Context. The ubiquitous presence of filamentary structures in the interstellar medium asks for an unbiased characterization of their properties including a stability analysis. Aims. We propose a ...novel technique to measure the spectrum of filaments in any two-dimensional data set. By comparing the power in isotropic and anisotropic structures we can measure the relative importance of spherical and cylindrical collapse modes. Methods. Using anisotropic wavelets we can quantify and distinguish local and global anisotropies and measure the size distribution of filaments. The wavelet analysis does not require any assumptions on the alignment or shape of filaments in the maps, but directly measures their typical spatial dimensions. In a rigorous test program, we calibrate the scale dependence of the method and test the angular and spatial sensitivity. We apply the method to molecular line maps from magneto-hydrodynamic (MHD) simulations and observed column-density maps from Herschel observations. Results. When applying the anisotropic wavelet analysis to the MHD data, we find that the observed filament sizes depend on the combination of magnetic-field-dominated density–velocity correlations and radiative transfer effects. This can be exploited by observing tracers with different optical depth to measure the transition from a globally ordered large-scale structure to small-scale filaments with entangled field lines. The unbiased view to Herschel column-density maps does not confirm a universal characteristic filament width. The map of the Polaris Flare shows an almost scale-free filamentary spectrum up to the size of the dominating filament of about 0.4 pc. For the Aquila molecular cloud the range of filament widths is limited to 0.05–0.2 pc. The filaments in Polaris show no preferential direction in contrast to the global alignment that we trace in Aquila. Conclusions. By comparing the power in isotropic and anisotropic structures we can measure the relative importance of spherical and cylindrical collapse modes and their spatial distribution.
Aims. We observationally investigate the relation between the photoelectric heating efficiency in photodissociation regions (PDRs) and the charge of polycyclic aromatic hydrocarbons (PAHs), which are ...considered to play a key role in photoelectric heating. Methods. Using PACS onboard Herschel, we observed six PDRs spanning a wide range of far-ultraviolet radiation fields (G0 = 100−105). To measure the photoelectric heating efficiency, we obtained the intensities of the main cooling lines in these PDRs, i.e., the O i 63 μm, 145 μm, and C ii 158 μm, as well as the far-infrared (FIR) continuum intensity. We used Spitzer/IRS spectroscopic mapping observations to investigate the mid-infrared (MIR; 5.5−14 μm) PAH features in the same regions. We decomposed the MIR PAH emission into that of neutral (PAH0) and positively ionized (PAH+) species to derive the fraction of the positively charged PAHs in each region, and compare it to the photoelectric heating efficiency. Results. The heating efficiency traced by (O i 63 μm + O i 145 μm + C ii 158 μm)/TIR, where TIR is the total infrared flux, ranges between 0.1% and 0.9% in different sources, and the fraction of PAH+ relative to (PAH0+ PAH+) spans from 0 (+11)% to 87 (±10)%. All positions with a high PAH+ fraction show a low heating efficiency, and all positions with a high heating efficiency have a low PAH+ fraction, supporting the scenario in which a positive grain charge results in a decreased heating efficiency. Theoretical estimates of the photoelectric heating efficiency show a stronger dependence on the charging parameter γ = G0T1/2/ne than the observed efficiency reported in this study, and the discrepancy is significant at low γ. The photoelectric heating efficiency on PAHs, traced by (O i 63 μm + O i 145 μm + C ii 158 μm)/(PAH-band emission + O i 63 μm + O i 145 μm + C ii 158 μm), shows a much better match between the observations and the theoretical estimates. Conclusions. The good agreement of the photoelectric heating efficiency on PAHs with a theoretical model indicates the dominant contribution of PAHs to the photoelectric heating. This study demonstrates the fundamental role that PAHs have in photoelectric heating. More studies of their charging behavior are crucial to understand the thermal balance of the interstellar medium.
We upgraded the chemical network from the UMIST Database for Astrochemistry 2006 to include isotopes such as 13C and 18O. 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, 13CO, and H13CO+ provide individual diagnostics to the fractionation status of C+, C, and CO.
The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic (MHD) turbulence in the interstellar medium. Lazarian & Pogosyan 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 for testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfvenic Mach numbers, which include radiative transfer effects of the super(13)CO transition. We numerically confirm the predictions of Lazarian & Pogosyan 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 the order of unity, shows mixed behavior: for super-Alfvenic 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-Alfvenic turbulence the spectral slopes are steeper with values near -3 which are similar to the very optically thick regime.
