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&

The degeneracy between dust colour temperature and spectral index. Comparison of methods for estimating the beta(T) relation

Sub-millimetre dust emission provides information on the physics of interstellar clouds and dust. Noise can produce anticorrelation between the colour temperature T_C and the spectral index beta. This must be separated from the intrinsic beta(T) relation of dust. We compare methods for the analysis of the beta(T) relation. We examine sub-millimetre observations simulated as simple modified black body emission or using 3D radiative transfer modelling. In addition to chi^2 fitting, we examine the results of the SIMEX method, basic Bayesian model, hierarchical models, and one method that explicitly assumes a functional form for beta(T). All methods exhibit some bias. Bayesian method shows significantly lower bias than direct chi^2 fits. The same is true for hierarchical models that also result in a smaller scatter in the temperature and spectral index values. However, significant bias was observed in cases with high noise levels. Beta and T estimates of the hierarchical model are biased towards the relation determined by the data with the highest S/N ratio. This can alter the recovered beta(T) function. With the method where we explicitly assume a functional form for the beta(T) relation, the bias is similar to the Bayesian method. In the case of an actual Herschel field, all methods agree, showing some degree of anticorrelation between T and beta. The Bayesian method and the hierarchical models can both reduce the noise-induced parameter correlations. However, all methods can exhibit non-negligible bias. This is particularly true for hierarchical models and observations of varying signal-to-noise ratios and must be taken into account when interpreting the results.Comment: Submitted to A&A, 18 page

Radiative transfer on hierarchial grids

We present new methods for radiative transfer on hierarchial grids. We develop a new method for calculating the scattered flux that employs the grid structure to speed up the computation. We describe a novel subiteration algorithm that can be used to accelerate calculations with strong dust temperature self-coupling. We compute two test models, a molecular cloud and a circumstellar disc, and compare the accuracy and speed of the new algorithms against existing methods. An adaptive model of the molecular cloud with less than 8 % of the cells in the uniform grid produced results in good agreement with the full resolution model. The relative RMS error of the surface brightness <4 % at all wavelengths, and in regions of high column density the relative RMS error was only 10^{-4}. Computation with the adaptive model was faster by a factor of ~5. The new method for calculating the scattered flux is faster by a factor of ~4 in large models with a deep hierarchy structure, when images of the scattered light are computed towards several observing directions. The efficiency of the subiteration algorithm is highly dependent on the details of the model. In the circumstellar disc test the speed-up was a factor of two, but much larger gains are possible. The algorithm is expected to be most beneficial in models where a large number of small, dense regions are embedded in an environment with a lower mean density.Comment: Accepted to A&A; 13 pages, 8 figures; (v2: minor typos corrected

Constrained simulations of the Antennae Galaxies: Comparison with Herschel-PACS observations

We present a set of hydro-dynamical numerical simulations of the Antennae galaxies in order to understand the origin of the central overlap starburst. Our dynamical model provides a good match to the observed nuclear and overlap star formation, especially when using a range of rather inefficient stellar feedback efficiencies (0.01 < q_EoS < 0.1). In this case a simple conversion of local star formation to molecular hydrogen surface density motivated by observations accounts well for the observed distribution of CO. Using radiative transfer post-processing we model synthetic far-infrared spectral energy distributions (SEDs) and two-dimensional emission maps for direct comparison with Herschel-PACS observations. For a gas-to-dust ratio of 62:1 and the best matching range of stellar feedback efficiencies the synthetic far-infrared SEDs of the central star forming region peak at values of ~65 - 81 Jy at 99 - 116 um, similar to a three-component modified black body fit to infrared observations. Also the spatial distribution of the far-infrared emission at 70 um, 100 um, and 160 um compares well with the observations: >50% (> 35%) of the emission in each band is concentrated in the overlap region while only < 30% (< 15%) is distributed to the combined emission from the two galactic nuclei in the simulations (observations). As a proof of principle we show that parameter variations in the feedback model result in unambiguous changes both in the global and in the spatially resolved observable far-infrared properties of Antennae galaxy models. Our results strengthen the importance of direct, spatially resolved comparative studies of matched galaxy merger simulations as a valuable tool to constrain the fundamental star formation and feedback physics.Comment: 17 pages, 8 figures, 4 tables, submitted to MNRAS, including revisions after first referee report, comments welcom

Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical parameter estimation is an ill-posed inverse problem, and thus it is sensitive to measurement and modeling errors. In this work, we propose a novel way to solve the inverse problem of quantitative photoacoustic tomography based on the perturbation Monte Carlo method. Monte Carlo method for light propagation is a stochastic approach for simulating photon trajectories in a medium with scattering particles. It is widely accepted as an accurate method to simulate light propagation in tissues. Furthermore, it is numerically robust and easy to implement. Perturbation Monte Carlo maintains this robustness and enables forming gradients for the solution of the inverse problem. We validate the method and apply it in the framework of Bayesian inverse problems. The simulations show that the perturbation Monte Carlo method can be used to estimate spatial distributions of both absorption and scattering parameters simultaneously. These estimates are qualitatively good and quantitatively accurate also in parameter scales that are realistic for biological tissues

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&

A CO survey on a sample of Herschel cold clumps

Context. The physical state of cold cloud clumps has a great impact on the process and efficiency of star formation and the masses of the forming stars inside these objects. The sub-millimetre survey of the Planck space observatory and the far-infrared follow-up mapping of the Herschel space telescope provide an unbiased, large sample of these cold objects. Aims. We have observed (CO)-C-12(1-0) and (CO)-C-13(1-0) emission in 35 high-density clumps in 26 Herschel fields sampling different environments in the Galaxy. Here, we aim to derive the physical properties of the objects and estimate their gravitational stability. Methods. The densities and temperatures of the clumps were calculated from both the dust continuum and the molecular line data. Kinematic distances were derived using (CO)-C-13(1-0) line velocities to verify previous distance estimates and the sizes and masses of the objects were calculated by fitting 2D Gaussian functions to their optical depth distribution maps on 250 mu m. The masses and virial masses were estimated assuming an upper and lower limit on the kinetic temperatures and considering uncertainties due to distance limitations. Results. The derived excitation temperatures are between 8.5-19.5 K, and for most clumps between 10 15 K, while the Herschel-derived dust colour temperatures are more uniform, between 12 16 K. The sizes (0.1-3 pc), (CO)-C-13 column densities (0.5-44 x 10(15) cm(-2)) and masses (from less than 0.1 M-circle dot to more than 1500 M-circle dot) of the objects all span broad ranges. We provide new kinematic distance estimates, identify gravitationally bound or unbound structures and discuss their nature. Conclusions. The sample contains objects on a wide scale of temperatures, densities and sizes. Eleven gravitationally unbound clumps were found, many of them smaller than 0.3 pc, but large, parsec-scale clouds with a few hundred solar masses appear as well. Colder clumps have generally high column densities but warmer objects appear at both low and higher column densities. The clump column densities derived from the line and dust observations correlate well, but are heavily affected by uncertainties of the dust properties, varying molecular abundances and optical depth effects.Peer reviewe

Accuracy of core mass estimates in simulated observations of dust emission

We study the reliability of mass estimates obtained for molecular cloud cores using sub-millimetre and infrared dust emission. We use magnetohydrodynamic simulations and radiative transfer to produce synthetic observations with spatial resolution and noise levels typical of Herschel surveys. We estimate dust colour temperatures using different pairs of intensities, calculate column densities and compare the estimated masses with the true values. We compare these results to the case when all five Herschel wavelengths are available. We investigate the effects of spatial variations of dust properties and the influence of embedded heating sources. Wrong assumptions of dust opacity and its spectral index beta can cause significant systematic errors in mass estimates. These are mainly multiplicative and leave the slope of the mass spectrum intact, unless cores with very high optical depth are included. Temperature variations bias colour temperature estimates and, in quiescent cores with optical depths higher than for normal stable cores, masses can be underestimated by up to one order of magnitude. When heated by internal radiation sources the observations recover the true mass spectra. The shape, although not the position, of the mass spectrum is reliable against observational errors and biases introduced in the analysis. This changes only if the cores have optical depths much higher than expected for basic hydrostatic equilibrium conditions. Observations underestimate the value of beta whenever there are temperature variations along the line of sight. A bias can also be observed when the true beta varies with wavelength. Internal heating sources produce an inverse correlation between colour temperature and beta that may be difficult to separate from any intrinsic beta(T) relation of the dust grains. This suggests caution when interpreting the observed mass spectra and the spectral indices.Comment: Revised version, 17 pages, 17 figures, submitted to A&

