The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

Smooth vortex precession in superfluid 4He

We have measured a precessing superfluid vortex line, stretched from a wire to the wall of a cylindrical cell. By contrast to previous experiments with a similar geometry, the motion along the wall is smooth. The key difference is probably that our wire is substantially off center. We verify several numerical predictions about the motion, including an asymmetry in the precession signature, the behavior of pinning events, and the temperature dependence of the precession.Comment: 8 pages, 8 figure

Trace element composition of silicate inclusions in sub-lithospheric diamonds from the Juina-5 kimberlite:Evidence for diamond growth from slab melts

The trace element compositions of inclusions in sub-lithospheric diamonds from the Juina-5 kimberlite, Brazil, are presented. Literature data for mineral/melt partition coefficients were collated, refitted and employed to interpret inclusion compositions. As part of this process an updated empirical model for predicting the partitioning behaviour of trivalent cations for garnet–melt equilibrium calibrated using data from 73 garnet-melt pairs is presented. High levels of trace element enrichment in inclusions interpreted as former calcium silicate perovskite and majoritic garnet preclude their origin as fragments of an ambient deep mantle assemblage. Inclusions believed to represent former bridgmanite minerals also display a modest degree of enrichment relative to mantle phases. The trace element compositions of ‘NAL’ and ‘CF phase’ minerals are also reported. Negative Eu, Ce, and Y/Ho anomalies alongside depletions of Sr, Hf and Zr in many inclusions are suggestive of formation from a low-degree carbonatitic melt of subducted oceanic crust. Observed enrichments in garnet and ‘calcium perovskite’ inclusions limit depths of melting to less than ~ 600 km, prior to calcium perovskite saturation in subducting assemblages. Less enriched inclusions in sub-lithospheric diamonds from other global localities may represent deeper diamond formation. Modelled source rock compositions that are capable of producing melts in equilibrium with Juina-5 ‘calcium perovskite’ and majorite inclusions are consistent with subducted MORB. Global majorite inclusion compositions suggest a common process is responsible for the formation of many superdeep diamonds, irrespective of geographic locality. Global transition zone inclusion compositions are reproduced by fractional crystallisation from a single parent melt, suggesting that they record the crystallisation sequence and melt evolution during this interaction of slab melts with ambient mantle. All observations are consistent with the previous hypothesis that many superdeep diamonds are created as slab-derived carbonatites interact with peridotitic mantle in the transition zone

An ALMA survey of CO in submillimetre galaxies: companions, triggering, and the environment in blended sources

We present ALMA observations of the mid-J 12CO emission from six single-dish selected 870-μm sources in the Extended Chandra Deep Field-South and UKIDSS Ultra-Deep Survey fields. These six single-dish submillimetre sources were selected based on previous ALMA continuum observations, which showed that each comprised a blend of emission from two or more individual submillimetre galaxies (SMGs), separated on 5–10 arcsec scales. The six single-dish submillimetre sources targeted correspond to a total of 14 individual SMGs, of which seven have previously measured robust optical/near-infrared spectroscopic redshifts, which were used to tune our ALMA observations. We detect CO(3–2) or CO(4–3) at z = 2.3–3.7 in 7 of the 14 SMGs, and in addition serendipitously detect line emission from three gas-rich companion galaxies, as well as identify four new 3.3 mm selected continuum sources in the six fields. Joint analysis of our CO spectroscopy and existing data suggests that 64(±18)percent of the SMGs in blended submillimetre sources are unlikely to be physically associated. However, three of the SMG fields (50 per cent) contain new, serendipitously detected CO-emitting (but submillimetre-faint) sources at similar redshifts to the 870 μm selected SMGs we targeted. These data suggest that the SMGs inhabit overdense regions, but that these are not sufficiently overdense on ∼100 kpc scales to influence the source blending given the short lifetimes of SMGs. We find that 21±12percent of SMGs have spatially distinct and kinematically close companion galaxies (∼8–150 kpc and ≲ 300 km s−1), which may have enhanced their star formation via gravitational interactions

An ALMA survey of the S2CLS UDS field: optically invisible submillimetre galaxies

