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Table of contents

Volume 216

Number 1, January 2015

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1

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The spectrum of the Fe i atom is critical to many areas of astrophysics and beyond. Measurements of the energies of its high-lying levels remain woefully incomplete, however, despite extensive laboratory and solar analysis. In this work, we use high-resolution archival absorption-line ultraviolet and optical spectra of stars whose warm temperatures favor moderate Fe i excitation. We derive the energy for a particular upper level in Kurucz's semiempirical calculations by adopting a trial value that yields the same wavelength for a given line predicted to be about as strong as that of a strong unidentified spectral line observed in the stellar spectra, then checking the new wavelengths of other strong predicted transitions that share the same upper level for coincidence with other strong observed unidentified lines. To date, this analysis has provided the upper energies of 66 Fe i levels. Many new energy levels are higher than those accessible to laboratory experiments; several exceed the Fe i ionization energy. These levels provide new identifications for over 2000 potentially detectable lines. Almost all of the new levels of odd parity include UV lines that were detected but unclassified in laboratory Fe i absorption spectra, providing an external check on the energy values. We motivate and present the procedure, provide the resulting new energy levels and their uncertainties, list all the potentially detectable UV and optical new Fe i line identifications and their gf values, point out new lines of astrophysical interest, and discuss the prospects for additional Fe i energy level determinations.

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The three Mn i lines at 17325, 17339, and 17349 Å are among the 25 strongest lines (log (gf) > 0.5) in the H band. They are all heavily broadened due to hyperfine structure, and the profiles of these lines have so far not been understood. Earlier studies of these lines even suggested that they were blended. In this work, the profiles of these three infrared (IR) lines have been studied theoretically and compared to experimental spectra to assist in the complete understanding of the solar spectrum in the IR. It is shown that the structure of these lines cannot be described in the conventional way using the diagonal A and B hyperfine interaction constants. The off-diagonal hyperfine interaction not only has a large impact on the energies of the hyperfine levels, but also introduces a large intensity redistribution among the hyperfine lines, changing the line profiles dramatically. By performing large-scale calculations of the diagonal and off-diagonal hyperfine interaction and the gf-values between the upper and lower hyperfine levels and using a semi-empirical fitting procedure, we achieved agreement between our synthetic and experimental spectra. Furthermore, we compare our results with observations of stellar spectra. The spectra of the Sun and the K1.5 III red giant star Arcturus were modeled in the relevant region, 1.73–1.74 μm, using our theoretically predicted gf-values and energies for each individual hyperfine line. Satisfactory fits were obtained and clear improvements were found using our new data compared with the old available Mn i data. A complete list of energies and gf-values for all the 3d54s(7S)4d e6D – 3d54s(7S)4f w6F hyperfine lines are available as supporting material, whereas only the stronger lines are presented and discussed in detail in this paper.

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State-to-state rate coefficients for ortho-H2O:He and para-H2O:He inelastic collisions in the 20–120 K thermal range are investigated by means of an improved experimental procedure. This procedure is based on the use of a kinetic master equation (MEQ) which describes the evolution of populations of H2O rotational levels along a supersonic jet of H2O highly diluted in helium. The MEQ is expressed in terms of experimental observables and rate coefficients for H2O:He inelastic collisions. The primary experimental observables are the local number density and the populations of the rotational energy levels of H2O, quantities which are determined along the jet with unprecedented accuracy by means of Raman spectroscopy with high space resolution. Sets of rate coefficients from the literature and from present close-coupling calculations using two different potential energy surfaces (PESs) have been tested against the experiment. The Green et al. rate coefficients are up to 50% too low compared to the experiment, while most rates calculated here from the Hodges et al. PES and the Patkowski et al. PES are much closer to the experimental values. Experimental rates with an estimated accuracy on the order of 10% have been obtained for ortho-H2O:He and para-H2O:He inelastic collisions between 20 and 120 K by scaling and averaging the theoretical rates to the experiment.

