Evolution of interstellar dust with<i>Herschel</i>. First results in the photodissociation regions of NGC 7023

<i>Context. <i/>In photodissociation regions (PDRs), the physical conditions and the excitation evolve on short spatial scales as a function of depth within the cloud, providing a unique opportunity to study how the dust and gas populations evolve with the excitation and physical conditions. The mapping of the PDRs in NGC 7023 performed during the science demonstration phase of <i>Herschel <i/> is part of the “Evolution of interstellar dust” key program. The goal of this project is to build a coherent database on interstellar dust emission from diffuse clouds to the sites of star formation. <i>Aims. <i/>We study the far-infrared/submillimeter emission of the PDRs and their fainter surrounding regions. We combine the <i>Herschel<i/> and <i>Spitzer<i/> maps to derive at each position the full emission spectrum of all dust components, which we compare to dust and radiative transfer models in order to learn about the spatial variations in both the excitation conditions and the dust properties. <i>Methods. <i/>We adjust the emission spectra derived from PACS and SPIRE maps using modified black bodies to derive the temperature and the emissivity index <i>β<i/> of the dust in thermal equilibrium with the radiation field. We present a first modeling of the NGC 7023-E PDR with standard dust properties and abundances.<i>Results. <i/>At the peak positions, a value of <i>β<i/> equal to 2 is compatible with the data. The detected spectra and the spatial structures are strongly influenced by radiative transfer effects. We are able to reproduce the spectra at the peak positions deduced from <i>Herschel<i/> maps and emitted by dust particles at thermal equilibrium, and also the evolution of the spatial structures observed from the near infrared to the submillimeter. On the other hand, the emission of the stochastically heated smaller particles is overestimated by a factor ~2.