An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds

We introduce a new method for observationally estimating the fraction of momentum density (${\rho}{\mathbf{v}}$) power contained in solenoidal modes (for which $\nabla \cdot {\rho}{\mathbf{v}} = 0$) in molecular clouds. The method is successfully tested with numerical simulations of supersonic turbulence that produce the full range of possible solenoidal/compressible fractions. At present the method assumes statistical isotropy, and does not account for anisotropies caused by (e.g.) magnetic fields. We also introduce a framework for statistically describing density--velocity correlations in turbulent clouds.Comment: 20 pages, 13 figures, accepted for publication in MNRA

A method for reconstructing the PDF of a 3D turbulent density field from 2D observations

We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by applying it to numerical simulations of hydrodynamic and magnetohydrodynamic turbulence in molecular clouds. To a good approximation, the PDF of log(normalised column density) is a compressed, shifted version of the PDF of log(normalised density). The degree of compression can be determined observationally from the column density power spectrum, under the assumption of statistical isotropy of the turbulence.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter

Turbulent Driving Scales in Molecular Clouds

Supersonic turbulence in molecular clouds is a dominant agent that strongly affects the clouds' evolution and star formation activity. Turbulence may be initiated and maintained by a number of processes, acting at a wide range of physical scales. By examining the dynamical state of molecular clouds, it is possible to assess the primary candidates for how the turbulent energy is injected. The aim of this paper is to constrain the scales at which turbulence is driven in the molecular interstellar medium, by comparing simulated molecular spectral line observations of numerical magnetohydrodynamic (MHD) models and molecular spectral line observations of real molecular clouds. We use principal component analysis, applied to both models and observational data, to extract a quantitative measure of the driving scale of turbulence. We find that only models driven at large scales (comparable to, or exceeding, the size of the cloud) are consistent with observations. This result applies also to clouds with little or no internal star formation activity. Astrophysical processes acting on large scales, including supernova-driven turbulence, magnetorotational instability, or spiral shock forcing, are viable candidates for the generation and maintenance of molecular cloud turbulence. Small scale driving by sources internal to molecular clouds, such as outflows, can be important on small scales, but cannot replicate the observed large-scale velocity fluctuations in the molecular interstellar medium.Comment: 8 pages, 7 figures, accepted for publication in A&

The Density Variance Mach Number Relation in the Taurus Molecular Cloud

Supersonic turbulence in molecular clouds is a key agent in generating density enhancements that may subsequently go on to form stars. The stronger the turbulence - the higher the Mach number - the more extreme the density fluctuations are expected to be. Numerical models predict an increase in density variance with rms Mach number of the form: sigma^{2}_{rho/rho_{0}} = b^{2}M^{2}, where b is a numerically-estimated parameter, and this prediction forms the basis of a large number of analytic models of star formation. We provide an estimate of the parameter b from 13CO J=1-0 spectral line imaging observations and extinction mapping of the Taurus molecular cloud, using a recently developed technique that needs information contained solely in the projected column density field to calculate sigma^{2}_{rho/rho_{0}}. We find b ~ 0.48, which is consistent with typical numerical estimates, and is characteristic of turbulent driving that includes a mixture of solenoidal and compressive modes. More conservatively, we constrain b to lie in the range 0.3-0.8, depending on the influence of sub-resolution structure and the role of diffuse atomic material in the column density budget. We also report a break in the Taurus column density power spectrum at a scale of ~1pc, and find that the break is associated with anisotropy in the power spectrum. The break is observed in both 13CO and dust extinction power spectra, which, remarkably, are effectively identical despite detailed spatial differences between the 13CO and dust extinction maps. [ abridged ]Comment: 8 pages, 9 figures. Accepted for publication in A&

Nonalcoholic fatty liver disease: Pros and cons of histologic systems of evaluation

The diagnostic phenotype of nonalcoholic fatty liver disease (NAFLD)—in particular, the most significant form in terms of prognosis, nonalcoholic steatohepatitis (NASH)—continues to rely on liver tissue evaluation, in spite of remarkable advances in non-invasive algorithms developed from serum-based tests and imaging-based or sonographically-based tests for fibrosis or liver stiffness. The most common tissue evaluation remains percutaneous liver biopsy; considerations given to the needle size and the location of the biopsy have the potential to yield the most representative tissue for evaluation. The pathologist’s efforts are directed to not only global diagnosis, but also assessment of severity of injury. Just as in other forms of chronic liver disease, these assessments can be divided into necroinflammatory activity, and fibrosis with parenchymal remodeling, in order to separately analyze potentially reversible (grade) and non-reversible (stage) lesions. These concepts formed the bases for current methods of evaluating the lesions that collectively comprise the phenotypic spectra of NAFLD. Four extant methods have specific applications; there are pros and cons to each, and this forms the basis of the review

A method for reconstructing the variance of a 3D physical field from 2D observations: Application to turbulence in the ISM

We introduce and test an expression for calculating the variance of a physical field in three dimensions using only information contained in the two-dimensional projection of the field. The method is general but assumes statistical isotropy. To test the method we apply it to numerical simulations of hydrodynamic and magnetohydrodynamic turbulence in molecular clouds, and demonstrate that it can recover the 3D normalised density variance with ~10% accuracy if the assumption of isotropy is valid. We show that the assumption of isotropy breaks down at low sonic Mach number if the turbulence is sub-Alfvenic. Theoretical predictions suggest that the 3D density variance should increase proportionally to the square of the Mach number of the turbulence. Application of our method will allow this prediction to be tested observationally and therefore constrain a large body of analytic models of star formation that rely on it.Comment: 8 pages, 9 figures, accepted for publication in MNRA

CO Abundance Variations in the Orion Molecular Cloud

Infrared stellar photometry from 2MASS and spectral line imaging observations of 12CO and 13CO J = 1-0 line emission from the FCRAO 14m telescope are analysed to assess the variation of the CO abundance with physical conditions throughout the Orion A and Orion B molecular clouds. Three distinct Av regimes are identified in which the ratio between the 13CO column density and visual extinction changes corresponding to the photon dominated envelope, the strongly self-shielded interior, and the cold, dense volumes of the clouds. Within the strongly self-shielded interior of the Orion A cloud, the 13CO abundance varies by 100% with a peak value located near regions of enhanced star formation activity. The effect of CO depletion onto the ice mantles of dust grains is limited to regions with AV > 10 mag and gas temperatures less than 20 K as predicted by chemical models that consider thermal-evaporation to desorb molecules from grain surfaces. Values of the molecular mass of each cloud are independently derived from the distributions of Av and 13CO column densities with a constant 13CO-to-H2 abundance over various extinction ranges. Within the strongly self-shielded interior of the cloud (Av > 3 mag), 13CO provides a reliable tracer of H2 mass with the exception of the cold, dense volumes where depletion is important. However, owing to its reduced abundance, 13CO does not trace the H2 mass that resides in the extended cloud envelope, which comprises 40-50% of the molecular mass of each cloud. The implied CO luminosity to mass ratios, M/L_{CO}, are 3.2 and 2.9 for Orion A and Orion B respectively, which are comparable to the value (2.9), derived from gamma-ray observations of the Orion region. Our results emphasize the need to consider local conditions when applying CO observations to derive H2 column densities.Comment: Accepted for publication in MNRAS. 21 pages, 14 figure