Abstract. We present benchmark problems and solutions for the continuum radiative transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo and two grid-based codes is tested by comparing their results for a set of well-defined cases which differ for optical depth and viewing angle. For all the configurations, the overall shape of the resulting temperature and spectral energy distribution is well reproduced. The solutions we provide can be used for the verification of other RT codes. We also point out the advantages and disadvantages of the various numerical techniques applied to solve the RT problem.

The Diserud-Ødegaard multiple-site similarity index makes use of data on species shared by two or more sites, but produces equal similarity values in two different circumstances: species loss and true species turnover. We developed a new multiple-site similarity measure, which is independent of richness and performs better than the Diserud-Ødegaard index under conditions of equal richness between sites, because it discriminates between situations in which shared species are distributed evenly among sites or concentrated in few pairs of sites. We conducted several simulations to assess the relative performance of both the indices. The use of the new measure is recommended, enabling the simultaneous analysis of turnover and richness gradients based on two independent measures.

Abstract. In this paper, we present a refined Monte Carlo method for the solution of multi-dimensional radiative transfer problems in dusty media, for instance in the circumstellar envelopes of AGB and post AGB stars. In order to push the performance of the Monte Carlo method, we have included several basic improvements of the standard procedure which avoid the usual increase of the noise level in extremely optically thin or optically thick situations. The improvements comprise an accurate temperature determination scheme, e.g. based on the calculation of mean intensities, and an inclusion of several deterministic elements for the treatment of the absorption during the photon propagation. The method is capable of accurately modelling discontinuous opacity structures, such as clumpy media, and is applicable in a broad range of optical depths. It can provide the gas and dust temperature structures required for a more complex physical modelling, e.g. hydrodynamics, chemistry or dust formation. It may be used to predict colours, spectral energy distributions, visibilities and monochromatic images. The paper is completed by an exploration of the influence of dust clouds and small holes in dust shells on the spectral energy distribution and their optical appearance in monochromatic images. The underlying temperature structures are discussed.

Context. Despite observational evidences, InfraRed (IR) excess of classical Cepheids are seldom studied and poorly understood, but probably induces systematics on the Period-Luminosity (PL) relation used in the calibration of the extragalactic distance scale. Aims. This study aims to understand the physical origin of the IR excess found in the spectral energy distribution (SED) of 5 Cepheids : RS Pup (P = 41.46d), ζ Gem (P = 10.15d), η Aql (P = 7.18d), V Cen (P = 5.49d) and SU Cyg (P = 3.85d). Methods. A time series of atmospheric models along the pulsation cycle are fitted to a compilation of data, including optical and near-IR photometry, Spitzer spectra (secured at a specific phase), interferometric angular diameters, effective temperature estimates, and radial velocity measurements. Herschel images in two bands are also analyzed qualitatively. In this fitting process, based on the SPIPS algorithm, a residual is found in the SED, whatever the pulsation phase, and for wavelengths larger than about 1.2µm, which corresponds to the so-determined infrared excess of Cepheids. This IR excess is then corrected from interstellar medium absorption in order to infer or not the presence of dust shells, and is finally used in order to fit a model of a shell of ionized gas. Results. For all Cepheids, we find a continuum IR excess increasing up to ≈-0.1 magnitudes at 30µm, which cannot be explained by a hot or cold dust model of CircumStellar Environment (CSE). However, a weak but significant dust emission at 9.7 µm is found for ζ Gem, η Aql and RS Pup, while clear interstellar clouds are seen in the Herschel images for V Cen and RS Pup. We show, for the first time, that the IR excess of Cepheids can be explained by free-free emission from a thin shell of ionized gas, with a thickness of 15% of the star radius, a mass of 10 −9 − 10 −7 M and a temperature ranging from 3500 to 4500K. Conclusions. The presence of a thin shell of ionized gas around Cepheids has to be tested with interferometers operating in visible, in the mid-IR or in the radio domain. The impact of such CSEs of ionized gas on the PL relation of Cepheids needs also more investigations.A&A proofs: manuscript no. draft_vh_paperI around 3 stellar radii and a flux contribution in the K band, ranging from 2% to 10% of the continuum, for medium-and longperiod Cepheids respectively, while it is around 10% or more in the N band. However, we still do not know how these CSEs are produced, neither their nature, nor their characteristics (density and temperature profiles, chemical composition...).This paper aims at building a phase-dependent Spectral Energy Distribution (SED) of a sample of Cepheids from visible to mid-IR wavelengths and compare it with dedicated atmospheric models in order to quantify and study their IR excess. We present the IR excess of the stars in the sample in Sect. 2 using photometric and Spitzer observations in various bands, and we study qualitatively far-infrared images from Herschel. In Sect. 3 we correct the spectra from interstellar foreground...