Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

I. A recirculating charged-couple device. II. The mercury selenide on N-silicon Schottky barrier

A recirculating charge-coupled device structure has been devised. Entrance and exit gates allow a signal to be admitted, recirculated a given number of times, and then examined. In this way a small device permits simulation of a very long shift register without passing the signal through input and output diffusions. An oscilloscope motion picture demonstrating degradation of an actual circulating signal has been made. The performance of the device in simulating degradation of a signal by a very long shift register is well fit by a simple model based on transfer inefficiency.

Electrical properties of the mercury selenide on n-type chemically-cleaned silicon Schottky barrier have been studied. Barrier heights measured were 0.96 volts for the photoresponse technique and 0.90 volts for the current-voltage technique. These are the highest barriers yet reported on n-type silicon.

Theory of viscous and thermal attenuation of sound by small spheres

The problem is to calculate the attenuation of plane sound waves passing through a viscous, heat-conducting fluid containing small spherical inhomogeneities. The attenuation is calculated by evaluating the rate of increase of entropy caused by two irreversible processes: (1) the mechanical work done by the viscous stresses in the presence of velocity gradients, and (2) the flow of heat down the thermal gradients. The method is first applied to a homogeneous fluid with no spheres and shown to give the classical Stokes-Kirchhoff expressions. The method is then used to calculate the additional viscous and thermal attenuation when small spheres are present. The viscous attenuation agrees with Epstein's result obtained in 1941 for a non-heat-conducting fluid. The thermal attenuation is found to be similar in form to the viscous attenuation and, for gases, of comparable magnitude. The general results are applied to the case of water drops in air and air bubbles in water.

For water drops in air the viscous and thermal attenuations are camparable; the thermal losses occur almost entirely in the air, the thermal dissipation in the water being negligible. The theoretical values are compared with Knudsen's experimental data for fogs and found to agree in order of magnitude and dependence on frequency. For air bubbles in water the viscous losses are negligible and the calculated attenuation is almost completely due to thermal losses occurring in the air inside the bubbles, the thermal dissipation in the water being relatively small. (These results apply only to non-resonant bubbles whose radius changes but slightly during the acoustic cycle.)

I. The crystal structure of trimesic acid. II. Topics in crystallographic calculations

I. Trimesic acid (1, 3, 5-benzenetricarboxylic acid) crystallizes with a monoclinic unit cell of dimensions a = 26.52 A, b = 16.42 A, c = 26.55 A, and β = 91.53° with 48 molecules /unit cell. Extinctions indicated a space group of Cc or C2/c; a satisfactory structure was obtained in the latter with 6 molecules/asymmetric unit - C₅₄O₃₆H₃₆ with a formula weight of 1261 g. Of approximately 12,000 independent reflections within the CuK_α sphere, intensities of 11,563 were recorded visually from equi-inclination Weissenberg photographs.

The structure was solved by packing considerations aided by molecular transforms and two- and three-dimensional Patterson functions. Hydrogen positions were found on difference maps. A total of 978 parameters were refined by least squares; these included hydrogen parameters and anisotropic temperature factors for the C and O atoms. The final R factor was 0.0675; the final "goodness of fit" was 1.49. All calculations were carried out on the Caltech IBM 7040-7094 computer using the CRYRM Crystallographic Computing System.

The six independent molecules fall into two groups of three nearly parallel molecules. All molecules are connected by carboxylto- carboxyl hydrogen bond pairs to form a continuous array of sixmolecule rings with a chicken-wire appearance. These arrays bend to assume two orientations, forming pleated sheets. Arrays in different orientations interpenetrate - three molecules in one orientation passing through the holes of three parallel arrays in the alternate orientation - to produce a completely interlocking network. One third of the carboxyl hydrogen atoms were found to be disordered.

II. Optical transforms as related to x-ray diffraction patterns are discussed with reference to the theory of Fraunhofer diffraction.

The use of a systems approach in crystallographic computing is discussed with special emphasis on the way in which this has been done at the California Institute of Technology.

