Bias-free Measurement of Giant Molecular Cloud Properties

(abridged) We review methods for measuring the sizes, line widths, and luminosities of giant molecular clouds (GMCs) in molecular-line data cubes with low resolution and sensitivity. We find that moment methods are robust and sensitive -- making full use of both position and intensity information -- and we recommend a standard method to measure the position angle, major and minor axis sizes, line width, and luminosity using moment methods. Without corrections for the effects of beam convolution and sensitivity to GMC properties, the resulting properties may be severely biased. This is particularly true for extragalactic observations, where resolution and sensitivity effects often bias measured values by 40% or more. We correct for finite spatial and spectral resolutions with a simple deconvolution and we correct for sensitivity biases by extrapolating properties of a GMC to those we would expect to measure with perfect sensitivity. The resulting method recovers the properties of a GMC to within 10% over a large range of resolutions and sensitivities, provided the clouds are marginally resolved with a peak signal-to-noise ratio greater than 10. We note that interferometers systematically underestimate cloud properties, particularly the flux from a cloud. The degree of bias depends on the sensitivity of the observations and the (u,v) coverage of the observations. In the Appendix to the paper we present a conservative, new decomposition algorithm for identifying GMCs in molecular-line observations. This algorithm treats the data in physical rather than observational units, does not produce spurious clouds in the presence of noise, and is sensitive to a range of morphologies. As a result, the output of this decomposition should be directly comparable among disparate data sets.Comment: Accepted to PASP (19 pgs., 12 figures). The submission describes an IDL software package available from http://cfa-www.harvard.edu/~erosolow/cprops

Quantum theory of an atom laser originating from a Bose-Einstein condensate or a Fermi gas in the presence of gravity

We present a 3D quantum mechanical theory of radio-frequency outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radio-frequency and for the beam wave function are given. We establish a sum rule for the energy integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and the radiation field. For a non-interacting Bose-Einstein condensate analytic solutions are derived which are subsequently extended to include the effects of atomic interactions. The interactions enhance interference effects in the beam profile and modify the outcoupling rate of the atom laser. We provide a complete quantum mechanical solution which is in line with experimental findings and allows to determine the validity of commonly used approximative methods. We also extend the formalism to a fermionic atom laser and analyze the effect of superfluidity on the outcoupling of atoms.Comment: 13 pages, 8 figures, slightly expanded versio

Derivation of Apollo 14 High-Al Basalts from Distinct Source Regions at Discrete Times: New Constraints

Apollo 14 basalts occur predominantly as clasts in breccias, but represent the oldest volcanic products that were returned from the Moon [1]. These basalts are relatively enriched in Al2O3 (11-16 wt%) compared to other mare basalts (7-11 wt%) and were originally classified into 5 compositional groups [2,3]. Neal et al. [4] proposed that a continuum of compositions existed. These were related through assimilation (of KREEP) and fractional crystallization (AFC). Age data, however, show that at least three volcanic episodes are recorded in the sample collection [1,5,6]. Recent work has demonstrated that there are three, possibly four groups of basalts in the Apollo 14 sample collection that were erupted from different source regions at different times [7]. This conclusion was based upon incompatible trace element (ITE) ratios of elements that should not be fractionated from one another during partial melting (Fig. 1). These groups are defined as Group A (Groups 4 & 5 of [3]), Group B (Groups 1 & 2 of [3]), and Group C (Group 3 of [3]). Basalt 14072 is distinct from Groups A-C

Quantum statistics of interacting dimer spin systems

The compound TlCuCl3 represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Wurtz [Phys. Rev. B 50, 13 515 (1994)] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important

A Catalog of HI Clouds in the Large Magellanic Cloud

A 21 cm neutral hydrogen interferometric survey of the Large Magellanic Cloud (LMC) combined with the Parkes multi-beam HI single-dish survey clearly shows that the HI gas is distributed in the form of clumps or clouds. The HI clouds and clumps have been identified using a thresholding method with three separate brightness temperature thresholds ($T_b$). Each catalog of HI cloud candidates shows a power law relationship between the sizes and the velocity dispersions of the clouds roughly following the Larson Law scaling $\sigma_v \propto R^{0.5}$, with steeper indices associated with dynamically hot regions. The clouds in each catalog have roughly constant virial parameters as a function mass suggesting that that the clouds are all in roughly the same dynamical state, but the values of the virial parameter are significantly larger than unity showing that turbulent motions dominate gravity in these clouds. The mass distribution of the clouds is a power law with differential indices between -1.6 and -2.0 for the three catalogs. In contrast, the distribution of mean surface densities is a log-normal distribution.Comment: 24 pages, 15 figures, ApJS, in pres

