Template matching method for the analysis of interstellar cloud structure

The structure of interstellar medium can be characterised at large scales in terms of its global statistics (e.g. power spectra) and at small scales by the properties of individual cores. Interest has been increasing in structures at intermediate scales, resulting in a number of methods being developed for the analysis of filamentary structures. We describe the application of the generic template-matching (TM) method to the analysis of maps. Our aim is to show that it provides a fast and still relatively robust way to identify elongated structures or other image features. We present the implementation of a TM algorithm for map analysis. The results are compared against rolling Hough transform (RHT), one of the methods previously used to identify filamentary structures. We illustrate the method by applying it to Herschel surface brightness data. The performance of the TM method is found to be comparable to that of RHT but TM appears to be more robust regarding the input parameters, for example, those related to the selected spatial scales. Small modifications of TM enable one to target structures at different size and intensity levels. In addition to elongated features, we demonstrate the possibility of using TM to also identify other types of structures. The TM method is a viable tool for data quality control, exploratory data analysis, and even quantitative analysis of structures in image data.Comment: 12 pages, accepted to A&

The degeneracy between the dust colour temperature and the spectral index. The problem of multiple chi^2 minima

Because of the Herschel and Planck satellite missions, there is strong interest in the interpretation the sub-millimetre dust spectra from interstellar clouds. Much work has been done to understand the dependence between the spectral index beta_Obs and the colour temperature T_C that is partly caused by the noise. The (T_C, beta_Obs) confidence regions are elongated, banana-shaped structures. We studied under which conditions these exhibit anomalous, strongly non-Gaussian behaviour that could affect the interpretation of the observed (T_C, beta_Obs) relations. We examined modified black body spectra and spectra calculated from radiative transfer models of filamentary clouds at wavelengths 100um-850um. We performed modified black body fits and examined the structure of the chi^2(T_, beta_Obs) function. We show cases where, when the signal-to-noise ratio is low, the chi^2 has multiple local minima in the (T_C, beta_Obs) plane. A small change in the weighting of the data points can cause the solution to jump to completely different values. In particular, noise can lead to the appearance of a separate population of solutions with low colour temperatures and high spectral indices. The anomalies are caused by the noise but the tendency to show multiple chi^2 minima depends on the model and the wavelengths analysed. Deviations from the assumed single modified black body spectrum are not important. The presence of local minima implies that the results obtained from the chi^2 minimisation depend on the starting point of the optimisation and may correspond to non-global minima. The (T_C,beta_Obs) distributions may be contaminated by a few solutions with unrealistically low colour temperatures and high spectral indices. Proper weighting must be applied to avoid the determination of the beta_Obs(T_C) relation to be unduly affected by these measurements.Comment: 11 pages, accepted to A&

Estimation of high-resolution dust column density maps: Empirical model fits

Sub-millimetre dust emission is an important tracer of density N of dense interstellar clouds. One has to combine surface brightness information at different spatial resolutions, and specific methods are needed to derive N at a resolution higher than the lowest resolution of the observations. Some methods have been discussed in the literature, including a method (in the following, method B) that constructs the N estimate in stages, where the smallest spatial scales being derived only use the shortest wavelength maps. We propose simple model fitting as a flexible way to estimate high-resolution column density maps. Our goal is to evaluate the accuracy of this procedure and to determine whether it is a viable alternative for making these maps. The new method consists of model maps of column density (or intensity at a reference wavelength) and colour temperature. The model is fitted using Markov chain Monte Carlo (MCMC) methods, comparing model predictions with observations at their native resolution. We analyse simulated surface brightness maps and compare its accuracy with method B and the results that would be obtained using high-resolution observations without noise. The new method is able to produce reliable column density estimates at a resolution significantly higher than the lowest resolution of the input maps. Compared to method B, it is relatively resilient against the effects of noise. The method is computationally more demanding, but is feasible even in the analysis of large Herschel maps. The proposed empirical modelling method E is demonstrated to be a good alternative for calculating high-resolution column density maps, even with considerable super-resolution. Both methods E and B include the potential for further improvements, e.g., in the form of better a priori constraints.Comment: Accepted to A&

On the stability of non-isothermal Bonnor-Ebert spheres. II. The effect of gas temperature on the stability

