Surface figure measurements of radio telescopes with a shearing interferometer

A new technique for determining the surface figure of large submillimeter wavelength telescopes is presented, which is based on measuring the telescope’s focal plane diffraction pattern with a shearing interferometer. In addition to the instrumental theory, results obtained using such an interferometer on the 10.4-m diam telescope of the Caltech Submillimeter Observatory are discussed. Using wavelengths near 1 mm, a measurement accuracy of 9 µm, or λ/115, has been achieved, and the rms surface accuracy has been determined to be just under 30 µm. The distortions of the primary reflector with changing elevation angle have also been measured and agree well with theoretical predictions of the dish deformation

Excitation of methyl cyanide in the hot core of Orion

The excitation of CH_3CN in the hot core of Orion is examined using high-sensitivity observational data at 1.3 mm. Observed line fluxes are analyzed by means of multilevel statistical equilibrium (SE) calculations which incorporate current theoretical values of the collisional excitation rates. The analysis is applied to both optically thin models of the hot core region and models with significant optical depths. Trapping is found to play a critical role in the excitation of CH_3CN. An optically thin analysis yields a kinetic temperature of 275 K and a cloud density of 2 x 10^6 cm^(-3). Unequal column densities are deduced in this case for the two symmetry species: N_A = 1.4 x 10^(14) cm^(-2) and N_E = 2.0 x 10^(14) cm^(-2). The deduced cloud density and temperature are lowered to 1.5 x 10^6 cm^(-3) and 240 K. The model with trapping is favored because of the agreement with measured sizes of the hot core source and the more plausible N_A/N_E ratio. Analysis of radiative excitation in the hot core indicates it is unlikely to significantly affect the ground vibrational state populations of CH_3CN. It most likely is significant for excitation of the V_8 band

On the Interpretation of the broad-band millimeter-wave flux from Orion

Spectral observations of the core of Orion A at wavelengths around 1.3 mm show a high density of strong, broad emission lines. The combined flux in lines with peak antenna temperatures stronger than 0.2 K accounts for approximately 40 percent of the broad-band millimeter-wave flux from the region. Thus the broad-band flux from Orion A is in large part due to sources other than dust emission

Molecular abundances in OMC-1: The chemical composition of interstellar molecular clouds and the influence of massive star formation

We present here an investigation of the chemical composition of the various regions in the core of the Orion molecular cloud (OMC-1) based on results from the Caltech Owens Valley Radio Observatory (OVRO) millimeter-wave spectral line survey (Sutton et al.; Blake et al.). This survey covered a 55 GHz interval in the 1.3 mm (230 GHz) atmospheric window and contained emission from over 800 resolved spectral features. Of the 29 identified species 14 have a sufficient number of detected transitions to be investigated with an LTE "rotation diagram" technique, in which large numbers of lines are used to estimate both the rotational excitation and the overall abundance. The rotational temperatures and column densities resulting from these fits have then been used to model the emission from those remaining species which either have too few lines or which are too weak to be so analyzed. When different kinematic sources of emission are blended to produce a single feature, Gaussian fits have been used to derive the individual contributions to the total line profile. The uniformly calibrated data in the unique and extensive Caltech spectral line survey lead to accurate estimates of the chemical and physical parameters of the Orion molecular cloud, and place significant constraints on models of interstellar chemistry. A global analysis of the observed abundances shows that the markedly different chemical compositions of the kinematically and spatially distinct Orion subsources may be interpreted in the framework of an evolving, initially quiescent, gas-phase chemistry influenced by the process of massive star formation. The chemical composition of the extended Orion cloud complex is similar to that found in a number of other objects, but the central regions of OMC-1 have had their chemistry selectively altered by the radiation and high-velocity outflow from the young stars embedded deep within the interior of the molecular cloud. Specifically, the extended ridge clouds are inferred to have a low (subsolar) gas-phase oxygen content from the prevalence of reactive carbon-rich species like CN, CCH, and C_3H_2 also found in more truly quiescent objects such as TMC-1. The similar abundances of these and other simple species in clouds like OMC-1, Sgr B2, and TMC-1 lend support to gas-phase ion-molecule models of interstellar chemistry, but grain processes may also play a significant role in maintaining the overall chemical balance in such regions through selective depletion mechanisms and grain mantle processing. In contrast, the chemical compositions of the more turbulent plateau and hot core components of OMC-1 are dominated by high-temperature, shock-induced gas and grain surface neutral-neutral reaction processes. The high silicon/sulfur oxide and water content of the plateau gas is best modeled by fast shock disruption of smaller grain cores to release the more refractory elements followed by a predominantly neutral chemistry in the cooling postshock regions, while a more passive release of grain mantle products driven toward kinetic equilibrium most naturally explains the prominence of fully hydrogenated N-containing species like HCN, NH_3 , CH_3CN, and C_2H_5CN in the hot core. The clumpy nature of the outflow is illustrated by the high-velocity emission observed from easily decomposed molecules such as H_2CO. Areas immediately adjacent to the shocked core in which the cooler, ion-rich gas of the surrounding molecular cloud is mixed with water/oxygen rich gas from the plateau source are proposed to give rise to the enhanced abundances of complex internal rotors such as CH_30H, HCOOCH_3 , and CH_30CH_3 whose line widths are similar to carbon-rich species such as CN and CCH found in the extended ridge, but whose rotational temperatures are somewhat higher and whose spatial extents are much more compact

