamide, are evaluated. It was found that hydroboration of esters appeared to be more sensitive to substitution in the aromatic ring of the substrates. Specifically, ortho-halogens were detrimental for diastereo- and enantioselectivity, possibly because of additional coordination with rhodium. In contrast, more Lewis-basic amide directing groups allowed for stronger chelation to the transition metal, leading to consistently high diastereo- and enantioselectivity in hydroboration across a broader range of substrates

Spitzer reveals what's behind Orion's Bar

We present Spitzer Space Telescope observations of 11 regions SE of the Bright Bar in the Orion Nebula, along a radial from the exciting star theta1OriC, extending from 2.6 to 12.1'. Our Cycle 5 programme obtained deep spectra with matching IRS short-high (SH) and long-high (LH) aperture grid patterns. Most previous IR missions observed only the inner few arcmin. Orion is the benchmark for studies of the ISM particularly for elemental abundances. Spitzer observations provide a unique perspective on the Ne and S abundances by virtue of observing the dominant ionization states of Ne (Ne+, Ne++) and S (S++, S3+) in Orion and H II regions in general. The Ne/H abundance ratio is especially well determined, with a value of (1.01+/-0.08)E-4. We obtained corresponding new ground-based spectra at CTIO. These optical data are used to estimate the electron temperature, electron density, optical extinction, and the S+/S++ ratio at each of our Spitzer positions. That permits an adjustment for the total gas-phase S abundance because no S+ line is observed by Spitzer. The gas-phase S/H abundance ratio is (7.68+/-0.30)E-6. The Ne/S abundance ratio may be determined even when the weaker hydrogen line, H(7-6) here, is not measured. The mean value, adjusted for the optical S+/S++ ratio, is Ne/S = 13.0+/-0.6. We derive the electron density versus distance from theta1OriC for [S III] and [S II]. Both distributions are for the most part decreasing with increasing distance. A dramatic find is the presence of high-ionization Ne++ all the way to the outer optical boundary ~12' from theta1OriC. This IR result is robust, whereas the optical evidence from observations of high-ionization species (e.g. O++) at the outer optical boundary suffers uncertainty because of scattering of emission from the much brighter inner Huygens Region.Comment: 60 pages, 16 figures, 10 tables. MNRAS accepte