The Planck-HFI all-sky survey from 353 to 857GHz combined with the 100 microns IRAS show that the dust properties vary in the diffuse ISM at high Galactic latitude (1e19<NH<2.5e20 H/cm2). Our aim is to explain these variations with changes in the ISM
properties and grain evolution. Our starting point is the latest core-mantle dust model. It consists of small aromatic-rich carbon grains, larger amorphous carbon grains with aliphatic-rich cores and aromatic-rich mantles, and amorphous silicates with Fe/FeS nano-inclusions covered by aromatic-rich carbon mantles. We explore whether variations in the radiation field or in the gas density distribution in the diffuse ISM could explain the observations. The dust properties are also varied in terms of mantle thickness, Fe/FeS inclusions, carbon abundance, and size distribution. Variations in the radiation field intensity and gas density distribution cannot explain the observed variations but radiation fields harder than the standard ISRF may participate in creating part of them. We further show that variations in the grain mantle thickness coupled with changes in the grain size distribution can reproduce most of the observations. We put a limit on the mantle thickness of the silicates (~10-15nm), and find that aromatic-rich mantles are needed for the carbon grains (at least 5-7.5nm thick). We also find that changes in the carbon abundance in the grains could explain part of the observed variations. Finally, we show that varying the composition of Fe/FeS inclusions in the silicates cannot account for the variations. With small variations in the dust properties, we are able to explain most of the variations in the dust emission observed by Planck-HFI in the diffuse ISM. We also find that the small realistic changes in the dust properties that we consider almost perfectly match the anti-correlation and scatter in the observed 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) rela
tion 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.
We investigate the uncertainties affecting the temperature profiles of dense cores of interstellar clouds. In regions shielded from external ultraviolet radiation, the problem is reduced to the balance between cosmic ray heating, line cooling, and th
e coupling between gas and dust. We show that variations in the gas phase abundances, the grain size distribution, and the velocity field can each change the predicted core temperatures by one or two degrees. We emphasize the role of non-local radiative transfer effects that often are not taken into account, for example, when modelling the core chemistry. These include the radiative coupling between regions of different temperature and the enhanced line cooling near the cloud surface. The uncertainty of the temperature profiles does not necessarily translate to a significant error in the column density derived from observations. However, depletion processes are very temperature sensitive and a two degree difference can mean that a given molecule no longer traces the physical conditions in the core centre.