Aims. We investigate the stability of non-isothermal Bonnor-Ebert spheres with a model that includes a self-consistent calculation of the gas temperature. This way we can discard the assumption of equality between the dust and gas temperatures, and study the stability as the gas temperature changes with chemical evolution of the gas. Methods. We use a gas-grain chemical model including a time-dependent treatment of depletion onto grain surfaces, which strongly influences the gas temperature as the main coolant, CO, depletes from the gas. Dust and gas temperatures are solved with radiative transfer. For comparison with previous work, we assume that the cores are deeply embedded in a larger external structure, corresponding to visual extinction $A_{\rm V}^{\rm ext}=10$ mag. Results. We find that the critical non-dimensional radius $\xi_1$ derived here is similar to our previous work where we assumed $T_{\rm dust}=T_{\rm gas}$; the $\xi_1$ values lie below the isothermal critical value $\xi_0\sim6.45$, but the difference is less than 10%. Chemical evolution does not affect notably the stability condition of low-mass cores (<0.75 $M_\odot$). For higher masses the decrease of cooling owing to CO depletion causes substantial temporal changes in the temperature and density profiles of the cores. In the mass range 1-2 $M_\odot$ , $\xi_1$ decreases with chemical evolution, whereas above 3 $M_\odot$ , $\xi_1$ instead increases. We also find that decreasing $A_{\rm V}^{\rm ext}$ increases the gas temperature especially when the gas is chemically old, causing $\xi_1$ to increase with respect to models with higher $A_{\rm V}^{\rm ext}$. The derived $\xi_1$ values are close to $\xi_0$. The density contrast between the core center and edge varies between 8 to 16 depending on core mass and the chemical age of the gas, compared to the constant value $\sim$ 14.1 for the isothermal BES.Comment: 7 pages, 5 figures; accepted for publication in A&A; abstract (heavily) abridged for arXi

A Corona Australis cloud filament seen in NIR scattered light II: Comparison with sub-millimeter data

We study a northern part of the Corona Australis molecular cloud that consists of a filament and a dense sub-millimetre core inside the filament. Our aim is to measure dust temperature and sub-mm emissivity within the region. We also look for confirmation that near-infrared (NIR) surface brightness can be used to study the structure of even very dense clouds. We extend our previous NIR mapping south of the filament. The dust colour temperatures are estimated using Spitzer 160um and APEX/Laboca 870um maps. The column densities derived based on the reddening of background stars, NIR surface brightness, and thermal sub-mm dust emission are compared. A three dimensional toy model of the filament is used to study the effect of anisotropic illumination on near-infrared surface brightness and the reliability of dust temperature determination. Relative to visual extinction, the estimated emissivity at 870um is kappa(870) = (1.3 +- 0.4) x 10^{-5} 1/mag. This is similar to the values found in diffuse medium. A significant increase in the sub-millimetre emissivity seems to be excluded. In spite of saturation, NIR surface brightness was able to accurately pinpoint, and better than measurements of the colour excesses of background stars, the exact location of the column density maximum. Both near- and far-infrared data show that the intensity of the radiation field is higher south of the filament.Comment: 9 pages, 9 figures, accepted to A&

On the stability of nonisothermal Bonnor-Ebert spheres. III. The role of chemistry in core stabilization

Aims. We investigate the effect of chemistry on the stability of starless cores against gravitational collapse. Methods. We combine chemical and radiative transfer simulations in the context of a modified Bonnor-Ebert sphere to model the effect of chemistry on the gas temperature, and study the effect of temperature changes on core stability. Results. We find that chemistry has in general very little effect on the nondimensional radius $\xi_{\rm out}$ which parametrizes the core stability. Cores that are initially stable or unstable tend to stay near their initial states, in terms of stability (i.e., $\xi_{\rm out} \sim$ constant), as the chemistry develops. This result is independent of the initial conditions. We can however find solutions where $\xi_{\rm out}$ decreases at late times ($t \gtrsim 10^6 \, \rm yr$) which correspond to increased stabilization caused by the chemistry. Even though the core stability is unchanged by the chemistry in most of the models considered here, we cannot rule out the possibility that a core can evolve from an unstable to a stable state owing to chemical evolution. The reverse case, where an initially stable core becomes ultimately unstable, seems highly unlikely. Conclusions. Our results indicate that chemistry should be properly accounted for in studies of star-forming regions, and that further investigations of core stability especially with hydrodynamical models are warranted.Comment: 8 pages, 10 figures; accepted for publication in A&

