Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1053. Adviser: Frederick K. Lamb. Includes bibliographical references (leaves ) Available on microfilm from Pro Quest Information and Learning.

We present three topics in this thesis: the next generation warp bridge sampling, Bayesian methods for modeling source intensities, and large-sample hypothesis testing procedures in multiple imputation. Bridge sampling is an effective Monte Carlo method to estimate the ratio of the normalizing constants of two densities. The Monte Carlo errors of the estimator are directly controlled by the overlap between the densities. In Chapter 1, we generalize the warp transformations in Meng and Schilling (2002), and introduce a class of stochastic transformation, called warp-U transformation, which aims at increasing the overlap of the densities of the transformed data without altering the normalizing constants. Warp-U transformation is determined by a Gaussian mixture distribution, which has reasonable amount of overlap with the density of unknown normalizing constant. We show warp-U transformation reduces the f-divergence of two densities, thus bridge sampling with warp-U transformed data has better statistical efficiency than that based on the original data. We then propose a computationally efficient method to find a Gaussian mixture distribution and investigate the performance of the corresponding warp-U bridge sampling. Finally, theoretical and simulation results are provided to shed light on how to choose the tuning parameters in the algorithm. In Chapter 2, we propose a Bayesian hierarchical model to study the distribution of the X-ray intensities of stellar sources. One novelty of the model is its use of a zero-inflated gamma distribution for the source intensities to reflect the possibility of “dark” sources with practically zero luminosity. To quantify the evidence for “dark” sources, we develop a Bayesian hypothesis testing procedure based on the posterior predictive p-value. Statistical properties of the model and the test are investigated via simulation. Finally, we apply our method to a real dataset from Chandra. Chapter 3 presents large-sample hypothesis testing procedures in multiple imputation, a common practice to handle missing data. Several procedures are classified, discussed, and compared in details. We also provide an improvement of a Wald-type procedure and investigate a practical issue of the likelihood-ratio based procedure. / Statistics

An understanding of radiation is paramount for connecting observations of accretion disks with the theory of black holes. In this thesis, we explore via radiative transfer postprocessing calculations the observational signatures of black holes. We investigate disk spectra by analyzing general relativistic magnetohydrodynamic (GRMHD) simulations of accretion disks. For the most part there are no surprises -- the resulting GRMHD spectrum is very close to the analytic Novikov & Thorne (1973) prediction from decades past, except for a small modification in the case of spinning black holes, which exhibit a high-energy power-law tail that is sourced by hot Comptonized gas from within the plunging region of the accretion flow. These conclusions are borne out by both 1D and 3D radiative transfer calculations of the disk. Significant effort was spent in developing from scratch the 3D radiative code that we used for the analysis. The code is named HERO (Hybrid Evaluator for Radiative Objects) and it is a new general purpose grid-based 3D general relativistic radiative solver. / Astronomy

We present full-sky, high-resolution maps of interstellar dust based on data from the Wide-field Infrared Survey Explorer (WISE) and Planck missions. We describe our custom processing of the entire WISE 12 micron All-Sky imaging data set, and present the resulting 15 arcsecond resolution, full-sky map of diffuse Galactic dust emission, free of compact sources and other contaminating artifacts. Our derived 12 micron dust map offers angular resolution far superior to that of all other existing full-sky, infrared dust emission maps, revealing a wealth of small-scale filamentary structure. We also apply the Finkbeiner et al. (1999) two-component thermal dust emission model to the Planck HFI maps. We derive full-sky 6.1 arcminute resolution maps of dust optical depth and temperature by fitting this two-component model to Planck 217-857 GHz along with DIRBE/IRAS 100 micron data. In doing so, we obtain the first ever full-sky 100-3000 GHz Planck-based thermal dust emission model, as well as a dust temperature correction with ~10 times enhanced angular resolution relative to DIRBE-based temperature maps. Analyzing the joint Planck/DIRBE dust spectrum, we show that two-component models provide a better fit to the 100-3000 GHz emission than do single-MBB models, though by a lesser margin than found by Finkbeiner et al. (1999) based on FIRAS and DIRBE. We find that, in diffuse sky regions, our two-component 100-217 GHz predictions are on average accurate to within 2.2%, while extrapolating the Planck Collaboration (2013) single-MBB model systematically underpredicts emission by 18.8% at 100 GHz, 12.6% at 143 GHz and 7.9% at 217 GHz. We calibrate our two-component optical depth to reddening, and compare with reddening estimates based on stellar spectra. We find the dominant systematic problems in our temperature/reddening maps to be zodiacal light on large angular scales and the cosmic infrared background anisotropy on small angular scales. Future work will focus on combining our WISE 12 micron dust map and Planck dust model to create a next-generation, full-sky dust extinction map with angular resolution several times better than Schlegel et al. (1998). / Physics

