Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier and Lapla
ce transforms. The new methods also yield new perturbative expansions when the integrals cannot be solved analytically. Here, we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives. The new methods can be used to express path integrals in terms of functional differentiation, and they also suggest new perturbative expansions in quantum field theory.
G0.253+0.016 is a molecular clump that appears to be on the verge of forming a high mass, Arches-like cluster. Here we present new ALMA observations of its small-scale (~0.07 pc) 3mm dust continuum and molecular line emission. The data reveal a compl
ex network of emission features, the morphology of which ranges from small, compact regions to extended, filamentary structures that are seen in both emission and absorption. The dust column density is well traced by molecules with higher excitation energies and critical densities, consistent with a clump that has a denser interior. A statistical analysis supports the idea that turbulence shapes the observed gas structure within G0.253+0.016. We find a clear break in the turbulent power spectrum derived from the optically thin dust continuum emission at a spatial scale of ~0.1 pc, which may correspond to the spatial scale at which gravity has overcome the thermal pressure. We suggest that G0.253+0.016 is on the verge of forming a cluster from hierarchical, filamentary structures that arise from a highly turbulent medium. Although the stellar distribution within Arches-like clusters is compact, centrally condensed and smooth, the observed gas distribution within G0.253+0.016 is extended, with no high-mass central concentration, and has a complex, hierarchical structure. If this clump gives rise to a high-mass cluster and its stars are formed from this initially hierarchical gas structure, then the resulting cluster must evolve into a centrally condensed structure via a dynamical process.
The Millimetre Astronomy Legacy Team 90 GHz (MALT90) survey has detected high-mass star-forming clumps with anomalous N$_2$H$^+$/HCO$^+$(1-0) integrated intensity ratios that are either unusually high (N$_2$H$^+$ rich) or unusually low (N$_2$H$^+$ po
or). With 3 mm observations from the Australia Telescope Compact Array (ATCA), we imaged two N$_2$H$^+$ rich clumps, G333.234-00.061 and G345.144-00.216, and two N$_2$H$^+$ poor clumps, G351.409+00.567 and G353.229+00.672. In these clumps, the N$_2$H$^+$ rich anomalies arise from extreme self-absorption of the HCO$^+$ line. G333.234-00.061 contains two of the most massive protostellar cores known with diameters of less than 0.1 pc, separated by a projected distance of only 0.12 pc. Unexpectedly, the higher mass core appears to be at an earlier evolutionary stage than the lower mass core, which may suggest that two different epochs of high-mass star formation can occur in close proximity. Through careful analysis of the ATCA observations and MALT90 clumps (including the G333, NGC 6334, and NGC 6357 star formation regions), we find that N$_2$H$^+$ poor anomalies arise at clump-scales and are caused by lower relative abundances of N$_2$H$^+$ due to the distinct chemistry of H II regions or photodissociation regions.
Despite the simplicity of theoretical models of supersonically turbulent, isothermal media, their predictions successfully match the observed gas structure and star formation activity within low-pressure (P/k < 10^5 K cm^-3) molecular clouds in the s
olar neighbourhood. However, it is unknown if these theories extend to clouds in high-pressure (P/k > 10^7 K cm^-3) environments, like those in the Galaxys inner 200 pc Central Molecular Zone (CMZ) and in the early Universe. Here we present ALMA 3mm dust continuum emission within a cloud, G0.253+0.016, which is immersed in the high-pressure environment of the CMZ. While the log-normal shape and dispersion of its column density PDF is strikingly similar to those of solar neighbourhood clouds, there is one important quantitative difference: its mean column density is 1--2 orders of magnitude higher. Both the similarity and difference in the PDF compared to those derived from solar neighbourhood clouds match predictions of turbulent cloud models given the high-pressure environment of the CMZ. The PDF shows a small deviation from log-normal at high column densities confirming the youth of G0.253+0.016. Its lack of star formation is consistent with the theoretically predicted, environmentally dependent volume density threshold for star formation which is orders of magnitude higher than that derived for solar neighbourhood clouds. Our results provide the first empirical evidence that the current theoretical understanding of molecular cloud structure derived from the solar neighbourhood also holds in high-pressure environments. We therefore suggest that these theories may be applicable to understand star formation in the early Universe.
We derive new all-purpose methods that involve the Dirac Delta distribution. Some of the new methods use derivatives in the argument of the Dirac Delta. We highlight potential avenues for applications to quantum field theory and we also exhibit a con
nection to the problem of blurring/deblurring in signal processing. We find that blurring, which can be thought of as a result of multi-path evolution, is, in Euclidean quantum field theory without spontaneous symmetry breaking, the strong coupling dual of the usual small coupling expansion in terms of the sum over Feynman graphs.
