Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Physics and Astronomy


Ralph E. Pudritz


Giant molecular clouds (GMCs) and cores, which are the sites of star formation in the Galaxy today, are supported against their own gravity and an external pressure by a combination of thermal and magnetic pressures, and by an internal turbulence which is characterized by gas velocity dispersions that increase outwards within a given cloud. Until now, however, models of isothermal spheres (in which velocity dispersion is independent of radius) have been used as the starting point for theories of star formation. Thus, this thesis presents a generalization of the classic Bonnor-Ebert stability analysis of pressure-bounded, self-gravitating spheres of isothermal gas, to include clouds with arbitrary equations of state (EOS). The results are applied to GMCs and cores in order to model their internal structure. It is found that the simplest EOS which is consistent with all the salient features of these clouds is a "pure logotrope," in which P/Pⅽ=1+A ln(ρ/ρc). Detailed comparisons with data are made to estimate the value of A, and an excellent fit to the observed dependence of velocity dispersion on radius in cores is obtained with A≃0.2. This phenomenological model is then used to construct a new theory for gravitational collapse and star formation in turbulent molecular gas. Points of similarity and contrast between this and the collapse of an isothermal sphere are discussed. In particular, it is found that the rate of mass accretion onto a protostar in a logotrope increases with time (as M∝ t³), rather than remaining constant as in an isothermal sphere. Low-mass stars therefore take longer to form than previously suspected, while high-mass stars form more rapidly. This result has implications for the interpretation of observations of young stellar objects (the so-called "Class 0" protostars are discussed explicitly), for the origin and form of the stellar initial mass function, and for the process of star formation in clusters.

GMCs and cores are further characterized by a mass spectrum, N(m)=dN/dm, which scales roughly as m⁻¹⋅⁵ and is reminiscent of the distribution of globular cluster masses in the globular cluster systems (GCSs) observed around most galaxies. This suggests that star formation in protogalaxies may have followed the same basic pattern that it does today, i.e., that globular clusters formed in clumps of gas embedded in much larger (∼10⁸-10⁹M⨀) protogalactic fragments. Within this framework, the first theory of the GCS N(m) (which is directly related to the more frequently discussed globular cluster luminosity function, dN/dMᵥ) is developed here. A kinetic equation is formulated to statistically follow the collisional build-up and subsequent disruption (by the side-effects of internal massive-star formation) of protocluster clumps within a parent fragment, and solved for the mass spectrum which gives a detailed balance between the rates of these processes. This N(m) agrees well with observations of the Milky Way, M31, and M87 GCSs, for cluster masses in excess of ∼10⁵M⨀. In addition, the theory naturally accounts for observations which suggest that, at least at these high masses, N(m) is largely independent of galactocentric radius within any one GCS. The model makes specific predictions, regarding the lifetimes of cluster-forming cores, that should be applicable to present-day Galactic GMCs and cores as well.

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