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&

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

Mantle formation, coagulation and the origin of cloud/core-shine: II. Comparison with observations

Many dense interstellar clouds are observable in emission in the near-IR, commonly referred to as "Cloudshine", and in the mid-IR, the so-called "Coreshine". These C-shine observations have usually been explained with grain growth but no model has yet been able to self-consistently explain the dust spectral energy distribution from the near-IR to the submm. We want to demonstrate the ability of our new core/mantle evolutionary dust model THEMIS (The Heterogeneous dust Evolution Model at the IaS), which has been shown to be valid in the far-IR and submm, to reproduce the C-shine observations. Our starting point is a physically motivated core/mantle dust model. It consists of 3 dust populations: small aromatic-rich carbon grains; bigger core/mantle grains with mantles of aromatic-rich carbon and cores either made of amorphous aliphatic-rich carbon or amorphous silicate. We assume an evolutionary path where these grains, when entering denser regions, may first form a second aliphatic-rich carbon mantle (coagulation of small grains, accretion of carbon from the gas phase), second coagulate together to form large aggregates, and third accrete gas phase molecules coating them with an ice mantle. To compute the corresponding dust emission and scattering, we use a 3D Monte-Carlo radiative transfer code. We show that our global evolutionary dust modelling approach THEMIS allows us to reproduce C-shine observations towards dense starless clouds. Dust scattering and emission is most sensitive to the cloud central density and to the steepness of the cloud density profile. Varying these two parameters leads to changes, which are stronger in the near-IR, in both the C-shine intensity and profile. With a combination of aliphatic-rich mantle formation and low-level coagulation into aggregates, we can self-consistently explain the observed C-shine and far-IR/submm emission towards dense starless clouds.Comment: Paper accepted for publication in A&A with companion paper "Mantle formation, coagulation and the origin of cloud/core-shine: I. Dust scattering and absorption in the IR", A.P Jones, M. Koehler, N. Ysard, E. Dartois, M. Godard, L. Gavila

Modelling the spinning dust emission from dense interstellar clouds

Electric dipole emission arising from PAHs is often invoked to explain the anomalous microwave emission (AME). This assignation is based on an observed tight correlation between the mid-IR emission of PAHs and the AME; and a good agreement between models of spinning dust and the broadband AME spectrum. So far often detected at large scale in the diffuse interstellar medium, the AME has recently been studied in detail in well-known dense molecular clouds with the help of Planck data. While much attention has been given to the physics of spinning dust emission, the impact of varying local physical conditions has not yet been considered in detail. Our aim is to study the emerging spinning dust emission from interstellar clouds with realistic physical conditions and radiative transfer. We use the DustEM code from Compiegne et al. to describe the extinction and IR emission of all dust populations. The spinning dust emission is obtained with SpDust, as described by Silsbee et al., that we have coupled to DustEM. We carry out full radiative transfer simulations and carefully estimate the local gas state as a function of position within interstellar clouds. We show that the spinning dust emission is sensitive to the abundances of the major ions and we propose a simple scheme to estimate these abundances. We also investigate the effect of changing the cosmic-ray rate. In dense media, where radiative transfer is mandatory, we show that the relationship between the spinning and mid-IR emissivities of PAHs is no longer linear and that the spinning dust emission may actually be strong at the centre of clouds where the mid-IR PAH emission is weak. These results provide new ways to trace grain growth from diffuse to dense medium and will be useful for the analysis of AME at the scale of interstellar clouds.Comment: 7 pages, 10 figures, accepted by A&

The dust masses of powerful radio galaxies: clues to the triggering of their activity

We use deep Herschel Space Observatory observations of a 90% complete sample of 32 intermediate-redshift 2Jy radio galaxies (0.05 < z < 0.7) to estimate the dust masses of their host galaxies and thereby investigate the triggering mechanisms for their quasar-like AGN. The dust masses derived for the radio galaxies (7.2x10^5 < M_d < 2.6x10^8 M_sun) are intermediate between those of quiescent elliptical galaxies on the one hand, and ultra luminous infrared galaxies (ULIRGs) on the other. Consistent with simple models for the co-evolution of supermassive black holes and their host galaxies, these results suggest that most of the radio galaxies represent the late time re-triggering of AGN activity via mergers between the host giant elliptical galaxies and companion galaxies with relatively low gas masses. However, a minority of the radio galaxies in our sample (~20%) have high, ULIRG-like dust masses, along with evidence for prodigious star formation activity. The latter objects are more likely to have been triggered in major, gas-rich mergers that represent a rapid growth phase for both their host galaxies and their supermassive black holes.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter

Dust models post-Planck: constraining the far-infrared opacity of dust in the diffuse interstellar medium

We compare the performance of several dust models in reproducing the dust spectral energy distribution (SED) per unit extinction in the diffuse interstellar medium (ISM). We use our results to constrain the variability of the optical properties of big grains in the diffuse ISM, as published by the Planck collaboration. We use two different techniques to compare the predictions of dust models to data from the Planck HFI, IRAS and SDSS surveys. First, we fit the far-infrared emission spectrum to recover the dust extinction and the intensity of the interstellar radiation field (ISRF). Second, we infer the ISRF intensity from the total power emitted by dust per unit extinction, and then predict the emission spectrum. In both cases, we test the ability of the models to reproduce dust emission and extinction at the same time. We identify two issues. Not all models can reproduce the average dust emission per unit extinction: there are differences of up to a factor $\sim2$ between models, and the best accord between model and observation is obtained with the more emissive grains derived from recent laboratory data on silicates and amorphous carbons. All models fail to reproduce the variations in the emission per unit extinction if the only variable parameter is the ISRF intensity: this confirms that the optical properties of dust are indeed variable in the diffuse ISM. Diffuse ISM observations are consistent with a scenario where both ISRF intensity and dust optical properties vary. The ratio of the far-infrared opacity to the $V$ band extinction cross-section presents variations of the order of $\sim20\%$ ($40-50\%$ in extreme cases), while ISRF intensity varies by $\sim30\%$ ($\sim60\%$ in extreme cases). This must be accounted for in future modelling.Comment: A&A, in pres

Mantle formation, coagulation and the origin of cloud/core shine: I. Modelling dust scattering and absorption in the infra-red

Context. The observed cloudshine and coreshine (C-shine) have been explained in terms of grain growth leading to enhanced scatter- ing from clouds in the J, H and K photometric bands and the Spitzer IRAC 3.6 and 4.5 {\mu}m bands. Aims. Using our global dust modelling approach THEMIS (The Heterogeneous dust Evolution Model at the IaS) we explore the effects of dust evolution in dense clouds, through aliphatic-rich carbonaceous mantle formation and grain-grain coagulation. Methods. We model the effects of wide band gap a-C:H mantle formation and the low-level aggregation of diffuse interstellar medium dust in the moderately-extinguished outer regions of molecular clouds. Results. The formation of wide band gap a-C:H mantles on amorphous silicate and amorphous carbon (a-C) grains leads to a decrease in their absorption cross-sections but no change in their scattering cross-sections at near-IR wavelengths, resulting in higher albedos. Conclusions. The evolution of dust, with increasing density and extinction in the diffuse to dense molecular cloud transition, through mantle formation and grain aggregation, appears to be a likely explanation for the observed C-shine.Comment: 12 pages, 15 figures, accepted for publication in A&A along with the companion paper entitled, Mantle formation, coagulation and the origin of cloud/core shine: II Comparison with observations, by Ysard et al. (also accepted for publication in A&A

New radio observations of anomalous microwave emission in the HII region RCW175

We have observed the HII region RCW175 with the 64m Parkes telescope at 8.4GHz and 13.5GHz in total intensity, and at 21.5GHz in both total intensity and polarization. High angular resolution, high sensitivity, and polarization capability enable us to perform a detailed study of the different constituents of the HII region. For the first time, we resolve three distinct regions at microwave frequencies, two of which are part of the same annular diffuse structure. Our observations enable us to confirm the presence of anomalous microwave emission (AME) from RCW175. Fitting the integrated flux density across the entire region with the currently available spinning dust models, using physically motivated assumptions, indicates the presence of at least two spinning dust components: a warm component with a relatively large hydrogen number density n_H=26.3/cm^3 and a cold component with a hydrogen number density of n_H=150/cm^3. The present study is an example highlighting the potential of using high angular-resolution microwave data to break model parameter degeneracies. Thanks to our spectral coverage and angular resolution, we have been able to derive one of the first AME maps, at 13.5GHz, showing clear evidence that the bulk of the AME arises in particular from one of the source components, with some additional contribution from the diffuse structure. A cross-correlation analysis with thermal dust emission has shown a high degree of correlation with one of the regions within RCW175. In the center of RCW175, we find an average polarized emission at 21.5GHz of 2.2\pm0.2(rand.)\pm0.3(sys.)% of the total emission, where we have included both systematic and statistical uncertainties at 68% CL. This polarized emission could be due to sub-dominant synchrotron emission from the region and is thus consistent with very faint or non-polarized emission associated with AME.Comment: Accepted for publication in the Astrophysical Journa