The rotational emission-line spectrum of Orion A between 247 and 263 GHz

Results are presented from a molecular line survey of the core of the Orion molecular cloud between 247 and 263 GHz. The spectrum contains a total of 243 resolvable lines from 23 different chemical species. When combined with the earlier survey of Orion from 215 to 247 GHz by Sutton et al. (1985), the complete data set includes over 780 emission features from 29 distinct molecules. Of the 23 molecules detected in this survey, only NO, CCH, and HCO^+ were not identified in the lower frequency data. As a result of the supporting laboratory spectroscopy performed to supplement existing millimeter-wave spectral line catalogs, only 33 of the more than 780 lines remain unidentified, of which 16 occur in the upper frequency band. A significant chance remains that a number of these unidentified lines are due to transitions between states of either isotopically substituted or highly excited abundant and complex molecules such as CH_3OH, CH_3OCH_3, and HCOOCH_3, whose rotational spectra are poorly known at present. The very small percentage and weak strength of the unidentified lines implies that the dominant chemical constituents visible at millimeter wavelengths have been identified in the Orion molecular cloud

Examples of derivation-based differential calculi related to noncommutative gauge theories

Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions". To appear in a special issue of International Journal of Geometric Methods in Modern Physic

Courts, care proceedings and outcomes uncertainty: the challenges of achieving and assessing ‘good outcomes’ for children after child protection proceedings

The professed aim of any social welfare or legal intervention in family life is often to bring about ‘better outcomes for the children’. But there is considerable ambiguity about ‘outcomes’, and the term is far too often used in far too simplistic a way. This paper draws on empirical research into the outcomes of care proceedings for a randomly selected sample of 616 children in England and Wales, about half starting proceedings in 2009-10, and the others in 2014-15. The paper considers the challenges of achieving and assessing ‘good outcomes’ for the children. Outcomes are complex and fluid for all children, whatever the court order. One has to assess the progress of the children in the light of their individual needs and in the context of ‘normal’ child development; and in terms of the legal provisions and policy expectations. A core paradox is that some of the most uncertain outcomes are for children who remain with or return to their parents; yet law and policy require that first consideration is given to this option. Greater transparency about the uncertainty of outcomes is a necessary step towards better understanding the risks and potential benefits of care proceedings

