T. Lunttila

Accuracy of core mass estimates in simulated observations of dust emission

Aims. We study the reliability of the mass estimates obtained for molecular cloud cores using sub-millimetre and infrared dust emission. Methods. 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 with opacity at one wavelength, 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. Results. Wrong assumptions of dust opacity and its spectral index β 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 the 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 dust in the core centre becomes visible and the observations recover the true mass spectra. Conclusions. 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 β whenever there are temperature variations along the line of sight. A bias can also be observed when the true β varies with wavelength. Internal heating sources produce an inverse correlation between colour temperature and β that may be difficult to separate from any intrinsic β(T ) relation of the dust grains. This suggests caution when interpreting the observed mass spectra and the spectral indices.

Galactic cold cores - II. Herschel study of the extended dust emission around the first Planck detections

Context. Within the project Galacticcoldcores we are carrying out Herschel photometric observations of cold interstellar clouds detected with the Planck satellite. The three fields observed as part of the Herschel science demonstration phase (SDP) provided the first glimpse into the nature of these sources. The aim of the project is to derive the physical properties of the full cold core population revealed by Planck. Aims: We examine the properties of the dust emission within the three fields observed during the SDP. We determine the dust sub-millimetre opacity, look for signs of spatial variations in the dust spectral index, and estimate how the apparent variations of the parameters could be affected by different sources of uncertainty. Methods: We use the Herschel observations where the zero point of the surface brightness scale is set with the help of the Planck satellite data. We derive the colour temperature and column density maps of the regions and determine the dust opacity by a comparison with extinction measurements. By simultaneously fitting the colour temperature and the dust spectral index values we look for spatial variations in the apparent dust properties. With a simple radiative transfer model we estimate to what extent these can be explained by line-of-sight temperature variations, without changes in the dust grain properties. Results: The analysis of the dust emission reveals cold and dense clouds that coincide with the Planck sources and confirm those detections. The derived dust opacity varies in the range κ(250 μm) ~ 0.05-0.2 cm2 g-1, higher values being observed preferentially in regions of high column density. The average dust spectral index β is ~1.9-2.2. There are indications that β increases towards the coldest regions. The spectral index decreases strongly near internal heating sources but, according to radiative transfer models, this can be explained by the line-of-sight temperature variations without a change in the dust properties. Planck (http://www.esa.int/Planck) is a project of the European Space Agency - ESA - with instruments provided by two scientific consortia funded by ESA member states (in particular the lead countries: France and Italy) with contributions from NASA (USA), and telescope reflectors provided in a collaboration between ESA and a scientific Consortium led and funded by Denmark.Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.Appendices are only available in electronic form at http://www.aanda.org

The degeneracy between dust colour temperature and spectral index - Comparison of methods for estimating the β(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.

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.

THE SUPER-ALFVÉNIC MODEL OF MOLECULAR CLOUDS: PREDICTIONS FOR MASS-TO-FLUX AND TURBULENT-TO-MAGNETIC ENERGY RATIOS

Recent measurements of the Zeeman effect in dark-cloud cores provide important tests for theories of cloud dynamics and prestellar core formation. In this Letter, we report results of simulated Zeeman measurements, based on radiative transfer calculations through a snapshot of a simulation of supersonic and super-Alfvenic turbulence. We have previously shown that the same simulation yields a relative mass-to-flux ratio (core versus envelope) in agreement with the observations (and in contradiction with the ambipolar-drift model of core formation). Here, we show that the mass-to-flux and turbulent-to-magnetic-energy ratios in the simulated cores agree with the observed values as well. The mean magnetic field strength in the simulation is very low, G, presumably lower than the mean field in molecular clouds. Nonetheless, high magnetic field values are found in dense cores, in agreement with the observations (the rms field, amplified by the turbulence, is B rms = 3.05 μG). We conclude that a strong large-scale mean magnetic field is not required by Zeeman effect measurements to date, although it is not ruled out by this work.

The Super-Alfvénic Model of Molecular Clouds: Predictions for Zeeman Splitting Measurements

We present synthetic OH Zeeman splitting measurements of a super-Alfvenic molecular cloud model. We select dense cores from synthetic13CO maps computed from the largest simulation to date of supersonic and super-Alfvenic turbulence. The synthetic Zeeman splitting measurements in the cores yield a relation between the magnetic field strength, B, and the column density, N, in good agreement with the observations. The large scatter in B at a fixed value of N is partly due to intrinsic variations in the magnetic field strength from core to core. We also compute the relative mass-to-flux ratio between the center of the cores and their envelopes, , and show that super-Alfvenic turbulence produces a significant scatter also in , including negative values (field reversal between core center and envelope). We find for 70% of the cores, and for 12%. Of the cores with | BLOS| > 10 μG, 81% have . These predictions of the super-Alfvenic model are in stark contrast to the ambipolar drift model of core formation, where only is allowed.