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The Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project is a dedicated multi-object RM experiment that has spectroscopically monitored a sample of 849 broad-line quasars in a single 7 deg2 field with the SDSS-III Baryon Oscillation Spectroscopic Survey spectrograph. The RM quasar sample is flux-limited to ipsf = 21.7 mag, and covers a redshift range of 0.1 < z < 4.5 without any other cuts on quasar properties. Optical spectroscopy was performed during 2014 January–July dark/gray time, with an average cadence of ∼4 days, totaling more than 30 epochs. Supporting photometric monitoring in the g and i bands was conducted at multiple facilities including the Canada–France–Hawaii Telescope (CFHT) and the Steward Observatory Bok telescope in 2014, with a cadence of ∼2 days and covering all lunar phases. The RM field (R.A., decl. = 14:14:49.00, +53:05:00.0) lies within the CFHT-LS W3 field, and coincides with the Pan-STARRS 1 (PS1) Medium Deep Field MD07, with three prior years of multi-band PS1 light curves. The SDSS-RM six month baseline program aims to detect time lags between the quasar continuum and broad line region (BLR) variability on timescales of up to several months (in the observed frame) for ∼10% of the sample, and to anchor the time baseline for continued monitoring in the future to detect lags on longer timescales and at higher redshift. SDSS-RM is the first major program to systematically explore the potential of RM for broad-line quasars at z > 0.3, and will investigate the prospects of RM with all major broad lines covered in optical spectroscopy. SDSS-RM will provide guidance on future multi-object RM campaigns on larger scales, and is aiming to deliver more than tens of BLR lag detections for a homogeneous sample of quasars. We describe the motivation, design, and implementation of this program, and outline the science impact expected from the resulting data for RM and general quasar science.

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We study the multi-dimensional properties of neutrino transfer inside supernova cores by solving the Boltzmann equations for neutrino distribution functions in genuinely six-dimensional phase space. Adopting representative snapshots of the post-bounce core from other supernova simulations in three dimensions, we solve the temporal evolution to stationary states of neutrino distribution functions using our Boltzmann solver. Taking advantage of the multi-angle and multi-energy feature realized by the Sn method in our code, we reveal the genuine characteristics of spatially three-dimensional neutrino transfer, such as nonradial fluxes and nondiagonal Eddington tensors. In addition, we assess the ray-by-ray approximation, turning off the lateral-transport terms in our code. We demonstrate that the ray-by-ray approximation tends to propagate fluctuations in thermodynamical states around the neutrino sphere along each radial ray and overestimate the variations between the neutrino distributions on different radial rays. We find that the difference in the densities and fluxes of neutrinos between the ray-by-ray approximation and the full Boltzmann transport becomes ∼20%, which is also the case for the local heating rate, whereas the volume-integrated heating rate in the Boltzmann transport is found to be only slightly larger (∼2%) than the counterpart in the ray-by-ray approximation due to cancellation among different rays. These results suggest that we should carefully assess the possible influences of various approximations in the neutrino transfer employed in current simulations of supernova dynamics. Detailed information on the angle and energy moments of neutrino distribution functions will be profitable for the future development of numerical methods in neutrino-radiation hydrodynamics.

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Using high-resolution, multiple-passband Hubble Space Telescope images spanning the entire optical/near-infrared wavelength range, we obtained a statistically complete U-band-selected sample of 846 extended star clusters across the disk of the nearby starburst galaxy M82. Based on a careful analysis of the clusters' spectral energy distributions, we determined their galaxy-wide age and mass distributions. The M82 clusters exhibit three clear peaks in their age distribution, thus defining relatively young, log (t yr−1) ⩽ 7.5, intermediate-age, log (t yr−1) ∈ [7.5, 8.5], and old samples, log (t yr−1) ⩾ 8.5. Comparison of the completeness-corrected mass distributions offers a firm handle on the galaxy's star cluster disruption history. The most massive star clusters in the young and old samples are (almost) all concentrated in the most densely populated central region, while the intermediate-age sample's most massive clusters are more spatially dispersed, which may reflect the distribution of the highest-density gas throughout the galaxy's evolutionary history, combined with the solid-body nature of the galaxy's central region.

