We investigate the collapse of non-spherical substructures, such as sheets and filaments, which are ubiquitous in molecular clouds. Such non-spherical substructures collapse homologously in their interiors but are influenced by an edge effect that causes their edges to be preferentially accelerated. We analytically compute the homologous collapse timescales of the interiors of uniform-density, self-gravitating filaments and find that the homologous collapse timescale scales linearly with the aspect ratio. The characteristic timescale for an edge-driven collapse mode in a filament, however, is shown to have a square-root dependence on the aspect ratio. For both filaments and circular sheets, we find that selective edge acceleration becomes more important with increasing aspect ratio. In general, we find that lower dimensional objects and objects with larger aspect ratios have longer collapse timescales. We show that estimates for star formation rates, based upon gas densities, can be overestimated by an order of magnitude if the geometry of a cloud is not taken into account.

We study the evolution of the interstellar and circumstellar media around massive stars (M 40M ⊙ ) from the main sequence through to the Wolf-Rayet stage by means of radiationhydrodynamic simulations. We use publicly available stellar evolution models to investigate the different possible structures that can form in the stellar wind bubbles around Wolf-Rayet stars. We find significant differences between models with and without stellar rotation, and between models from different authors. More specifically, we find that the main ingredients in the formation of structures in the Wolf-Rayet wind bubbles are the duration of the Red Supergiant (or Luminous Blue Variable) phase, the amount of mass lost, and the wind velocity during this phase, in agreement with previous authors. Thermal conduction is also included in our models. We find that main-sequence bubbles with thermal conduction are slightly smaller, due to extra cooling which reduces the pressure in the hot, shocked bubble, but that thermal conduction does not appear to significantly influence the formation of structures in post-main-sequence bubbles. Finally, we study the predicted X-ray emission from the models and compare our results with observations of the Wolf-Rayet bubbles S 308, NGC 6888, and RCW 58. We find that bubbles composed primarily of clumps have reduced X-ray luminosity and very soft spectra, while bubbles with shells correspond more closely to observations.

Molecular clouds often exhibit filamentary or sheet-like shapes. We compute the free-fall time (τ ff ) for finite, uniform, self-gravitating circular sheets and filamentary clouds of small but finite thickness, so that their volume density ρ can still be defined. We find that, for thin sheets, the free-fall time is larger than that of a uniform sphere with the same volume density by a factor proportional to √ A, where the aspect ratio A is given by A = R/h, R being the sheet's radius and h is its thickness. For filamentary clouds, the aspect ratio is defined as A = L/R, where L is the filament's half length and R is its (small) radius, and the modification factor is a more complicated, although in the limit of large A it again reduces to nearly √ A. We propose that our result for filamentary shapes naturally explains the ubiquitous configuration of clumps fed by filaments observed in the densest structures of molecular clouds. Also, the longer free-fall times for non-spherical geometries in general may contribute towards partially alleviating the "star-formation conundrum", namely, that the star formation rate in the Galaxy appears to be proceeding in a timescale much larger than the total molecular mass in the Galaxy divided by its typical free-fall time. If molecular clouds are in general formed by thin sheets and long filaments, then their relevant free-fall time may have been systematically underestimated, possibly by factors of up to one order of magnitude.