Local luminous infrared galaxies. I. Spatially resolved observations with the Spitzer infrared spectrograph

We present results from the Spitzer Infrared Spectrograph spectral mapping observations of 15 local luminous infrared galaxies (LIRGs). In this paper, we investigate the spatial variations of the mid-IR emission which includes fine structure lines, molecular hydrogen lines, polycyclic aromatic features (PAHs), continuum emission, and the 9.7 μm silicate feature. We also compare the nuclear and integrated spectra. We find that the star formation takes place in extended regions (several kpc) as probed by the PAH emission, as well as the [Ne II]12.81 μm and [Ne III]15.56 μm emissions. The behavior of the integrated PAH emission and 9.7 μm silicate feature is similar to that of local starburst galaxies. We also find that the minima of the [Ne III]15.56 μm/[Ne II]12.81 μm ratio tends to be located at the nuclei and its value is lower than that of H II regions in our LIRGs and nearby galaxies. It is likely that increased densities in the nuclei of LIRGs are responsible for the smaller nuclear [Ne III]15.56 μm/[Ne II]12.81 μm ratios. This includes the possibility that some of the most massive stars in the nuclei are still embedded in ultracompact H II regions. In a large fraction of our sample, the 11.3 μm PAH emission appears more extended than the dust 5.5 μm continuum emission. We find a dependency of the 11.3 μm PAH/7.7 μm PAH and [Ne II]12.81 μm/11.3 μm PAH ratios with the age of the stellar populations. Smaller and larger ratios, respectively, indicate recent star formation. The estimated warm (300 K local starbursts, and Seyfert galaxies. Finally we find that the [Ne II]12.81 μm velocity fields for most of the LIRGs in our sample are compatible with a rotating disk at ~kpc scales, and they are in a good agreement with Hα velocity fields.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.