A Model for SEP Escape

Magnetic reconnection in the solar atmosphere is believed to be the driver of most solar explosive phenomena. Therefore, the topology of the coronal magnetic field is central to understanding the solar drivers of space weather. Of particular importance to space weather are the impulsive Solar Energetic particles that are associated with some CME/eruptive flare events. Observationally, the magnetic configuration of active regions where solar eruptions originate appears to agree with the standard eruptive flare model. According to this model, particles accelerated at the flare reconnection site should remain trapped in the corona and the ejected plasmoid. However, flare-accelerated particles frequently reach the Earth long before the CME does. We present a model that may account for the injection of energetic particles onto open magnetic flux tubes connecting to the Earth. Our model is based on the well-known 2.5D breakout topology, which has a coronal null point (null line) and a four-flux system. A key new addition, however, is that we include an isothermal solar wind with open-flux regions. Depending on the location of the open flux with respect to the null point, we find that the flare reconnection can consist of two distinct phases. At first, the flare reconnection involves only closed field, but if the eruption occurs close to the open field, we find a second phase involving interchange reconnection between open and closed. We argue that this second reconnection episode is responsible for the injection of flare-accelerated particles into the interplanetary medium. We will report on our recent work toward understanding how flare particles escape to the heliosphere. This work uses high-resolution 2.5D MHD numerical simulations performed with the Adaptively Refined MHD Solver (ARMS)

The Effect of Magnetic Topology on the Escape of Flare Particles

Magnetic reconnection in the solar atmosphere is believed to be the driver of most solar explosive phenomena. Therefore, the topology of the coronal magnetic field is central to understanding the solar drivers of space weather. Of particular importance to space weather are the impulsive Solar Energetic particles that are associated with some CME/eruptive flare events. Observationally, the magnetic configuration of active regions where solar eruptions originate appears to agree with the standard eruptive flare model. According to this model, particles accelerated at the flare reconnection site should remain trapped in the corona and the ejected plasmoid. However, flare-accelerated particles frequently reach the Earth long before the CME does. We present a model that may account for the injection of energetic particles onto open magnetic flux tubes connecting to the Earth. Our model is based on the well-known 2.5D breakout topology, which has a coronal null point (null line) and a four-flux system. A key new addition, however, is that we include an isothermal solar wind with open-flux regions. Depending on the location of the open flux with respect to the null point, we find that the flare reconnection can consist of two distinct phases. At first, the flare reconnection involves only closed field, but if the eruption occurs close to the open field, we find a second phase involving interchange reconnection between open and closed. We argue that this second reconnection episode is responsible for the injection of flare-accelerated particles into the interplanetary medium. We will report on our recent work toward understanding how flare particles escape to the heliosphere. This work uses high-resolution 2.5D MHD numerical simulations performed with the Adaptively Refined MHD Solver (ARMS)

HC3N maps of OMC1

We have made 3.8 sec resolution maps of HC3N (J = 12-11) and 2.7 mm continuum emission in OMC1 using the OVRO mm interferometer. The continuum map, which traces dust column density, shows that the hot core region consists of several clumps, the densest of which lies 3 sec SE of IRc2. HC3N, which traces dense gas, shows the velocity structure in the region. There is no simple pattern of rotation or expansion, nor does the emission resemble a disk centered on IRc2. Since the velocity difference between the hot core and IRc2 and the velocity dispersion in the hot core are comparable with the orbital velocity at a distance of 3 sec. from a 20 M(solar) object, it is possible that the hot core material is bound to IRc2. In the channel at 10.4 km s(-1) V(LSR), we detect strong emission from the source 20 sec NE of IRc2, which confirms indications from continuum and CS (J = 2-1) maps that this is a very dense, possibly protostellar, object. This emission is clearly resolved from the hot core and is elongated north-south, along the direction of the ridge emission. An additional interesting feature in these maps is a compact high velocity source located 4 sec SW of IRc2. This source has a velocity dispersion greather than 20 km/s (FWHM) and is spatially coincident with the zero-offset source seen by Pauls et al. (1983) and a point source in the near IR images taken by Allen et al. (1984). The large localized velocity, dispersion and the highly obscured IR source suggest that this compact source is an outflow from a young stellar companion to IRc2