Statistics – Computation
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........26h&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF CALIFORNIA, BERKELEY, 1995.Source: Dissertation Abstracts International, Volume: 57-03, Section: B
Statistics
Computation
4
Star Formation
Scientific paper
We present a theoretical formalism to evaluate the structure of molecular clouds and to determine precollapse conditions in star-forming regions. Models consist of pressure-bounded, self-gravitating spheres of a single -fluid ideal gas. We treat the case without rotation. The analysis is generalized to consider states in hydrostatic equilibrium maintained by multiple pressure components. Individual pressures vary with density as P_i(r) ~ rho^{gamma {rm p},i}(r), where gamma_{rm p},i is the polytropic index. Evolution depends additionally on whether conduction occurs on a dynamical time scale and on the adiabatic index gammai of each component, which is modified to account for the effects of any thermal coupling to the environment of the cloud. Special attention is given to properly representing the major contributors to dynamical support in molecular clouds: the pressures due to static magnetic fields, Alfven waves, and thermal motions. Straightforward adjustments to the model allow us to treat the intrinsically anisotropic support provided by the static fields. We derive structure equations, as well as perturbation equations for performing a linear stability analysis. The analysis provides insight on the nature of dynamical motions due to collapse from an equilibrium state and estimates the mass of condensed objects that form in such a process. After presenting a set of general results, we describe models of star-forming regions that include the major pressure components. We parameterize the extent of ambipolar diffusion. The analysis contributes to the physical understanding of several key results from observations of these regions. Commonly observed quantities are explicitly cross-referenced with model results. We theoretically determine density and linewidth profiles on scales ranging from that of molecular cloud cores to that of giant molecular clouds (GMCs). The model offers an explanation of the mean pressures in GMCs, which are observed to be high relative to that in the intercloud medium. We estimate what fraction of a cloud on the verge of gravitational collapse will ultimately form a condensed object, and we predict the qualitative appearance of the collapse. Finally, we simulate fragmentation--a key step in the star-forming process whereby molecular clouds or clumps within more massive clouds break up into substantially less massive cores that can in turn condense into stars. Fragmentation occurs in the context of dynamical collapse--a highly nonlinear process--so it has been difficult to reach a consensus on its specific appearance or on the influence of initial conditions. Increases in density by several orders of magnitude and the unknown, time-dependent positions of the rapidly evolving fragments present difficulties for the simulation of fragmentation. In order to increase the efficiency and effective resolution with which we can model this process, we have assembled can adaptive mesh refinement (AMR) hydrodynamics algorithm and an adaptive elliptical solver for self-gravity. The code is adaptive in the sense that it can dynamically and automatically alter the configuration of a recursively finer mesh in the computational domain. A test suite helps confirm the proper operation of the algorithm. Using initial conditions adopted in previous fragmentation studies, we simulate the collapse of a molecular cloud core. (Abstract shortened by UMI.).
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