Carbon Fractionation in PDRs

We upgraded the chemical network from the UMIST Database for Astrochemistry 2006 to include isotopes such as ^{13}C and ^{18}O. This includes all corresponding isotopologues, their chemical reactions and the properly scaled reaction rate coefficients. We study the fractionation behavior of astrochemically relevant species over a wide range of model parameters, relevant for modelling of photo-dissociation regions (PDRs). We separately analyze the fractionation of the local abundances, fractionation of the total column densities, and fractionation visible in the emission line ratios. We find that strong C^+ fractionation is possible in cool C^+ gas. Optical thickness as well as excitation effects produce intensity ratios between 40 and 400. The fractionation of CO in PDRs is significantly different from the diffuse interstellar medium. PDR model results never show a fractionation ratio of the CO column density larger than the elemental ratio. Isotope-selective photo-dissociation is always dominated by the isotope-selective chemistry in dense PDR gas. The fractionation of C, CH, CH^+, and HCO^+ is studied in detail, showing that the fractionation of C, CH and CH^+ is dominated by the fractionation of their parental species. The light hydrides chemically derive from C^+, and, consequently, their fractionation state is coupled to that of C^+. The fractionation of C is a mixed case depending on whether formation from CO or HCO^+ dominates. Ratios of the emission lines of [C II], [C I], ^{13}CO, and H^{13}CO^+ provide individual diagnostics to the fractionation status of C^+, C, and CO.Comment: to be published in A&

Wavelet-based cross-correlation analysis of structure scaling in turbulent clouds

We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well defined spatial properties, we calibrate the method and test its limitations to ultimately apply it to a set of observed maps. We develop the wavelet-based weighted cross-correlation (WWCC) method to study the relative contribution of structures of different sizes and their degree of correlation in two maps as a function of spatial scale, and the mutual displacement of structures in the molecular cloud maps. We test the WWCC for circular structures having a single prominent scale and fractal structures showing a self-similar behavior without prominent scales. Observational noise and a finite map size limit the scales where the cross-correlation coefficients and displacement vectors can be reliably measured. For fractal maps containing many structures on all scales, the limitation from the observational noise is negligible for signal-to-noise ratios >5. (abbrev). Application of the WWCC to the observed line maps of the giant molecular cloud G333 allows to add specific scale information to the results obtained earlier using the principle component analysis. It confirms the chemical and excitation similarity of $^{13}$CO and C$^{18}$O on all scales, but shows a deviation of HCN at scales of up to 7' (~7 pc). This can be interpreted as a chemical transition scale. The largest structures also show a systematic offset along the filament, probably due to a large-scale density gradient. The WWCC can compare correlated structures in different maps of molecular clouds identifying scales that represent structural changes such as chemical and phase transitions and prominent or enhanced dimensions.Comment: 26 pages, 41 figures, accepted to A&

Turbulent Velocity Structure in Molecular Clouds

We compare velocity structure in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We use several different statistical methods to compare models and observations. The Delta-variance wavelet transform is most sensitive to characteristic scales and scaling laws, but is limited by a lack of intensity weighting. The scanning-beam size-linewidth relation is more robust with respect to noisy data. Obtaining the global velocity scaling behaviour requires that large-scale trends in the maps not be removed but treated as part of the turbulent cascade. We compare the true velocity PDF in our models to velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better unless the map size is comparable to the total line-of-sight thickness of the cloud. Comparison of line profiles to velocity centroid PDFs can thus be used to measure the line-of-sight depth of a cloud. The observed density and velocity structure is consistent with supersonic turbulence with a driving scale at or above the size of the molecular cloud and dissipative processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. The velocity PDFs exclude small-scale driving such as that from stellar outflows as a dominant process in the observed region. In the models, large-scale driving is the only process that produces deviations from a Gaussian PDF shape consistent with observations. Strong magnetic fields impose a clear anisotropy on the velocity field, reducing the velocity variance in directions perpendicular to the field. (abridged)Comment: 21 pages, 24 figures, accepted by A&A, with some modifications, including change of claimed direct detection of dissipation scale to an upper limi

The Turbulence Power Spectrum in Optically Thick Interstellar Clouds

The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic turbulence in the interstellar medium. Lazarian & Pogosyan (2004) predicted that the spectral slope should saturate to -3 for an optically thick medium and many observations exist in support of their prediction. However, there have not been any numerical studies to-date testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfv\'enic Mach numbers, which include radiative transfer effects of the $^{13}$CO transition. We confirm numerically the predictions of Lazarian & Pogosyan (2004) that the spectral slope of line intensity maps of an optically thick medium saturates to -3. Furthermore, for very optically thin supersonic CO gas, where the density or CO abundance values are too low to excite emission in all but the densest shock compressed gas, we find that the spectral slope is shallower than expected from the column density. Finally, we find that mixed optically thin/thick CO gas, which has average optical depths on order of unity, shows mixed behavior: for super-Alfv\'enic turbulence, the integrated intensity power spectral slopes generally follow the same trend with sonic Mach number as the true column density power spectrum slopes. However, for sub-Alfv\'enic turbulence the spectral slopes are steeper with values near -3 which are similar to the very optically thick regime.Comment: accepted to Ap