A wide range of potentially rocky transiting planets in the habitable zone (HZ) have been detected by Kepler as well as ground-based searches. The spectral type of the host star will influence our ability to detect atmospheric features with future space and ground based missions like JWST, GMT and E-ELT. For my thesis, I present a complete suit of stellar models with a stellar effective temperature ranging from Teff = 2300K to Teff = 7000K, sampling the entire FGKM stellar type range, for modeling extrasolar planets. I also have a grid of model atmospheres for an Earth-analogue planet orbiting stars and derive remotely detectable spectral atmospheric features. The UV emission from a planet's host star dominates the photochemistry and thus the resultant observable spectral features. Using the latest UV spectra obtained by Hubble as well as IUE, I model Earth-like planets for a wide range of host stars. I detail the results of activity on the primary detectable atmospheric features that indicate habitability on Earth, namely: H2O, O3, CH4, N2O and CH3Cl. I model the emergent spectra of Earth-analogue planets orbiting our grid of FGKM stars in the VIS/NIR (0.4 - 4 microns) and the IR (5 - 20 microns) range in accordance with future mission design concepts like JWST and direct detection missions like HDST/LUVOIR in the more distant horizon. We also model the amount of UV flux reaching the surface of Earth-like planets at various geological epochs ranging from a pre-biotic world through the rise of oxygen and for Earth-like planets orbiting FGKM stars at equivalent stages of evolution. / Astronomy

Gamma-ray bursts (GRBs) are the most energetic explosions in the Universe, thus providing a unique laboratory for the study of extreme astrophysical processes. In parallel, their large luminosity makes GRBs a premier probe of the early Universe. My thesis has explored and exploited both aspects of GRB science by addressing the following fundamental open questions: 1) what is the nature of the GRB ejecta?, 2) how does the GRB progenitor population evolve with redshift, and 3) how can GRBs be used to probe the high-redshift Universe? To answer these questions, I present the first multi-wavelength detection and modeling of a GRB reverse shock, a comprehensive analysis of the plateau phase of GRB light curves, studies of the evolution of the progenitor population to redshifts, z~9, and demonstrate the use of GRBs as probes of galaxy formation and evolution through the first galaxy mass-metallicity relation at z~3-5. I find support for baryonic ejecta in GRB~130427A, evidence that GRB jets contain a large amount of energy in slow-moving ejecta, and proof that the GRB progenitor population does not evolve to the highest redshifts at which it has yet been observed. Building on the decade of observations by the Swift GRB mission, future observations and modeling of GRBs and their host galaxies will provide clues to these and other open questions in GRB science, allowing for the first statistical studies of their progenitors and host environments to the epoch of reionization and beyond. / Astronomy