Benchmarking the calculation of stochastic heating and emissivity of dust grains in the context of radiative transfer simulations

Context. Thermal emission by stochastically heated dust grains (SHGs) plays an important role in the radiative transfer (RT) problem for a dusty medium. It is therefore essential to verify that RT codes properly calculate the dust emission before studying the effects of spatial distribution and other model parameters on the simulated observables. Aims. We define an appropriate problem for benchmarking dust emissivity calculations in the context of RT simulations, specifically including the emission from SHGs. Our aim is to provide a self-contained guide for implementors of such functionality and to offer insight into the effects of the various approximations and heuristics implemented by the participating codes to accelerate the calculations. Methods. The benchmark problem definition includes the optical and calorimetric material properties and the grain size distributions for a typical astronomical dust mixture with silicate, graphite, and PAH components. It also includes a series of analytically defined radiation fields to which the dust population is to be exposed and instructions for the desired output. We processed this problem using six RT codes participating in this benchmark effort and compared the results to a reference solution computed with the publicly available dust emission code DustEM. Results. The participating codes implement different heuristics to keep the calculation time at an acceptable level.We study the effects of these mechanisms on the calculated solutions and report on the level of (dis)agreement between the participating codes. For all but the most extreme input fields, we find agreement within 10% across the important wavelength range 3 μm ≤1000 μm. Conclusions. We conclude that the relevant modules in RT codes can and do produce fairly consistent results for the emissivity spectra of SHGs. This work can serve as a reference for implementors of dust RT codes, and it will pave the way for a more extensive benchmark effort focusing on the RT aspects of the various codes.

Radiative transfer on hierarchial grids

Context. Continuum radiative-transfer simulations are necessary for the interpretation of observations of dusty astrophysical objects and for relating the results of magnetohydrodynamical simulations to observations. The calculations are computationally difficult, and simulations of objects with high optical depths in particular require considerable computational resources. Aims. Our aim is to show how radiative transfer calculations on adaptive three-dimensional grids can be accelerated. Methods. We show how the hierarchial tree structure of the model can be used in the calculations. 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. Results. An adaptive model of the molecular cloud with fewer than 8% of the cells in the uniform grid produces results in good agreement with the full resolution model. The relative root-mean-square (rms) error of the surface brightness is <4% at all wavelengths, and in regions of high column density the relative rms error is only ∼10 −4 . Computation with the adaptive model is faster by a factor of ∼5. Our new method for calculating the scattered flux is faster by a factor of about four 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 is 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 of low mean density.

Gas and dust in the star-forming region ρ Oph A ∗, ∗∗, ∗∗∗: The dust opacity exponent β and the gas-to-dust mass ratio g2d

We aim at determining the spatial distribution of the gas and dust in star-forming regions and address their relative abundances in quantitative terms. We also examine the dust opacity exponent beta for spatial and/or temporal variations. Using mapping observations of the very dense rho Oph A core, we examined standard 1D and non-standard 3D methods to analyse data of far-infrared and submillimeter (submm) continuum radiation. The resulting dust surface density distribution can be compared to that of the gas. The latter was derived from the analysis of accompanying molecular line emission, observed with Herschel from space and with APEX from the ground. As a gas tracer we used N2H+, which is believed to be much less sensitive to freeze-out than CO and its isotopologues. Radiative transfer modelling of the N2H+(J=3-2) and (J=6-5) lines with their hyperfine structure explicitly taken into account provides solutions for the spatial distribution of the column density N(H2), hence the surface density distribution of the gas. The gas-to-dust mass ratio is varying across the map, with very low values in the central regions around the core SM 1. The global average, =88, is not far from the canonical value of 100, however. In rho Oph A, the exponent beta of the power-law description for the dust opacity exhibits a clear dependence on time, with high values of 2 for the envelope-dominated emission in starless Class -1 sources to low values close to 0 for the disk-dominated emission in Class III objects. beta assumes intermediate values for evolutionary classes in between. Since beta is primarily controlled by grain size, grain growth mostly occurs in circumstellar disks. The spatial segregation of gas and dust, seen in projection toward the core centre, probably implies that, like C18O, also N2H+ is frozen onto the grains.

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.