I. A 3D externally illuminated slab benchmark for dust radiative transfer

Context. The radiative transport of photons through arbitrary three-dimensional (3D) structures of dust is a challenging problem due to the anisotropic scattering of dust grains and strong coupling between different spatial regions. The radiative transfer problem in 3D is solved using Monte Carlo or Ray Tracing techniques as no full analytic solution exists for the true 3D structures. Aims. We provide the first 3D dust radiative transfer benchmark composed of a slab of dust with uniform density externally illuminated by a star. This simple 3D benchmark is explicitly formulated to provide tests of the different components of the radiative transfer problem including dust absorption, scattering, and emission. Methods. The details of the external star, the slab itself, and the dust properties are provided. This benchmark includes models with a range of dust optical depths fully probing cases that are optically thin at all wavelengths to optically thick at most wavelengths. The dust properties adopted are characteristic of the diffuse Milky Way interstellar medium. This benchmark includes solutions for the full dust emission including single photon (stochastic) heating as well as two simplifying approximations: One where all grains are considered in equilibrium with the radiation field and one where the emission is from a single effective grain with size-distribution-averaged properties. A total of six Monte Carlo codes and one Ray Tracing code provide solutions to this benchmark. Results. The solution to this benchmark is given as global spectral energy distributions (SEDs) and images at select diagnostic wavelengths from the ultraviolet through the infrared. Comparison of the results revealed that the global SEDs are consistent on average to a few percent for all but the scattered stellar flux at very high optical depths. The image results are consistent within 10%, again except for the stellar scattered flux at very high optical depths. The lack of agreement between different codes of the scattered flux at high optical depths is quantified for the first time. Convergence tests using one of the Monte Carlo codes illustrate the sensitivity of the solutions to various model parameters. Conclusions. We provide the first 3D dust radiative transfer benchmark and validate the accuracy of this benchmark through comparisons between multiple independent codes and detailed convergence tests.Peer reviewe

Reliability of NH3 as the temperature probe of cold cloud cores

The temperature is a central parameter affecting the chemical and physical properties of dense cores of interstellar clouds and their evolution to star formation. The chemistry and the dust properties are temperature dependent and the interpretation of observation requires the knowledge of the temperature and its variations. Measurement of the gas kinetic temperature is possible with molecular line spectroscopy, the ammonia molecule, NH3, being the most commonly used tracer. We want to determine the accuracy of the temperature estimates derived from ammonia spectra. The normal interpretation of NH3 observations assumes that all the hyperfine line components are tracing the same gas volume. In the case of temperature gradients they may be sensitive to different layers and cause errors in the optical depth and gas temperature estimates. We examine a series of spherical cloud models, 1.0 and 0.5 M_Sun Bonnor-Ebert spheres, with different radial temperature profiles. We calculate synthetic NH3 spectra and compare the derived column densities and temperatures to the true values. For high signal-to-noise observations, the estimated gas kinetic temperatures are within ~0.3 K of the real mass averaged temperature and the column densities are correct to within ~10%. When the S/N ratio of the (2,2) spectrum decreases below 10, the temperature errors are of the order of 1K but without a significant bias. When the density of the models is increased by a factor of a few, the results begin to show significant bias because of the saturation of the (1,1) main group. The ammonia spectra are found to be a reliable tracer of the mass averaged gas temperature. Because the radial temperature profiles of the cores are not well constrained, the central temperature could still differ from this value. If the cores are optically very thick, there are no guarantees of the accuracy.Comment: 7 pages, accepted to A&