We analyse a robust sample of 30 near-infrared-faint (KAB > 25.3, 5σ) submillimetre galaxies (SMGs) selected from a 0.96 deg2 field to investigate their properties and the cause of their faintness in optical/near-infrared wavebands. Our analysis exploits precise identifications based on Atacama Large Millimeter Array (ALMA) 870-μm continuum imaging, combined with very deep near-infrared imaging from the UKIDSS Ultra Deep Survey. We estimate that SMGs with KAB > 25.3 mag represent 15 ± 2 per cent of the total population brighter than S870 = 3.6 mJy, with a potential surface density of ∼450 deg−2 above S870 ≥ 1 mJy. As such, they pose a source of contamination in surveys for both high-redshift ‘quiescent’ galaxies and very high redshift Lyman-break galaxies. We show that these K-faint SMGs represent the tail of the broader submillimetre population, with comparable dust and stellar masses to KAB ≤ 25.3 mag SMGs, but lying at significantly higher redshifts (z = 3.44 ± 0.06 versus z = 2.36 ± 0.11) and having higher dust attenuation (AV = 5.2 ± 0.3 versus AV = 2.9 ± 0.1). We investigate the origin of the strong dust attenuation and find indications that these K-faint galaxies have smaller dust continuum sizes than the KAB ≤ 25.3 mag galaxies, as measured by ALMA, which suggests their high attenuation is related to their compact sizes. We identify a correlation of dust attenuation with star formation rate surface density (SFR), with the K-faint SMGs representing the higher SFR and highest AV galaxies. The concentrated, intense star formation activity in these systems is likely to be associated with the formation of spheroids in compact galaxies at high redshifts, but as a result of their high obscuration these galaxies are completely missed in ultraviolet, optical, and even near-infrared surveys

An ALMA Survey of the SCUBA-2 Cosmology Legacy Survey UKIDSS/UDS Field: The Far-infrared/Radio Correlation for High-redshift Dusty Star-forming Galaxies

We study the radio properties of 706 submillimeter galaxies (SMGs) selected at 870 μm with the Atacama Large Millimeter Array from the SCUBA-2 Cosmology Legacy Survey map of the Ultra Deep Survey field. We detect 273 SMGs at >4σ in deep Karl G. Jansky Very Large Array 1.4 GHz observations, of which a subset of 45 SMGs are additionally detected in 610 MHz Giant Metre-Wave Radio Telescope imaging. We quantify the far-infrared/radio correlation (FIRRC) through parameter q IR, defined as the logarithmic ratio of the far-infrared and radio luminosity, and include the radio-undetected SMGs through a stacking analysis. We determine a median q IR = 2.20 ± 0.03 for the full sample, independent of redshift, which places these z ~ 2.5 dusty star-forming galaxies 0.44 ± 0.04 dex below the local correlation for both normal star-forming galaxies and local ultra-luminous infrared galaxies (ULIRGs). Both the lack of redshift evolution and the offset from the local correlation are likely the result of the different physical conditions in high-redshift starburst galaxies, compared to local star-forming sources. We explain the offset through a combination of strong magnetic fields (B gsim 0.2 mG), high interstellar medium (ISM) densities and additional radio emission generated by secondary cosmic rays. While local ULIRGs are likely to have similar magnetic field strengths, we find that their compactness, in combination with a higher ISM density compared to SMGs, naturally explains why local and high-redshift dusty star-forming galaxies follow a different FIRRC. Overall, our findings paint SMGs as a homogeneous population of galaxies, as illustrated by their tight and nonevolving far-infrared/radio correlation

The SCUBA-2 Cosmology Legacy Survey: ALMA resolves the bright-end of the submillimeter number counts

We present high-resolution 870 μm Atacama Large Millimeter/sub-millimeter Array (ALMA) continuum maps of 30 bright sub-millimeter sources in the UKIDSS UDS field. These sources are selected from deep, 1 degree2 850 μm maps from the SCUBA-2 Cosmology Legacy Survey, and are representative of the brightest sources in the field (median = 8.7 ± 0.4 mJy). We detect 52 sub-millimeter galaxies (SMGs) at >4σ significance in our 30 ALMA maps. In of the ALMA maps the single-dish source comprises a blend of ≥2 SMGs, where the secondary SMGs are Ultra-luminous Infrared Galaxies (ULIRGs) with 1012 . The brightest SMG contributes on average of the single-dish flux density, and in the ALMA maps containing ≥2 SMGs the secondary SMG contributes of the integrated ALMA flux. We construct source counts and show that multiplicity boosts the apparent single-dish cumulative counts by 20% at S870 > 7.5 mJy, and by 60% at S870 > 12 mJy. We combine our sample with previous ALMA studies of fainter SMGs and show that the counts are well-described by a double power law with a break at 8.5 ± 0.6 mJy. The break corresponds to a luminosity of ~6 × 1012 or a star formation rate (SFR) of ~103 . For the typical sizes of these SMGs, which are resolved in our ALMA data with = 1.2 ± 0.1 kpc, this yields a limiting SFR density of ~100 yr−1 kpc−2 Finally, the number density of S870 2 mJy SMGs is 80 ± 30 times higher than that derived from blank-field counts. An over-abundance of faint SMGs is inconsistent with line-of-sight projections dominating multiplicity in the brightest SMGs, and indicates that a significant proportion of these high-redshift ULIRGs are likely to be physically associated