An efficient manner of calculating Fourier and Patterson maps on a digital computer is presented. Expressions for the calculation of to-scale maps for standard sections and for general-plane sections are developed; space-group-specific expressions in a form suitable for computers are given for all space groups except the hexagonal ones.

Expressions for the calculation of settings for an Eulerian-cradle diffractometer are developed for both the general triclinic case and the orthogonal case.

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Stopping power of gases for heavy ions

Pulse-height and time-of-flight methods have been used to measure the electronic stopping cross sections for projectiles of ¹²C, ¹⁶O, ¹⁹F, ²³Na, ²⁴Mg, and ²⁷Al, slowing in helium, neon, argon, krypton, and xenon. The ion energies were in the range 185 keV ≤ E ≤ 2560 keV.

A semiempirical calculation of the electronic stopping cross section for projectiles with atomic numbers between 6 and 13 passing through the inert gases has been performed using a modification of the Firsov model. Using Hartree-Slater-Fock orbitals, and summing over the losses for the individual charge states of the projectiles, good agreement has been obtained with the experimental data. The main features of the stopping cross section seen in the data, such as the Z₁ oscillation and the variation of the velocity dependence on Z₁ and Z₂, are present in the calculation. The inclusion of a modified form of the Bethe-Bloch formula as an additional term allows the increase of the velocity dependence for projectile velocities above v_o to be reproduced in the calculation.

Effect of Microstructural Interfaces on the Mechanical Response of Crystalline Metallic Materials

Advances in nano-scale mechanical testing have brought about progress in the understanding of physical phenomena in materials and a measure of control in the fabrication of novel materials. In contrast to bulk materials that display size-invariant mechanical properties, sub-micron metallic samples show a critical dependence on sample size. The strength of nano-scale single crystalline metals is well-described by a power-law function, σαD^-n, where D is a critical sample size and n is a experimentally-fit positive exponent. This relationship is attributed to source-driven plasticity and demonstrates a strengthening as the decreasing sample size begins to limit the size and number of dislocation sources. A full understanding of this size-dependence is complicated by the presence of microstructural features such as interfaces that can compete with the dominant dislocation-based deformation mechanisms. In this thesis, the effects of microstructural features such as grain boundaries and anisotropic crystallinity on nano-scale metals are investigated through uniaxial compression testing. We find that nano-sized Cu covered by a hard coating displays a Bauschinger effect and the emergence of this behavior can be explained through a simple dislocation-based analytic model. Al nano-pillars containing a single vertically-oriented coincident site lattice grain boundary are found to show similar deformation to single-crystalline nano-pillars with slip traces passing through the grain boundary. With increasing tilt angle of the grain boundary from the pillar axis, we observe a transition from dislocation-dominated deformation to grain boundary sliding. Crystallites are observed to shear along the grain boundary and molecular dynamics simulations reveal a mechanism of atomic migration that accommodates boundary sliding. We conclude with an analysis of the effects of inherent crystal anisotropy and alloying on the mechanical behavior of the Mg alloy, AZ31. Through comparison to pure Mg, we show that the size effect dominates the strength of samples below 10 μm, that differences in the size effect between hexagonal slip systems is due to the inherent crystal anisotropy, suggesting that the fundamental mechanism of the size effect in these slip systems is the same.

Microelectrode Implants for Spinal Cord Stimulation in Rats

Paralysis is a debilitating condition afflicting millions of people across the globe, and is particularly deleterious to quality of life when motor function of the legs is severely impaired or completely absent. Fortunately, spinal cord stimulation has shown great potential for improving motor function after spinal cord injury and other pathological conditions. Many animal studies have shown stimulation of the neural networks in the spinal cord can improve motor ability so dramatically that the animals can even stand and step after a complete spinal cord transaction.