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We present results from a high-contrast adaptive optics imaging search for giant planets and brown dwarfs (≳1 MJup) around 122 newly identified nearby (≲40 pc) young M dwarfs. Half of our targets are younger than 135 Myr and 90% are younger than the Hyades (620 Myr). After removing 44 close stellar binaries (implying a stellar companion fraction of >35.4% ± 4.3% within 100 AU), 27 of which are new or spatially resolved for the first time, our remaining sample of 78 single M dwarfs makes this the largest imaging search for planets around young low-mass stars (0.1–0.6 M) to date. Our H- and K-band coronagraphic observations with Keck/NIRC2 and Subaru/HiCIAO achieve typical contrasts of 12–14 mag and 9–13 mag at 1'', respectively, which correspond to limiting planet masses of 0.5–10 MJup at 5–33 AU for 85% of our sample. We discovered four young brown dwarf companions: 1RXS J235133.3+312720 B (32 ± 6 MJup; L0$^{+2}_{-1}$; 120 ± 20 AU), GJ 3629 B (64$^{+30}_{-23}$ MJup; M7.5 ± 0.5; 6.5 ± 0.5 AU), 1RXS J034231.8+121622 B (35 ± 8 MJup; L0 ± 1; 19.8 ± 0.9 AU), and 2MASS J15594729+4403595 B (43 ± 9 MJup; M8.0 ± 0.5; 190 ± 20 AU). Over 150 candidate planets were identified; we obtained follow-up imaging for 56% of these but all are consistent with background stars. Our null detection of planets enables strong statistical constraints on the occurrence rate of long-period giant planets around single M dwarfs. We infer an upper limit (at the 95% confidence level) of 10.3% and 16.0% for 1–13 MJup planets between 10–100 AU for hot-start and cold-start (Fortney) evolutionary models, respectively. Fewer than 6.0% (9.9%) of M dwarfs harbor massive gas giants in the 5–13 MJup range like those orbiting HR 8799 and β Pictoris between 10–100 AU for a hot-start (cold-start) formation scenario. The frequency of brown dwarf (13–75 MJup) companions to single M dwarfs between 10–100 AU is 2.8$^{+2.4}_{-1.5}$%. Altogether we find that giant planets, especially massive ones, are rare in the outskirts of M dwarf planetary systems. Although the first directly imaged planets were found around massive stars, there is currently no statistical evidence for a trend of giant planet frequency with stellar host mass at large separations as predicted by the disk instability model of giant planet formation.

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X-ray flares have been discovered in black hole systems such as gamma-ray bursts, the tidal disruption event Swift J1644+57, the supermassive black hole Sagittarius A* at the center of our Galaxy, and some active galactic nuclei. Occurrences of X-ray flares are always accompanied by relativistic jets. However, it is still unknown whether or not there is a physical analogy among such X-ray flares produced in black hole systems spanning nine orders of magnitude in mass. Here, we report observed data of X-ray flares and show that they have three statistical properties similar to solar flares, including power-law distributions of their energies, durations, and waiting times, which can be explained by a fractal-diffusive, self-organized criticality model. These statistical similarities, together with the fact that solar flares are triggered by a magnetic reconnection process, suggest that all of the X-ray flares are consistent with magnetic reconnection events, implying that their concomitant relativistic jets may be magnetically dominated.

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We present the stellar and ionized gas kinematics of 13 bright peculiar Virgo cluster galaxies observed with the DensePak Integral Field Unit at the WIYN 3.5 m telescope in order to look for kinematic evidence that these galaxies have experienced gravitational interactions or gas stripping. Two-dimensional maps of the stellar velocity V, stellar velocity dispersion σ, and the ionized gas velocity (Hβ and/or [O iii]) are presented for the galaxies in the sample. The stellar rotation curves and velocity dispersion profiles are determined for 13 galaxies, and the ionized gas rotation curves are determined for 6 galaxies. Misalignments between the optical and kinematical major axes are found in several galaxies. While in some cases this is due to a bar, in other cases it seems to be associated with gravitational interaction or ongoing ram pressure stripping. Non-circular gas motions are found in nine galaxies, with various causes including bars, nuclear outflows, or gravitational disturbances. Several galaxies have signatures of kinematically distinct stellar components, which are likely signatures of accretion or mergers. For all of our galaxies, we compute the angular momentum parameter λR. An evaluation of the galaxies in the λR ellipticity plane shows that all but two of the galaxies have significant support from random stellar motions, and have likely experienced gravitational interactions. This includes some galaxies with very small bulges and truncated/compact Hα morphologies, indicating that such galaxies cannot be fully explained by simple ram pressure stripping, but must have had significant gravitational encounters. Most of the sample galaxies show evidence for ICM-ISM stripping as well as gravitational interactions, indicating that the evolution of a significant fraction of cluster galaxies is likely strongly impacted by both effects.

