Date of Award

12-2012

Level of Access Assigned by Author

Campus-Only Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor

Neil F. Comins

Second Committee Member

David J. Batuski

Third Committee Member

Susan R. McKay

Abstract

This work hypothesizes that supernovae and other extreme astrophysical phenomena, recently recognized as much more inhomogeneous and turbulent than previously supposed, give rise to and then eject substellar-mass or Dwarf Black Holes (DBHs), along with their other ejecta. Two independent methods for detecting regions within a data set from a simulation of a high energy astrophysical event, such as a supernova, that are unstable to gravitational collapse. These methods can be used where the resolution, spatial domain, time span, and/or treatment of general relativity of the simulation may not be sufficient to evolve the region to gravitational collapse natively.

The first method seeks acoustic instability against gravitational collapse. That is, some hypothetical bodies exhibit perturbative eigenmodes that grow in amplitude, rather than oscillate, and Subrahmanyan Chandrasekhar derived a theorem to prove whether such modes exist for a given distribution of matter. The Chandrasekhar (acoustic) stability theorem is adapted for use within a hot, dense medium. The accuracy of this method is demonstrated by applying it to various spherical mass distributions whose stability is known through other means. This method has already been used in the analysis of data sets from three simulations, with negative results. The adaptation is limited to DBHs of masses above a minimum threshold, however, prompting the division of DBH progenitors into Type I, the more massive subclass that can be treated fully within the acoustic stability framework, and Type II, which range in mass from the bottom of the Type I mass range down to arbitrarily small.

The second method for detecting instability against gravitational collapse seeks gravitational collapse induced by inward-propagating, spherically symmetric shocks in the Groah and Temple [1,2] (GST) theoretical prescription. Using the only extant general-relativistic shockwave simulator, written by Zeke Vogler, it is revealed that all solutions to the GST prescription are related via simple coordinate transformations. This insight is proved analytically by removing the dimensions from the metric and all related equations, revealing that the parameter that indexes the family of GST solutions vanishes entirely.

An algorithm is developed for determining the appropriate scaling of the dimensionless GST solution when comparing that solution to regions within a data set from a simulation of an extreme astrophysical phenomenon. This method is applied to the same data set as the primary acoustic analysis, and again returns negative results.

A family of original numeric integration methods based on the neglected Adams- Bashforth [3] (AB) and Adams-Moulton [4] (AM) linear multistep methods is presented. This method family, which I call the adaptive mesh Adams-Bashforth-Moulton (ABM) predictor-corrector methods, was developed in order to reduce the computational time required for this project. The methods were implemented, validated, and tested for performance against a series of testbed problems increasing in complexity. These problems included the integration of a known polynomial and solving the famous Tolman- Oppenheimer-Volkoff [5] (TOV) problem of determining the maximum mass of fully relativistic neutrons that can support themselves hydrostatically (non-rotating) against gravitational collapse in a fully general relativistic context. The adaptive mesh ABM predictor-corrector methods have a suite of advantageous features that compares well with state of the art integration methods.

Finally, the physical and observational consequences of the ongoing production of low-mass, high-velocity black holes are outlined.

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