This thesis presents work to successfully provide a chronically implantable device for rats that greatly enhances the ability to control the site of spinal cord stimulation. This is achieved through the use of a parylene-C based microelectrode array, which enables a density of stimulation sites unattainable with conventional wire electrodes. While many microelectrode devices have been proposed in the past, the spinal cord is a particularly challenging environment due to the bending and movement it undergoes in a live animal. The developed microelectrode array is the first to have been implanted in vivo while retaining functionality for over a month. In doing so, different neural pathways can be selectively activated to facilitate standing and stepping in spinalized rats using various electrode combinations, and important differences in responses are observed.

An engineering challenge for the usability of any high density electrode array is connecting the numerous electrodes to a stimulation source. This thesis develops several technologies to address this challenge, beginning with a fully passive implant that uses one wire per electrode to connect to an external stimulation source. The number of wires passing through the body and the skin proved to be a hazard for the health of the animal, so a multiplexed implant was devised in which active electronics reduce the number of wires. Finally, a fully wireless implant was developed. As these implants are tested in vivo, encapsulation is of critical importance to retain functionality in a chronic experiment, especially for the active implants, and it was achieved without the use of costly ceramic or metallic hermetic packaging. Active implants were built that retained functionality 8 weeks after implantation, and achieved stepping in spinalized rats after just 8-10 days, which is far sooner than wire-based electrical stimulation has achieved in prior work.

Photoproduction of charged pion pairs from hydrogen at energies up to 1500 MeV

Charged pion pair photoproduction has been investigated up to a gamma energy of 1500 MeV, using the Caltech 12-inch heavy liquid bubble chamber with a small diameter, high intensity photon beam passing through a central beam tube gaseous hydrogen target surrounded by the sensitive Freon. Scanning, analysis, and data reduction techniques have been developed to deal with the problems of two-vie stereo, hidden event origins, absence of magnetic field, and the range-energy and multiple scattering relationships that occur in the heavy materials. Roughly 5700 pictures have been scanned and analyzed, yielding 754 acceptable events. Cross section and parameter distributions are generally consistent with the results of previous experiments. A statistically insignificant “bump” was observed in the dipion mass spectrum in the region of 500 MeV, the disputed σ meson mass. This region was investigated as carefully as the limited statistics would allow; dipion angular distributions are consistent with isotropy, and there is indication that some of the events in this region might come from decay of an intermediate N*₁₁ (1425) into a proton and dipion.

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CP and the three pion decay of the K°

The time distribution of the decays of an initially pure K° beam into π+π-π° has been analyzed to determine the complex parameter W (also known as Ƞ^+-° and (x + iy)). The K° beam was produced in a brass target by the interactions of a 2.85 GeV/c π- beam which was generated on an internal target in the Lawrence Radiation Laboratory (LRL) Bevatron. The counters and hodoscopes in the apparatus selected for events with a neutral (K°) produced in the brass target, two charged secondaries passing through a magnet spectrometer and a ɣ-ray shower in a shower hodoscope.

From the 275K apparatus triggers, 148 K → π+π-π° events were isolated. The presence of a ɣ-ray shower in the optical shower chambers and a two-prong vee in the optical spark chambers were devices used to isolate the events. The backgrounds were further reduced by reconstructing the momenta of the two charged secondaries and applying kinematic constraints.

The best fit to the final sample of 148 events distributed between .3 and 7.0 K_S lifetimes gives:

ReW = -.05 ±.17

ImW = +.39 +.35/-.37

This result is consistent with both CPT invariance (ReW = 0) and CP invariance (W = 0). Backgrounds are estimated to be less than 10% and systematic effects have also been estimated to be negligible.

An analysis of the present data on CP violation in this decay mode and other K° decay modes has estimated the phase of ɛ to be 45.3 ± 2.3 degrees. This result is consistent with the super weak theories of CP violation which predicts the phase of ɛ to be 43°. This estimate is in turn used to predict the phase of Ƞ°° to be 48.0 ± 7.9 degrees. This is a substantial improvement on presently available measurements. The largest error in this analysis comes from the present limits on W from the world average of recent experiments. The K → πuʋ mode produces the next largest error. Therefore further experimentation in these modes would be useful.