Estimation of high-resolution dust column density maps. Comparison of modified black-body fits and radiative transfer modelling

Sub-millimetre dust emission is often used to derive the column density N of dense interstellar clouds. The observations consist of data at several wavelengths but of variable resolution. We examine two procedures that been proposed for the estimation of high resolution N maps. Method A uses a low-resolution temperature map combined with higher resolution intensity data while Method B combines N estimates from different wavelength ranges. Our aim is to determine the accuracy of the methods relative to the true column densities and the estimates obtainable with radiative transfer modelling. We use magnetohydrodynamical (MHD) simulations and radiative transfer calculations to simulate sub-millimetre observations at the wavelengths of the Herschel Space Observatory. The observations are analysed with the methods and the results compared to the true values and to the results from radiative transfer modelling of observations. Both methods A and B give relatively reliable column density estimates at the resolution of 250um data while also making use of the longer wavelengths. For high signal-to-noise data, the results of Method B are better correlated with the true column density, while Method A is less sensitive to noise. When the cloud has internal heating, results of Method B are consistent with those that would be obtained with high-resolution data. Because of line-of-sight temperature variations, these underestimate the true column density and, because of a favourable cancellation of errors, Method A can sometimes give more correct values. Radiative transfer modelling, even with very simple 3D cloud models, can provide better results. However, the complexity of the models required for improvements increases rapidly with the complexity and opacity of the clouds.Comment: 14 pages, Accepted to A&

Profiles of interstellar cloud filaments. Observational effects in synthetic sub-millimetre observations

Sub-millimetre observations suggest that the filaments of interstellar clouds have rather uniform widths and can be described with the so-called Plummer profiles. The shapes of the filament profiles are linked to their physical state. Before drawing conclusions on the observed column density profiles, we must evaluate the observational uncertainties. We want to estimate the bias that could result from radiative transfer effects or from variations of submm dust emissivity. We use cloud models obtained with magnetohydrodynamic simulations and carry out radiative transfer calculations to produce maps of sub-millimetre emission. Column densities are estimated based on the synthetic observations. For selected filaments, the estimated profiles are compared to those derived from the original column density. Possible effects from spatial variations of dust properties are examined. With instrumental noise typical of the Herschel observations, the parameters derived for nearby clouds are correct to within a few percent. The radiative transfer effects have only a minor effect on the results. If the signal-to-noise ratio is degraded by a factor of four, the errors become significant and for half of the examined filaments the values cannot be constrained. The errors increase in proportion to the cloud distance. Assuming the resolution of Herschel instruments, the model filaments are barely resolved at a distance of ~400 pc and the errors in the parameters of the Plummer function are several tens of per cent. The Plummer parameters, in particular the power-law exponent p, are sensitive to noise but can be determined with good accuracy using Herschel data. One must be cautious about possible line-of-sight confusion. In our models, a large fraction of the filaments seen in the column density maps are not continuous structures in three dimensions.Comment: 12 pages, 14 figures, accepted to A&

Efficient Monte Carlo methods for continuum radiative transfer

We discuss the efficiency of Monte Carlo methods in solving continuum radiative transfer problems. The sampling of the radiation field and convergence of dust temperature calculations in the case of optically thick clouds are both studied. For spherically symmetric clouds we find that the computational cost of Monte Carlo simulations can be reduced, in some cases by orders of magnitude, with simple importance weighting schemes. This is particularly true for models consisting of cells of different sizes for which the run times would otherwise be determined by the size of the smallest cell. We present a new idea of extending importance weighting to scattered photons. This is found to be useful in calculations of scattered flux and could be important for three-dimensional models when observed intensity is needed only for one general direction of observations. Convergence of dust temperature calculations is studied for models with optical depths 10-10000. We examine acceleration methods where radiative interactions inside a cell or between neighbouring cells are treated explicitly. In optically thick clouds with strong self-coupling between dust temperatures the run times can be reduced by more than one order of magnitude. The use of a reference field was also examined. This eliminates the need for repeating simulation of constant sources (e.g., background radiation) after the first iteration and significantly reduces sampling errors. The applicability of the methods for three-dimensional models is discussed.Comment: submitted to A&A, 19 page