The chemical changes of high-mass star-forming regions provide a potential method for classifying their evolutionary stages and, ultimately, ages. In this study, we search for correlations between molecular abundances and the evolutionary stages of d
ense molecular clumps associated with high-mass star formation. We use the molecular line maps from Year 1 of the Millimetre Astronomy Legacy Team 90 GHz (MALT90) Survey. The survey mapped several hundred individual star-forming clumps chosen from the ATLASGAL survey to span the complete range of evolution, from prestellar to protostellar to H II regions. The evolutionary stage of each clump is classified using the Spitzer GLIMPSE/MIPSGAL mid-IR surveys. Where possible, we determine the dust temperatures and H2 column densities for each clump from Herschel Hi-GAL continuum data. From MALT90 data, we measure the integrated intensities of the N2H+, HCO+, HCN and HNC (1-0) lines, and derive the column densities and abundances of N2H+ and HCO+. The Herschel dust temperatures increase as a function of the IR-based Spitzer evolutionary classification scheme, with the youngest clumps being the coldest, which gives confidence that this classification method provides a reliable way to assign evolutionary stages to clumps. Both N2H+ and HCO+ abundances increase as a function of evolutionary stage, whereas the N2H+ (1-0) to HCO+ (1-0) integrated intensity ratios show no discernable trend. The HCN (1-0) to HNC(1-0) integrated intensity ratios show marginal evidence of an increase as the clumps evolve.
The Open Cluster Chemical Analysis and Mapping (OCCAM) Survey aims to produce a comprehensive, uniform, infrared-based dataset for hundreds of open clusters, and constrain key Galactic dynamical and chemical parameters from this sample. This first co
ntribution from the OCCAM survey presents analysis of 141 members stars in 28 open clusters with high-resolution metallicities derived from a large uniform sample collected as part of the SDSS-III/Apache Point Observatory Galactic Evolution Experiment (APOGEE). This sample includes the first high-resolution metallicity measurements for 22 open clusters. With this largest ever uniformly observed sample of open cluster stars we investigate the Galactic disk gradients of both [M/H] and [alpha/M]. We find basically no gradient across this range in [alpha/M], but [M/H] does show a gradient for R_{GC} < 10 kpc and a significant flattening beyond R_{GC} = 10 kpc. In particular, whereas fitting a single linear trend yields an [M/H] gradient of -0.09 +/- 0.03$ dex/kpc --- similar to previously measure gradients inside 13 kpc --- by independently fitting inside and outside 10 kpc separately we find a significantly steeper gradient near the Sun (7.9 <= R_{GC} <= 10) than previously found (-0.20 +/- 0.08 dex/kpc) and a nearly flat trend beyond 10 kpc (-0.02 +/- 0.09 dex/kpc).
ALMA will revolutionize our understanding of star formation within our galaxy, but before we can use ALMA we need to know where to look. The Millimeter Astronomy Legacy Team 90 GHz (MALT90) Survey is a large international project to map the molecular
line emission of over 2,000 dense clumps in the Galactic plane. MALT90 serves as a pathfinder for ALMA, providing a large public database of dense molecular clumps associated with high-mass star formation. In this proceedings, we describe the survey parameters and share early science highlights from the survey, including (1) a comparison between galactic and extragalactic star formation relations, (2) chemical trends in MALT90 clumps, (3) the distribution of high-mass star formation in the Milky Way, and (4) a discussion of the Brick, the target of successful ALMA Cycle 0 and Cycle 1 proposals.
We describe a pilot survey conducted with the Mopra 22-m radio telescope in preparation for the Millimeter Astronomy Legacy Team Survey at 90 GHz (MALT90). We identified 182 candidate dense molecular clumps using six different selection criteria and
mapped each source simultaneously in 16 different lines near 90 GHz. We present a summary of the data and describe how the results of the pilot survey shaped the design of the larger MALT90 survey. We motivate our selection of target sources for the main survey based on the pilot detection rates and demonstrate the value of mapping in multiple lines simultaneously at high spectral resolution.
By relaxing the conventional assumption of a purely gravitational interaction between dark energy and dark matter, substantial alterations to the growth of cosmological structure can occur. In this work we focus on the homogeneous transfer of energy
from a decaying form of dark energy. We present simple analytic solutions to the modified growth rates of matter fluctuations in these models, and demonstrate that neglecting physics within the dark sector may induce a significant bias in the inferred growth rate, potentially offering a false signature of modified gravity.
