Ph.D. Thesis [2000-2004]
Désordre et cohérence dans les structures du milieu interstellaire: analyse statistique, filtrage interférométrique et transfert radiatif
Supervisors : Edith Falgarone & François Viallefond
Observations of the molecular phase of the interstellar medium reveal a hierarchy of complex structures, both in density and velocity, over more than four decades. The understanding of physical phenomena leading to this structuration and to the first stages of star formation, calls for a proper description of fields which observers do not have direct access to. It is therefore necessary to understand the chain of physical, observational and instrumental processes providing the observer with meaningful quantities. Three aspects of this problem are considered here.
The observed structures are the result of a complex projection of three-dimensional fields onto a position-position-velocity space, from which two-dimensional maps of intensity and velocity centroids are constructed. We establish the relationships between the statistical properties of these maps and those of the original fields. In particular, we show that the spectral index of the velocity centroids' map is equal to that of the velocity field, in the approximation of small density fluctuations, which is discussed numerically.
Also, interferometric observations impose a filtering of spatial frequencies, which degrades the brightness distributions over the plane of the sky. In the purpose of evaluating the performances of the forthcoming ALMA instrument, we show, using numerical simulations, that the power spectrum is the most suited tool to recover structural characteristics from the dirty maps. We furthermore introduce a new and promising method of analysis, based on the increments of Fourier phases.
Finally, we consider the problem of interstellar line formation in the framework of a one-dimensional stochastic radiative transfer formalism. We introduce the case of correlations between the velocity and density fields through a polytropic relation, and we come up with a generalized transfer equation. We show that the probability distribution function of line-of-sight velocities is non-Gaussian, contrary to the uncorrelated case, which strongly suggests that these correlations should be taken into account in the interpretation of line profiles.
Part I : Structuration du milieu interstellaire
Part II : Éléments mathématiques et outils d'analyse
Part III : Statistique des centroïdes de vitesse
Part IV : Filtrage interférométrique des structures
Part V : Transfert radiatif dans les milieux complexes