Modelling clumpy PDRs in 3D - Understanding the Orion Bar stratification

Context. Models of photon-dominated regions (PDRs) still fail to fully reproduce some of the observed properties, in particular the combination of the intensities of different PDR cooling lines together with the chemical stratification, as observed e.g. for the Orion Bar PDR. Aims. We aim to construct a numerical PDR model, KOSMA-\tau 3D, to simulate full spectral cubes of line emission from arbitrary PDRs in three dimensions (3D). The model is to reproduce the intensity of the main cooling lines from the Orion Bar PDR and the observed layered structure of the different transitions. Methods. We build up a 3D compound, made of voxels ("3D pixels") that contain a discrete mass distribution of spherical "clumpy" structures, approximating the fractal ISM. To analyse each individual clump the new code is combined with the KOSMA-\tau PDR model. Probabilistic algorithms are used to calculate the local FUV flux for each voxel as well as the voxel-averaged line emissivities and optical depths, based on the properties of the individual clumps. Finally, the computation of the radiative transfer through the compound provides full spectral cubes. To test the new model we try to simulate the structure of the Orion Bar PDR and compare the results to observations from HIFI/Herschel and from the Caltech Submillimetre Observatory (CSO). In this context new Herschel data from the HEXOS guaranteed-time key program is presented. Results. Our model is able to reproduce the line integrated intensities within a factor 2.5 and the observed stratification pattern within 0.016 pc for the [Cii] 158 \mu m and different 12/13 CO and HCO+ transitions, based on the representation of the Orion Bar PDR by a clumpy edge-on cavity wall. In the cavity wall, a large fraction of the total mass needs to be contained in clumps. The mass of the interclump medium is constrained by the FUV penetration. Furthermore, ...Comment: Major changes compared to v1. Also several references have been adde

Structure analysis of interstellar clouds: I. Improving the Delta-variance method

The Delta-variance analysis, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. The implementation presently in use, however, has several shortcomings. We propose and test an improved Delta-variance algorithm for two-dimensional data sets, which is applicable to maps with variable error bars and which can be quickly computed in Fourier space. We calibrate the spatial resolution of the Delta-variance spectra. The new Delta-variance algorithm is based on an appropriate filtering of the data in Fourier space. It allows us to distinguish the influence of variable noise from the actual small-scale structure in the maps and it helps for dealing with the boundary problem in non-periodic and/or irregularly bounded maps. We try several wavelets and test their spatial sensitivity using artificial maps with well known structure sizes. It turns out that different wavelets show different strengths with respect to detecting characteristic structures and spectral indices, i.e. different aspects of map structures. As a reasonable universal compromise for the optimum Delta-variance filter, we propose the Mexican-hat filter with a ratio between the diameters of the core and the annulus of 1.5.Comment: Accepted for publication in A&A, Sect. 1

A Tidally-Disrupted Asteroid Around the White Dwarf G29-38

The infrared excess around the white dwarf G29-38 can be explained by emission from an opaque flat ring of dust with an inner radius 0.14 of the radius of the Sun and an outer radius approximately equal to the Sun's. This ring lies within the Roche region of the white dwarf where an asteroid could have been tidally destroyed, producing a system reminiscent of Saturn's rings. Accretion onto the white dwarf from this circumstellar dust can explain the observed calcium abundance in the atmosphere of G29-38. Either as a bombardment by a series of asteroids or because of one large disruption, the total amount of matter accreted onto the white dwarf may have been comparable to the total mass of asteroids in the Solar System, or, equivalently, about 1% of the mass in the asteroid belt around the main sequence star zeta Lep.Comment: ApJ Letters, in pres

Calculating Cross Sections of Composite Interstellar Grains

Interstellar grains may be composite collections of particles of distinct materials, including voids, agglomerated together. We determine the various optical cross sections of such composite grains, given the optical properties of each constituent, using an approximate model of the composite grain. We assume it consists of many concentric spherical layers of the various materials, each with a specified volume fraction. In such a case the usual Mie theory can be generalized and the extinction, scattering, and other cross sections determined exactly. We find that the ordering of the materials in the layering makes some difference to the derived cross sections, but averaging over the various permutations of the order of the materials provides rapid convergence as the number of shells (each of which is filled by all of the materials proportionately to their volume fractions) is increased. Three shells, each with one layer of a particular constituent material, give a very satisfactory estimate of the average cross section produced by larger numbers of shells. We give the formulae for the Rayleigh limit (small size parameter) for multi-layered spheres and use it to propose an ``Effective Medium Theory'' (EMT), in which an average optical constant is taken to represent the ensemble of materials. Multi-layered models are used to compare the accuracies of several EMTs already in the literature.Comment: 29 pages, 6 figures, accepted for publication in the Astrophysical Journal (part 1, scheduled in Vol. 526, #1, Nov. 20

The Structure of Molecular Clouds: III - A link between cloud structure and star formation mode

We analyse extinction maps of nearby Giant Molecular Clouds to forge a link between driving processes of turbulence and modes of star formation. Our investigation focuses on cloud structure in the column density range above the self shielding threshold of 1mag Av and below the star formation threshold -- the regime in which turbulence is expected to dominate. We identify clouds with shallow mass distributions as cluster forming. Clouds that form stars in a less clustered or isolated mode show a steeper mass distribution. Structure functions prove inadequate to distinguish between clouds of different star formation mode. They may, however, suggest that the turbulence in the average cloud is governed by solenoidal forcing. The same is found using the Delta-variance analysis which also indicates that clouds with a clustered mode of star formation show an enhanced component of compressive driving in the turbulent field. Thus, while star formation occurs in each cloud, independent of the turbulent driving mechanism, compressive forcing appears to be associated with the formation of stellar clusters.Comment: 10 pages, 3 figures, 2 tables, accepted for publication by MNRAS, a version with higher resolution figures can be found at http://astro.kent.ac.uk/~df