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Nearby resolved dwarf galaxies provide excellent opportunities for studying the dust-producing late stages of stellar evolution over a wide range of metallicity (−2.7 ≲ [Fe/H] ≲ −1.0). Here, we describe DUSTiNGS (DUST in Nearby Galaxies with Spitzer): a 3.6 and 4.5 μm post-cryogen Spitzer Space Telescope imaging survey of 50 dwarf galaxies within 1.5 Mpc that is designed to identify dust-producing asymptotic giant branch (AGB) stars and massive stars. The survey includes 37 dwarf spheroidal, 8 dwarf irregular, and 5 transition-type galaxies. This near-complete sample allows for the building of statistics on these rare phases of stellar evolution over the full metallicity range. The photometry is >75% complete at the tip of the red giant branch for all targeted galaxies, with the exception of the crowded inner regions of IC 10, NGC 185, and NGC 147. This photometric depth ensures that the majority of the dust-producing stars, including the thermally pulsing AGB stars, are detected in each galaxy. The images map each galaxy to at least twice the half-light radius to ensure that the entire evolved star population is included and to facilitate the statistical subtraction of background and foreground contamination, which is severe at these wavelengths. In this overview, we describe the survey, the data products, and preliminary results. We show evidence for the presence of dust-producing AGB stars in eight of the targeted galaxies, with metallicities as low as [Fe/H] = −1.9, suggesting that dust production occurs even at low metallicity.

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A capillary discharge tube was used to record the Xe spectrum in the 400–5500 Å  region. A set of 243 lines of the Xe vi spectrum was observed, and 146 of them were classified for the first time. For all known lines, we calculated the weighted oscillator strengths (gf) and weighted transition probabilities (gA) using the configuration interaction in a relativistic Hartree–Fock approach. The energy matrix was calculated using energy parameters adjusted to fit the experimental energy levels. Core polarization effects were taken into account in our calculations. Experimental energy values and calculated lifetimes are also presented for a set of 88 levels. From these levels, 32 were classified for the first time and 33 had their values revised. Our analysis of the 5s5p5d and 5s5p6s configurations was extended in order to clarify discrepancies among previous works.

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We present and study the largest and most comprehensive catalog of microlensing events ever constructed. The sample of standard microlensing events comprises 3718 unique events from 2001–2009 with 1409 events that had not been detected before in real-time by the Early Warning System of the Optical Gravitational Lensing Experiment. The search pipeline uses machine learning algorithms to help find rare phenomena among 150 million objects and to derive the detection efficiency. Applications of the catalog can be numerous, from analyzing individual events to large statistical studies of the Galactic mass, kinematics distributions, and planetary abundances. We derive maps of the mean Einstein ring crossing time of events spanning 31 deg2 toward the Galactic center and compare the observed distributions with the most recent models. We find good agreement within the observed region and we see the signature of the tilt of the bar in the microlensing data. However, the asymmetry of the mean timescales seems to rise more steeply than predicted, indicating either a somewhat different orientation of the bar or a larger bar width. The map of events with sources in the Galactic bulge shows a dependence of the mean timescale on the Galactic latitude, signaling an increasing contribution from disk lenses closer to the plane relative to the height of the disk. Our data present a perfect set for comparing and enhancing new models of the central parts of the Milky Way and creating a three-dimensional picture of the Galaxy.