Nano-grain depletion in photon-dominated regions

Context. Carbonaceous nano-grains play a fundamental role in the physico-chemistry of the interstellar medium (ISM) and especially of photon-dominated regions (PDRs). Their properties vary with the local physical conditions and affect the local chemistry and dynamics. Aims. We aim to highlight the evolution of carbonaceous nano-grains in three different PDRs and propose a scenario of dust evolution as a response to the physical conditions. Methods. We used Spitzer/IRAC (3.6, 4.5, 5.8, and 8 $\mu$m) and Spitzer/MIPS (24 $\mu$m) together with Herschel/PACS (70 $\mu$m) to map dust emission in IC63 and the Orion Bar. To assess the dust properties, we modelled the dust emission in these regions using the radiative transfer code SOC together with the THEMIS dust model. Results. Regardless of the PDR, we find that nano-grains are depleted and that their minimum size is larger than in the diffuse ISM (DISM), which suggests that the mechanisms that lead nano-grains to be photo-destroyed are very efficient below a given critical size limit. The evolution of the nano-grain dust-to-gas mass ratio with both G0 and the effective temperature of the illuminating star indicates a competition between the nano-grain formation through the fragmentation of larger grains and nano-grain photo-destruction. We modelled dust collisions driven by radiative pressure with a classical 1D approach to show that this is a viable scenario for explaining nano-grain formation through fragmentation and, thus, the variations observed in nano-grain dust-to-gas mass ratios from one PDR to another. Conclusions. We find a broad variation in the nano-grain dust properties from one PDR to another, along with a general trend of nano-grain depletion in these regions. We propose a viable scenario of nano-grain formation through fragmentation of large grains due to radiative pressure-induced collisions

Dust evolution across the Horsehead nebula

Context. Micro-physical processes on interstellar dust surfaces are tightly connected to dust properties (i.e. dust composition, size, and shape) and play a key role in numerous phenomena in the interstellar medium (ISM). The large disparity in physical conditions (i.e. density and gas temperature) in the ISM triggers an evolution of dust properties. The analysis of how dust evolves with the physical conditions is a stepping stone towards a more thorough understanding of interstellar dust.Aims. We highlight dust evolution in the Horsehead nebula photon-dominated region.Methods. We used Spitzer/IRAC (3.6, 4.5, 5.8 and 8 mu m) and Spitzer/MIPS (24 mu m) together with Herschel/PACS (70 and 160 mu m) and Herschel/SPIRE (250, 350 and 500 mu m) to map the spatial distribution of dust in the Horsehead nebula over the entire emission spectral range. We modelled dust emission and scattering using the THEMIS interstellar dust model together with the 3D radiative transfer code SOC.Results. We find that the nano-grain dust-to-gas ratio in the irradiated outer part of the Horsehead is 6-10 times lower than in the diffuse ISM. The minimum size of these grains is 2-2.25 times larger than in the diffuse ISM, and the power-law exponent of their size distribution is 1.1-1.4 times lower than in the diffuse ISM. In the denser part of the Horsehead nebula, it is necessary to use evolved grains (i.e. aggregates, with or without an ice mantle).Conclusions. It is not possible to explain the observations using grains from the diffuse medium. We therefore propose the following scenario to explain our results. In the outer part of the Horsehead nebula, all the nano-grain have not yet had time to re-form completely through photo-fragmentation of aggregates and the smallest of the nano-grain that are sensitive to the radiation field are photo-destroyed. In the inner part of the Horsehead nebula, grains most likely consist of multi-compositional mantled aggregates.Peer reviewe