Superluminous supernovae (SLSNe) are a rare class of stellar explosions discovered by wide-field optical transient surveys in the past decade. They are characterized by peak luminosities 10-100 times that of ordinary core-collapse and Type Ia SNe, and radiated energies of order 10^51 erg, comparable to the entire kinetic energy of a canonical supernova explosion. Proposed sources of these tremendous energies include interaction between the supernova ejecta and dense circumstellar material (CSM), energy injection from the spin-down of a rapidly rotating and highly magnetized neutron star, or the pair-instability explosion of a very massive star producing several solar masses of radioactive nickel. In this thesis, I present results from the Pan-STARRS1 Medium Deep Survey (PS1/MDS), which discovered 15 hydrogen-poor SLSNe out to redshift 1.6 over the four years of its operation. I address the nature of SLSNe from two different angles. First, I characterize the SNe themselves, and compare their observed properties to model predictions. The PS1/MDS SLSN sample exhibits a diversity of light curve properties, and a wider range of peak luminosities than previously reported, particularly when accounting for the flux-limited nature of the survey. The light curves can generally be fit with magnetar spin-down models, though our sample also contains one very slowly evolving event that could plausibly be powered by radioactive decay. Second, I present the first comprehensive study of SLSN host galaxy environments and the sub-galactic environments, demonstrating that H-poor SLSNe preferentially occur in low-luminosity, low-mass, low-metallicity galaxies with high specific star formation rates. Their host galaxies are statistically distinct from the hosts of core-collapse SNe, but share many similarities with the galaxies that host long gamma-ray bursts (LGRBs). This suggests that the environmental factors leading to a massive star forming either a SLSN or a LGRB are similar, with a possible common ingredient being a preference for low-metallicity environments through the need of a progenitor with high core angular momentum. In terms of their local environments, resolved Hubble Space Telescope imaging reveals that SLSN locations are correlated with the UV light, though not as strongly as LGRBs are. Although a larger sample size is needed to distinguish them statistically, this trend is also consistent with the interpretation that SLSN progenitors are lower-mass than those of LGRBs, collapsing to form a rapidly spinning neutron star rather than a black hole launching a relativistic jet. / Astronomy

This thesis presents a series of studies on the dynamics of high mass ratio multiples, with applications to planetary systems orbiting stars and stellar systems orbiting supermassive black holes (SMBHs). Almost two thousand exoplanetary systems have recently been discovered, and their configurations gave rise to new puzzles to planetary formation theories. We studied the dynamics of planetary systems aiming to understand how the configuration of planetary system is sculptured and to probe the origin of planetary systems. First, we discussed hierarchical three-body dynamics, which can be applied to planets that are orbiting a star while perturbed by a planet or a star that is farther away. The perturbation from the farther object can flip the planetary orbits and produce counter orbiting hot Jupiters, which cannot be formed in the classical planetary formation theory. In addition, we have studied the scatter encounter of planetary systems in clusters, which produce eccentric and inclined planets. Moreover, we investigated the obliquity variation of planets, which can be applied to exoplanetary systems. The obliquity variation is important to the habitability of the exoplanets. The long term dynamics is also important to stellar systems orbiting SMBHs. SMBHs are common in the center of galaxies and lead to rich dynamical interactions with nearby stars. At the same time, dynamical features of the nearby stars reveal important properties of the SMBHs. The aforementioned hierarchical three-body dynamics can be applied to stars near SMBH binaries, which are natural consequences of galaxy mergers. We found that the distribution of stars surrounding one of the SMBHs results in a shape of torus due to the perturbation from the other SMBH, and the dynamical interactions contribute to an enhancement of tidal disruption rates, which can help identify the SMBH binaries. In addition, we investigated the heating of stars near SMBHs, where the heating of stars due to gravitational waves as the SMBHs merge may mark the merger, and provide electromagnetic counterpart for gravitational wave detection. Moreover, the accumulated tidal heating of stars may cause the stars to be more vulnerable for tidal disruptions, as the stars orbit around a SMBH in an eccentric orbit. / Astronomy

This thesis describes three investigations of the galactic abundance and properties of small planets. First, I revised the properties of the smallest Kepler target stars and searched their light curves for transits using a custom transit detection pipeline. Combining the detected population of 156 planet candidates (including one previously undetected candidate) with an empirical estimate of the search completeness based on transit injection and recovery simulations, I found occurrence rates of 0.24 (+0.18/-0.08) Earth-size planets (1− 1.5 Earth radii) and 0.21 (+0.11/-0.06) super-Earths (1.5−2 Earth radii) per M dwarf habitable zone. Consequently, the most probable distances to the nearest non-transiting and transiting potentially habitable planets are 2.6 ± 0.4 pc and 10.6 (+1.6/-1.8) pc, respectively. Second, I conducted an adaptive optics imaging survey of 87 bright Kepler target stars with ARIES at the MMT to search for nearby stars that might be diluting the depths of the planetary transits. I identified visual companions within 1” for 5 stars, between 1” and 2” for 7 stars, and between 2” and 4” for 15 stars. For all stars observed, I placed limits (typically delta Ks = 5.3 at 1” and delta Ks = 5.7 at 2”) on the presence of undetected nearby stars. Third, I investigated the composition of Kepler-93b, a 1.478 ± 0.019 Earth radius planet with a 4.7-day orbit around a bright (V = 10.2) asteroseismically-characterized host star with a mass of 0.911 ± 0.033 solar masses and a radius of 0.919 ± 0.011 solar radii. Based on two seasons of observations with HARPS-N at the Telescopio Nazionale Galileo and archival observations from Keck/HIRES, I found a mass of 4.02 ± 0.68 Earth masses and a density of 6.88 ± 1.18 g/cc. Comparing Kepler-93b to the other nine exoplanets smaller than 2.7 Earth radii with well-constrained parameters, I found that all dense exoplanets with masses of approximately 1 – 6 Earth masses are consistent with the same fixed ratio of iron to rock as the Earth and Venus. There are currently no such planets with masses greater than 7 Earth masses. Future measurements of the masses and radii of a larger sample of planets receiving a wider range of stellar insolations will reveal whether the fixed compositional model found for these seven highly-irradiated dense exoplanets extends to the full population of dense 1 – 6 Earth mass planets. / Astronomy