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We present an Analytic Model of Intergalactic-medium and GAlaxy (AMIGA) evolution since the dark ages. AMIGA is in the spirit of the popular semi-analytic models of galaxy formation, although it does not use halo merger trees but interpolates halo properties in grids that are progressively built. This strategy is less memory-demanding and allows one to start modeling at sufficiently high redshifts and low halo masses to have trivial boundary conditions. The number of free parameters is minimized by making a causal connection between physical processes usually treated as independent of each other, which leads to more reliable predictions. However, the strongest points of AMIGA are the following: (1) the inclusion of molecular cooling and metal-poor, population III (Pop III) stars with the most dramatic feedback and (2) accurate follow up of the temperature and volume filling factor of neutral, singly ionized, and doubly ionized regions, taking into account the distinct halo mass functions in those environments. We find the following general results. Massive Pop III stars determine the intergalactic medium metallicity and temperature, and the growth of spheroids and disks is self-regulated by that of massive black holes (MBHs) developed from the remnants of those stars. However, the properties of normal galaxies and active galactic nuclei appear to be quite insensitive to Pop III star properties due to the much higher yield of ordinary stars compared to Pop III stars and the dramatic growth of MBHs when normal galaxies begin to develop, which cause the memory loss of the initial conditions.

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One of the key issues when running a simulation on multiple CPUs is maintaining a proper load balance throughout the run and minimizing communications between CPUs. We propose a novel method of utilizing a Voronoi diagram to achieve a nearly perfect load balance without the need of any global redistributions of data. As a show case, we implement our method in RICH, a two-dimensional moving mesh hydrodynamical code, but it can be extended trivially to other codes in two or three dimensions. Our tests show that this method is indeed efficient and can be used in a large variety of existing hydrodynamical codes.

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Extensive rovibrational line lists were computed for nine isotopologues of the CO molecule, namely, 12C16O, 12C17O, 12C18O, 13C16O, 13C17O, 13C18O, 14C16O, 14C17O, and 14C18O in the ground electronic state with v ⩽ 41, Δv ⩽ 11, and J ⩽ 150. The line intensity and position calculations were carried out using a newly determined piece-wise dipole moment function (DMF) in conjunction with the wavefunctions calculated from an experimentally determined potential energy function from Coxon & Hajigeorgiou. A direct-fit method that simultaneously fits all the reliable experimental rovibrational matrix elements has been used to construct the dipole moment function near equilibrium internuclear distance. In order to extend the amount and quality of input experimental parameters, new Cavity Ring Down Spectroscopy experiments were carried out to enable measurements of the lines in the 4–0 band with low uncertainty as well as the first measurements of lines in the 6–0 band. A new high-level ab initio DMF, derived from a finite field approach has been calculated to cover internuclear distances far from equilibrium. Accurate partition sums have been derived for temperatures up to 9000 K. In addition to air- and self-induced broadening and shift parameters, those induced by CO2 and H2 are now provided for planetary applications. A complete set of broadening and shift parameters was calculated based on sophisticated extrapolation of high-quality measured data. The line lists, which follow HITRAN formalism, are provided as supplementary material.

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We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ∼(100 Mpc)3 cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 32003 Eulerian grid cells and dark matter particles.

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We present 2.5–5.0 μm spectra of 83 nearby (0.002 < z < 0.48) and bright (K < 14 mag) type-1 active galactic nuclei (AGNs) taken with the Infrared Camera on board AKARI. The 2.5–5.0 μm spectral region contains emission lines such as Brβ (2.63 μm), Brα (4.05 μm), and polycyclic aromatic hydrocarbons (3.3 μm), which can be used for studying the black hole (BH) masses and star formation activity in the host galaxies of AGNs. The spectral region also suffers less dust extinction than in the ultra violet (UV) or optical wavelengths, which may provide an unobscured view of dusty AGNs. Our sample is selected from bright quasar surveys of Palomar-Green and SNUQSO, and AGNs with reverberation-mapped BH masses from Peterson et al. Using 11 AGNs with reliable detection of Brackett lines, we derive the Brackett-line-based BH mass estimators. We also find that the observed Brackett line ratios can be explained with the commonly adopted physical conditions of the broad line region. Moreover, we fit the hot and warm dust components of the dust torus by adding photometric data of SDSS, 2MASS, WISE, and ISOto the AKARI spectra, finding hot and warm dust temperatures of ∼1100 K and ∼220 K, respectively, rather than the commonly cited hot dust temperature of 1500 K.

