Hacheme Ayasso

Evolution of dust in the Orion Bar with Herschel - I. Radiative transfer modelling

Context . Interstellar dust is a key element in our understanding of the interstellar medium and star formation. The manner in which dust populations evolve with the excitation and the physical conditions is a first step in comprehending the evolution of interstellar dust. Aims . Within the framework of the Evolution of interstellar dust Herschel key programme, we have acquired PACS and SPIRE spectrophotometric observations of various photodissociation regions, to characterise this evolution. The aim of this paper is to trace the evolution of dust grains in the Orion Bar photodissociation region. Methods . We used Herschel /PACS (70 and 160 μm) and SPIRE (250, 350 and 500 μm) together with Spitzer /IRAC observations to map the spatial distribution of the dust populations across the Bar. Brightness profiles were modelled using the DustEM model coupled with a radiative transfer code. Results . Thanks to Herschel , we are able to probe in great detail the dust emission of the densest parts of the Orion Bar with a resolution from 5.6″ to 35.1″. These new observations allow us to infer the temperature of the biggest grains at different positions in the Bar, which reveals a gradient from ~70 K to 35 K coupled with an increase of the spectral emissivity index from the ionization front to the densest regions. Combining Spitzer /IRAC observations, which are sensitive to the dust emission from the surface, with Herschel maps, we were able to measure the Orion Bar emission from 3.6 to 500 μm. We find a stratification in the different dust components that can be quantitatively reproduced by a simple radiative transfer model without dust evolution (diffuse interstellar medium abundances and optical properties). However, including dust evolution is needed to explain the brightness in each band. Polycyclic aromatic hydrocarbon (PAH) abundance variations, or a combination of PAH abundance variations with an enhancement of the biggest grain emissivity caused by coagulation give good results. Another hypothesis is to consider a length of the Bar along the line of sight different at the ionization front than in the densest parts.

Bayesian inversion for optical diffraction tomography

In this paper, optical diffraction tomography is considered as a non-linear inverse scattering problem and tackled within the Bayesian estimation framework. The object under test is a man-made object known to be composed of compact regions made of a finite number of different homogeneous materials. This a priori knowledge is appropriately translated by a Gauss–Markov–Potts prior. Hence, a Gauss–Markov random field is used to model the contrast distribution whereas a hidden Potts–Markov field accounts for the compactness of the regions. First, we express the a posteriori distributions of all the unknowns and then a Gibbs sampling algorithm is used to generate samples and estimate the posterior mean of the unknowns. Some preliminary results, obtained by applying the inversion algorithm to laboratory controlled data, are presented.

Physical structure of the photodissociation regions in NGC 7023 - Observations of gas and dust emission with Herschel

Context. The determination of the physical conditions in molecular clouds is a key step towards our understanding of their formation and evolution of associated star formation. We investigate the density, temperature, and column density of both dust and gas in the photodissociation regions (PDRs) located at the interface between the atomic and cold molecular gas of the NGC 7023 reflection nebula. We study how young stars affect the gas and dust in their environment. Aims. Several Herschel Space Telescope programs provide a wealth of spatial and spectral information of dust and gas in the heart of PDRs. We focus our study on Spectral and Photometric Image Receiver (SPIRE) Fourier-Transform Spectrometer (FTS) fully sampled maps that allow us for the first time to study the bulk of cool/warm dust and warm molecular gas (CO) together. In particular, we investigate if these populations spatially coincide, if and how the medium is structured, and if strong density and temperature gradients occur, within the limits of the spatial resolution obtained with Herschel. Methods. The SPIRE FTS fully sampled maps at different wavelengths are analysed towards the northwest (NW) and the east (E) PDRs in NGC 7023. We study the spatial and spectral energy distribution of a wealth of intermediate rotational (CO)-C-12 4 \textless= J(u) \textless= 13 and (CO)-C-13 5 \textless= J(u) \textless= 10 lines. A radiative transfer code is used to assess the gas kinetic temperature, density, and column density at different positions in the cloud. The dust continuum emission including Spitzer, the Photoconductor Array Camera and Spectrometer (PACS), and SPIRE photometric and the Institute for Radio Astronomy in the Millimeter Range (IRAM) telescope data is also analysed. Using a single modified black body and a radiative transfer model, we derive the dust temperature, density, and column density. Results. The cloud is highly inhomogeneous, containing several irradiated dense structures. Excited (CO)-C-12 and (CO)-C-13 lines and warm dust grains localised at the edge of the dense structures reveal high column densities of warm/cool dense matter. Both tracers give a good agreement in the local density, column density, and physical extent, leading to the conclusion that they trace the same regions. The derived density profiles show a steep gradient at the cloud edge reaching a maximum gas density of 10(5) -10(6) cm(-3) in the PDR NGC 7023 NW and 10(4)-10(5) cm(-3) in the PDR NGC 7023 E and a subsequent decrease inside the cloud. Close to the PDR edges, the dust temperature (30 K and 20 K for the NW and E PDRs, respectively) is lower than the gas temperature derived from CO lines (65-130 K and 45-55 K, respectively). Further inside the cloud, the dust and gas temperatures are similar. The derived thermal pressure is about 10 times higher in NGC 7023 NW than in NGC 7023 E. Comparing the physical conditions to the positions of known young stellar object candidates in NGC 7023 NW, we find that protostars seem to be spatially correlated with the dense structures. Conclusions. Our approach combining both dust and gas delivers strong constraints on the physical conditions of the PDRs. We find dense and warm molecular gas of high column density in the PDRs.

Optical diffraction tomography within a variational Bayesian framework

Optical diffraction tomography techniques aim to find an image of an unknown object (e.g. a map of its refraction index) using measurements of the scattered field that results from its interaction with a known interrogating wave. We address this issue as a nonlinear inverse scattering problem. The forward model is based upon domain integral representations of the electric field whose discrete counterparts are obtained by means of a method of moments. The inverse problem is tackled in a Bayesian estimation framework involving a hierarchical prior model that accounts for the piece-wise homogeneity of the object. A joint unsupervised estimation approach is adopted to estimate the induced currents, the contrast and all the other parameters introduced in the prior model. As an analytic expression for the joint maximum a posteriori (MAP) and posterior mean (PM) estimators is hard to obtain, a tractable approximation of the latter is proposed. This approximation is based upon a variational Bayesian technique and consists in the best separable distribution that approximates the true posterior distribution in the Kullback–Leibler sense. This leads to an implicit parametric optimization scheme which is solved iteratively.

Variational Bayes and Mean Field Approximations for Markov field unsupervised estimation

We consider the problem of parameter estimation of Markovian models where the exact computation of the partition function is not possible or computationally too expensive withMCMCmethods. The main idea is then to approximate the expression of the likelihood by a simpler one where we can either have an analytical expression or compute it more efficiently. We consider two approaches: Variational Bayes Approximation (VBA) and Mean Field Approximation (MFA) and study the properties of such approximations and their effects on the estimation of the parameters.

Variational Bayes Approach For Tomographic Reconstruction

In this paper, we apply the Bayesian inference method in a tomographic reconstruction problem. For this purpose, we propose a Gauss‐Markov field with Potts region label model for the images. Most of model parameters are unknown and we wish to estimate them jointly with the object of interest. Using the variational Bayes framework, the joint posterior law is approximated by a product of marginal laws whose shaping parameter equations are derived. An application to tomographic reconstruction is presented with discussion of convergence and quality of this estimation.