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.

Context. Submillimetre dust emission provides information on the physics of interstellar clouds and dust. However, noise can produce a spurious anticorrelation between the colour temperature T C and the spectral index β. These artefacts must be separated from the intrinsic β(T ) relation of dust emission. Aims. We compare methods that can be used to analyse the β(T ) relation. We wish to quantify their accuracy and bias, especially for observations similar to those made with Planck and Herschel. Methods. We examine submillimetre observations that are simulated either as simple, modified black body emission or using 3D radiative transfer modelling. We used different methods to recover the (T , β) values of individual objects and the parameters of the β(T ) relation. In addition to χ 2 fitting, we examined the results of the SIMEX method, basic Bayesian model, hierarchical models, and a method that explicitly assumes a functional form for β(T ). The methods were also applied to one field observed by Herschel. Results. All methods exhibit some bias, even in the idealised case of white noise. The results of the Bayesian method show significantly lower bias than direct χ 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. When the signal-to-noise ratios are different for different sources, all β and T estimates of the hierarchical model are biased towards the relation determined by the data with the highest signal-to-noise ratio. This can significantly alter the recovered β(T ) function. With the method where we explicitly assume a functional form for the β(T ) relation, the bias is similar to the Bayesian method. In the case of the actual Herschel field, all methods agree on some degree of anticorrelation between T and β. Conclusions. 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-tonoise ratios and this must be taken into account when interpreting the results.

Context. Within the project Galactic cold cores 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 submillimetre 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 cm 2 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.