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We present fully sampled ∼3' resolution images of 12CO(J = 2–1), 13CO(J = 2–1), and C18O(J = 2–1) emission taken with the newly developed 1.85 m millimeter–submillimeter telescope over the entire area of the Orion A and B giant molecular clouds. The data were compared with J = 1–0 of the 12CO, 13CO, and C18O data taken with the Nagoya 4 m telescope and the NANTEN telescope at the same angular resolution to derive the spatial distributions of the physical properties of the molecular gas. We explore the large velocity gradient formalism to determine the gas density and temperature using line combinations of 12CO(J = 2–1), 13CO(J = 2–1), and 13CO(J = 1–0) assuming a uniform velocity gradient and abundance ratio of CO. The derived gas density is in the range of 500 to 5000 cm−3, and the derived gas temperature is mostly in the range of 20 to 50 K along the cloud ridge with a temperature gradient depending on the distance from the star forming region. We found that the high-temperature region at the cloud edge faces the H ii region, indicating that the molecular gas is interacting with the stellar wind and radiation from the massive stars. In addition, we compared the derived gas properties with the young stellar objects distribution obtained with the Spitzer telescope to investigate the relationship between the gas properties and the star formation activity therein. We found that the gas density and star formation efficiency are positively well correlated, indicating that stars form effectively in the dense gas region.

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There is increasing evidence for the presence of multiple red giant branches (RGBs) in the color–magnitude diagrams of massive globular clusters (GCs). In order to investigate the origin of this split on the RGB, we have performed new narrow-band Ca photometry and low-resolution spectroscopy for M22, NGC 1851, and NGC 288. We find significant differences (more than 4σ) in calcium abundance from the spectroscopic HK' index for M22 and NGC 1851. We also find more than 8σ differences in CN-band strength between the Ca-strong and Ca-weak subpopulations for these GCs. For NGC 288, however, a large difference is detected only in the CN strength. The calcium abundances of RGB stars in this GC are identical to within the errors. This is consistent with the conclusion from our new Ca photometry where the RGB splits are confirmed in M22 and NGC 1851, but not in NGC 288. We also find interesting differences in the CN–CH correlations among these GCs. While CN and CH are anti-correlated in NGC 288, they show a positive correlation in M22. NGC 1851, however, shows no difference in CH between the two groups of stars with different CN strengths. We suggest that all of these systematic differences would be best explained by how strongly Type II supernovae enrichment has contributed to the chemical evolution of these GCs.

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The Blanco Cosmology Survey is a four-band (griz) optical-imaging survey of ∼80 deg2 of the southern sky. The survey consists of two fields centered approximately at (R.A., decl.) = (23h, −55°) and (5h30m, −53°) with imaging sufficient for the detection of L galaxies at redshift z ⩽ 1. In this paper, we present our reduction of the survey data and describe a new technique for the separation of stars and galaxies. We search the calibrated source catalogs for galaxy clusters at z ⩽ 0.75 by identifying spatial over-densities of red-sequence galaxies and report the coordinates, redshifts, and optical richnesses, λ, for 764 galaxy clusters at z ⩽ 0.75. This sample, >85% of which are new discoveries, has a median redshift of z = 0.52 and median richness λ(0.4 L) = 16.4. Accompanying this paper we also release full survey data products including reduced images and calibrated source catalogs. These products are available at http://data.rcc.uchicago.edu/dataset/blanco-cosmology-survey.

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The matrix elements and energies needed to calculate vibrational-rotational state resolved cross sections and rate coefficients for radiative association of H and H+ and for photodissociation of ${\rm H}_2^+$ are presented for applications to simulations of chemistry in the early universe and to stellar atmospheres.