Limitations on the smooth confinement of an unstretchable manifold

We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball B_r^d \subset {\mathbb R}^d of radius r < 1/2 unless one of two conditions is met -- (1)The embedding manifold has dimension d >= 2m. (2) The embedding is not smooth. The proof uses differential geometry to show that if d<2m and the embedding is smooth and isometric, we can construct a line from the center of D^m to the boundary that is geodesic in both D^m and in the embedding manifold {\mathbb R}^d. Since such a line has length 1, the diameter of the embedding ball must exceed 1.Comment: 20 Pages, 3 Figure

Molecular line mapping of the giant molecular cloud associated with RCW 106 - II. Column density and dynamical state of the clumps

We present a fully sampled C^{18}O (1-0) map towards the southern giant molecular cloud (GMC) associated with the HII region RCW 106, and use it in combination with previous ^{13}CO (1-0) mapping to estimate the gas column density as a function of position and velocity. We find localized regions of significant ^{13}CO optical depth in the northern part of the cloud, with several of the high-opacity clouds in this region likely associated with a limb-brightened shell around the HII region G333.6-0.2. Optical depth corrections broaden the distribution of column densities in the cloud, yielding a log-normal distribution as predicted by simulations of turbulence. Decomposing the ^{13}CO and C^{18}O data cubes into clumps, we find relatively weak correlations between size and linewidth, and a more sensitive dependence of luminosity on size than would be predicted by a constant average column density. The clump mass spectrum has a slope near -1.7, consistent with previous studies. The most massive clumps appear to have gravitational binding energies well in excess of virial equilibrium; we discuss possible explanations, which include magnetic support and neglect of time-varying surface terms in the virial theorem. Unlike molecular clouds as a whole, the clumps within the RCW 106 GMC, while elongated, appear to show random orientations with respect to the Galactic plane.Comment: 17 pages, to appear in MNRA

Star formation in clusters: a survey of compact mm-wave sources in the Serpens core

We report the results of a millimeter interferometric survey of compact 3 mm continuum sources in the inner 5.5'x5.5' region of the Serpens core. We detect 32 discrete sources above 4.0 mJy/beam, 21 of which are new detections at millimeter wavelengths. By comparing our data with published infrared surveys, we estimate that 26 sources are probably protostellar condensations and derive their mass assuming optically thin thermal emission from dust grains. The mass spectrum of the clumps, dN/dM~M^(-2.1), is consistent with the stellar initial mass function, supporting the idea that the stellar masses in young clusters are determined by the fragmentation of turbulent cloud cores.Comment: To be published on The Astrophysical Journal Letters, 11 pages, 4 figures, aastex macros neede

The effect of magnetic field and disorders on the electronic transport in graphene nanoribbons

We developed a unified mesoscopic transport model for graphene nanoribbons, which combines the non-equilibrium Green's function (NEGF) formalism with the real-space {\pi}-orbital model. Based on this model, we probe the spatial distributions of electrons under a magnetic field, in order to obtain insights into the various signature Hall effects in disordered armchair graphene nanoribbons (AGNR). In the presence of a uniform perpendicular magnetic field (B\perp-field), a perfect AGNR shows three distinct spatial current profiles at equilibrium, depending on its width. Under non-equilibrium conditions (i.e. in the presence of an applied bias), the net electron flow is restricted to the edges and occurs in opposite directions depending on whether the Fermi level lies within the valence or conduction band. For electrons at energy level below the conduction window, the B\perp-field gives rise to local electron flux circulation, although the global flux is zero. Our study also reveals the suppression of electron backscattering as a result of the edge transport which is induced by the B\perp-field. This phenomenon can potentially mitigate the undesired effects of disorders, such as the bulk and edge vacancies, on the transport properties of AGNR. Lastly, we show that the effect of B\perp-field on electronic transport is less significant in the multimode compared to the single mode electron transport.Comment: 21 pages, 4 figure