Context. Chemical fractionation reactions in the interstellar medium can result in molecular isotopologue abundance ratios that differ by many orders of magnitude from the isotopic abundance ratios. ...Understanding variations in the molecular abundance ratios through astronomical observations provides a new toolto sensitively probe the underlying physical conditions. Aims. Recently, we have introduced detailed isotopic chemistry into the KOSMA-τ model for photon-dominated regions (PDRs), which allows calculating abundances of carbon isotopologues as a function of PDR parameters. Radiative transfer computations then allow to predict the observed C ii/13C ii line intensity ratio for specific geometries. Here, we compare these model predictions with new Herschel observations. Methods. We performed Herschel/HIFI observations of the C ii 158 μm line in a number of PDRs. In all sources, we observed at least two hyperfine components of the 13C ii transition, allowing determination of the C ii/13C ii intensity ratio, using revised intrinsic hyperfine ratios. Comparing the observed line ratios with the predictions from the updated KOSMA-τ model, we identify conditions under which the chemical fractionation effects are important, and not masked by the high optical depth of the main isotopic line. Results. An observable enhancement of the C ii/13C ii intensity ratio due to chemical fractionation depends mostly on the source geometry and velocity structure,and to a lesser extent on the gas density and radiation field strength. The enhancement is expected to be largest for PDR layers that are somewhat shielded from UV radiation, but not completely hidden behind a surface layer of optically thick C ii. In our observations the C ii/13C ii integrated line intensity ratio is always dominated by the optical depth of the main isotopic line. However, an enhanced intensity ratio isfound for particular velocity components in several sources: in the red-shifted material in the ultracompact H ii region Mon R2, in the wings of the turbulent line profile in the Orion Bar, and possibly in the blue wing in NGC 7023. Mapping of the 13C ii lines in the Orion Bar gives a C+ column density map, which confirms the temperature stratification of the C+ layer, in agreement with the PDR models of this region. Conclusions. Carbon fractionation can be significant even in relatively warm PDRs, but a resulting enhanced C ii/13C ii intensity ratio is only observable for special configurations. In most cases, a reduced C ii/13C ii intensity ratiocan be used instead to derive the C ii optical depth, leading to reliable column density estimates that can be compared with PDR model predictions. The C+ column densities show that, for all sources, at the position of the C ii peak emission, the dominant fraction of the gas-phase carbon is in the form of C+.
Context. In bright photodissociation regions (PDR) associated with massive star formation, the presence of dense “clumps” that are immersed in a less dense interclump medium is often proposed to ...explain the difficulty of models to account for the observed gas emission in high-excitation lines. Aims. We aim to present a comprehensive view of the modelling of the CO rotational ladder in PDRs, including the high-J lines that trace warm molecular gas at PDR interfaces. Methods. We observed the 12CO and 13CO ladders in two prototypical PDRs, the Orion Bar and NGC 7023 NW using the instruments onboard Herschel. We also considered line emission from key species in the gas cooling of PDRs (C+, O, and H2) and other tracers of PDR edges such as OH and CH+. All the intensities are collected from Herschel observations, the literature and the Spitzer archive and were analysed using the Meudon PDR code. Results. A grid of models was run to explore the parameter space of only two parameters: thermal gas pressure and a global scaling factor that corrects for approximations in the assumed geometry. We conclude that the emission in the high-J CO lines, which were observed up to Jup = 23 in the Orion Bar (Jup = 19 in NGC 7023), can only originate from small structures with typical thicknesses of a few 10−3 pc and at high thermal pressures (Pth ~ 108 K cm−3). Conclusions. Compiling data from the literature, we find that the gas thermal pressure increases with the intensity of the UV radiation field given by G0, following a trend in line with recent simulations of the photoevaporation of illuminated edges of molecular clouds. This relation can help to rationalise the analysis of high-J CO emission in massive star formation and provides an observational constraint for models which study stellar feedback on molecular clouds.
