Numerical Investigations of Star Formation and Interstellar Clouds

This thesis explores several related questions on the physics of star formation and interstellar clouds. Chapter 2 addresses the remarkable independence of the stellar initial mass function to gas metallicity across a wide a range of galactic and extra-galactic environments. I perform analytic calculations that suggest the temperature structure of a centrally heated, dusty gas cloud should be relatively insensitive to the dust-to-gas ratio over the range of variation probed by observations. I support these calculations with full radiation-hydrodynamic simulations. Chapter 3 investigates the fragmentation of magnetized, massive cores via direct numerical simulation, finding that a combination of magnetic fields and protostellar heating strongly suppresses core fragmentation. These results could explain why the stellar initial mass function so closely resembles the dense core mass function, even at very high core masses. Chapter 4 analyzes the magnetic field structure around a rotationally-dominated protostellar disk formed in the above simulations. I present a map of the column density, magnetic field vectors, and outflow lobes at various length scales and viewing angles that can be compared against observations. I find that the disk begins to influence the geometry of the magnetic field on ∼ 100 AU scales, which should begin to be probed in nearby stellar cores by the next generation of radio interferometers. Chapter 5 addresses the long-standing question of the high CH+ abundance along diffuse molecular sight lines. I compute the CH+ abundance in a turbulent, diffuse molecular cloud by post-processing numerical simulations of magnetohydrodynamic turbulence. The results agree well with observations of the column densities of CH+ and of rotationally-excited H2. Finally, Chapter 6 presents the results of radiation-magnetohydrodynamic simulations of star formation at the cluster scale. The results show that the magnetic field plays a role in determining the star formation rate, the degree of fragmentation, and the characteristic stellar mass