A High Statistics Search for Ultra-High Energy Gamma-Ray Emission from Cygnus X-3 and Hercules X-1

We have carried out a high statistics (2 Billion events) search for ultra-high energy gamma-ray emission from the X-ray binary sources Cygnus X-3 and Hercules X-1. Using data taken with the CASA-MIA detector over a five year period (1990-1995), we find no evidence for steady emission from either source at energies above 115 TeV. The derived upper limits on such emission are more than two orders of magnitude lower than earlier claimed detections. We also find no evidence for neutral particle or gamma-ray emission from either source on time scales of one day and 0.5 hr. For Cygnus X-3, there is no evidence for emission correlated with the 4.8 hr X-ray periodicity or with the occurrence of large radio flares. Unless one postulates that these sources were very active earlier and are now dormant, the limits presented here put into question the earlier results, and highlight the difficulties that possible future experiments will have in detecting gamma-ray signals at ultra-high energies.Comment: 26 LaTeX pages, 16 PostScript figures, uses psfig.sty to be published in Physical Review

The SCUBA-2 Cosmology Legacy Survey: Ultraluminous star-forming galaxies in a z=1.6 cluster

We analyze new SCUBA-2 submillimeter and archival SPIRE far-infrared imaging of a z = 1.62 cluster, Cl 0218.3–0510, which lies in the UKIRT Infrared Deep Sky Survey/Ultra-Deep Survey field of the SCUBA-2 Cosmology Legacy Survey. Combining these tracers of obscured star-formation activity with the extensive photometric and spectroscopic information available for this field, we identify 31 far-infrared/submillimeter-detected probable cluster members with bolometric luminosities 1012 L ☉ and show that by virtue of their dust content and activity, these represent some of the reddest and brightest galaxies in this structure. We exploit ALMA submillimeter continuum observations, which cover one of these sources, to confirm the identification of a SCUBA-2-detected ultraluminous star-forming galaxy in this structure. Integrating the total star-formation activity in the central region of the structure, we estimate that it is an order of magnitude higher (in a mass-normalized sense) than clusters at z ~ 0.5-1. However, we also find that the most active cluster members do not reside in the densest regions of the structure, which instead host a population of passive and massive, red galaxies. We suggest that while the passive and active populations have comparable near-infrared luminosities at z = 1.6, MH ~ –23, the subsequent stronger fading of the more active galaxies means that they will evolve into passive systems at the present day that are less luminous than the descendants of those galaxies that were already passive at z ~ 1.6 (MH ~ –20.5 and MH ~ –21.5, respectively, at z ~ 0). We conclude that the massive galaxy population in the dense cores of present-day clusters were already in place at z = 1.6 and that in Cl 0218.3–0510 we are seeing continuing infall of less extreme, but still ultraluminous, star-forming galaxies onto a pre-existing structure

An ALMA Survey of the SCUBA-2 Cosmology Legacy Survey UKIDSS/UDS Field: Number Counts of Submillimeter Galaxies

We report the first results of AS2UDS, an 870 μm continuum survey with the Atacama Large Millimeter/Submillimeter Array (ALMA) of a total area of ~50 arcmin2 comprising a complete sample of 716 submillimeter sources drawn from the SCUBA-2 Cosmology Legacy Survey (S2CLS) map of the UKIDSS/UDS field. The S2CLS parent sample covers a 0.96 degree2 field at σ 850 = 0.90 ± 0.05 mJy beam−1. Our deep, high-resolution ALMA observations with σ 870 ~ 0.25 mJy and a 0farcs15–0farcs30 FWHM synthesized beam, provide precise locations for 695 submillimeter galaxies (SMGs) responsible for the submillimeter emission corresponding to 606 sources in the low-resolution, single-dish map. We measure the number counts of SMGs brighter than S 870 ≥ 4 mJy, free from the effects of blending and show that the normalization of the counts falls by 28% ± 2% in comparison with the SCUBA-2 published counts, but that the shape remains unchanged. We determine that ${44}_{-14}^{+16}$% of the brighter single-dish sources with S 850 ≥ 9 mJy consist of a blend of two or more ALMA-detectable SMGs brighter than S 870 ~ 1 mJy (corresponding to a galaxy with a total-infrared luminosity of L IR gsim 1012 L ⊙), in comparison with 28% ± 2% for the single-dish sources at S 850 ≥ 5 mJy. Using the 46 single-dish submillimeter sources that contain two or more ALMA-detected SMGs with photometric redshifts, we show that there is a significant statistical excess of pairs of SMGs with similar redshifts (<1% probability of occurring by chance), suggesting that at least 30% of these blends arise from physically associated pairs of SMGs