We report the novel detection of complex high column density tails in the probability distribution functions (PDFs) for three high-mass star-forming regions (CepOB3, MonR2, NGC 6334), obtained from ...dust emission observed with Herschel. The low column density range can be fitted with a lognormal distribution. A first power-law tail starts above an extinction (A
V) of ∼6–14. It has a slope of α = 1.3–2 for the ρ ∝ r
−α profile for an equivalent density distribution (spherical or cylindrical geometry), and is thus consistent with free-fall gravitational collapse. Above A
V ∼40, 60, and 140, we detect an excess that can be fitted by a flatter power-law tail with α > 2. It correlates with the central regions of the cloud (ridges/hubs) of size ∼1 pc and densities above 104 cm−3. This excess may be caused by physical processes that slow down collapse and reduce the flow of mass towards higher densities. Possible are: (1) rotation, which introduces an angular momentum barrier, (2) increasing optical depth and weaker cooling, (3) magnetic fields, (4) geometrical effects, and (5) protostellar feedback. The excess/second power-law tail is closely linked to high-mass star-formation though it does not imply a universal column density threshold for the formation of (high-mass) stars.
ABSTRACT
The paper aims to study relation between the distributions of the young stellar objects (YSOs) of different ages and the gas-dust constituents of the S254–S258 star formation complex. This ...is necessary to study the time evolution of the YSO distribution with respect to the gas and dust compounds that are responsible for the birth of the young stars. For this purpose, we use correlation analysis between different gas, dust, and YSO tracers. We compared the large-scale CO, HCO+, near-IR extinction, and far-IR Herschel maps with the density of YSOs of the different evolutionary classes. The direct correlation analysis between these maps was used together with the wavelet-based spatial correlation analysis. This analysis reveals a much tighter correlation of the gas-dust tracers with the distribution of class I YSOs than with that of class II YSOs. We argue that class I YSOs that were initially born in the central bright cluster S255-IR (both N and S parts) during their evolution to class II stage (∼2 Myr) had enough time to travel through the whole S254–S258 star formation region. Given that the region contains several isolated YSO clusters, the evolutionary link between these clusters and the bright central S255-IR (N and S) cluster can be considered. Despite the complexity of the YSO cluster formation in the non-uniform medium, the clusters of class II YSOs in the S254-258 star formation region can contain objects born in the different locations of the complex.
Context.The Allan variance is a standard technique to characterise the stability of spectroscopic instruments used in astronomical observations. The period for switching between source and reference ...measurement is often derived from the Allan minimum time. However, various methods are applied to compute the Allan variance spectrum and to use its characteristics in the setup of astronomical observations. Aims. We propose a new approach for the computation of the Allan variance of spectrometer data combining the advantages of the two existing methods into a unified scheme. Using the Allan variance spectrum we derive the optimum strategy for symmetric observing schemes minimising the total uncertainty of the data resulting from radiometric and drift noise. Methods.The unified Allan variance computation scheme is designed to trace total-power and spectroscopic fluctuations within the same framework. The method includes an explicit error estimate both for the individual Allan variance spectra and for the derived stability time. A new definition of the instrument stability time allows to characterise the instrument even in the case of a fluctuation spectrum shallower than $1/f$, as measured for the total power fluctuations in high-electron-mobility transistors. Results. A first analysis of test measurements for the HIFI instrument shows that gain fluctuations represent the main cause of instrumental instabilities leading to large differences between the stability times relevant for measurements aiming at an accurate determination of the continuum level and for purely spectroscopic measurements. Fast switching loops are needed for a reliable determination of the continuum level, while most spectroscopic measurements can be set up in such a way that baseline residuals due to spectroscopic drifts are at a lower level than the radiometric noise. We find a non-linear impact of the binning of spectrometer channels on the resulting noise and the Allan time deviating from the description in existing theoretical treatments.
Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud- and star-formation (SF) studies. With the Herschel satellite it is now possible to ...precisely determine the column density from dust emission, which is the best tracer of the bulk of material in molecular clouds. However, line-of-sight (LOS) contamination from fore- or background clouds can lead to overestimating the dust emission of molecular clouds, in particular for distant clouds. This implies values that are too high for column density and mass, which can potentially lead to an incorrect physical interpretation of the column density probability distribution function (PDF). In this paper, we use observations and simulations to demonstrate how LOS contamination affects the PDF. At higher column densities, collapse and external pressure can form the power-law tail. The relative importance of the twoprocesses can vary between clouds and thus lead to the observed differences in PDF and column density structure.
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