Relatively massive B-type stars with closely orbiting stellar companions can evolve to produce Type Ia supernovae, X-ray binaries, millisecond pulsars, mergers of neutron stars, gamma ray bursts, and sources of gravitational waves. However, the formation mechanism, intrinsic frequency, and evolutionary processes of B-type binaries are poorly understood. As of 2012, the binary statistics of massive stars had not been measured at low metallicities, extreme mass ratios, or intermediate orbital periods. This thesis utilizes large data sets of eclipsing binaries to measure the physical properties of B-type binaries in these previously unexplored portions of the parameter space. The updated binary statistics provide invaluable insight into the formation of massive stars and binaries as well as reliable initial conditions for population synthesis studies of binary star evolution. We first compare the properties of B-type eclipsing binaries in our Milky Way Galaxy and the nearby Magellanic Cloud Galaxies. We model the eclipsing binary light curves and perform detailed Monte Carlo simulations to recover the intrinsic properties and distributions of the close binary population. We find the frequency, period distribution, and mass-ratio distribution of close B-type binaries do not significantly depend on metallicity or environment. These results indicate the formation of massive binaries are relatively insensitive to their chemical abundances or immediate surroundings. Second, we search for low-mass eclipsing companions to massive B-type stars in the Large Magellanic Cloud Galaxy. In addition to finding such extreme mass-ratio binaries, we serendipitously discover a new class of eclipsing binaries. Each system comprises a massive B-type star that is fully formed and a nascent low-mass companion that is still contracting toward its normal phase of evolution. The large low-mass secondaries discernibly reflect much of the light they intercept from the hot B-type stars, thereby producing sinusoidal variations in perceived brightness as they orbit. These nascent eclipsing binaries are embedded in the hearts of star-forming emission nebulae, and therefore provide a unique snapshot into the formation and evolution of massive binaries and stellar nurseries. We next examine a large sample of B-type eclipsing binaries with intermediate orbital periods. To achieve such a task, we develop an automated pipeline to classify the eclipsing binaries, measure their physical properties from the observed light curves, and recover the intrinsic binary statistics by correcting for selection effects. We find the population of massive binaries at intermediate separations differ from those orbiting in close proximity. Close massive binaries favor small eccentricities and have correlated component masses, demonstrating they coevolved via competitive accretion during their formation in the circumbinary disk. Meanwhile, B-type binaries at slightly wider separations are born with large eccentricities and are weighted toward extreme mass ratios, indicating the components formed relatively independently and subsequently evolved to their current configurations via dynamical interactions. By using eclipsing binaries as accurate age indicators, we also reveal that the binary orbital eccentricities and the line-of-sight dust extinctions are anticorrelated with respect to time. These empirical relations provide robust constraints for tidal evolution in massive binaries and the evolution of the dust content in their surrounding environments. Finally, we compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, adaptive optics, lucky imaging, high-contrast photometry, and common proper motion. We combine the samples from the various surveys and correct for their respective selection effects to determine a comprehensive nature of the intrinsic binary statistics of massive stars. We find the probability distributions of primary mass, secondary mass, orbital period, and orbital eccentricity are all interrelated. These updated multiplicity statistics imply a greater frequency of low-mass X-ray binaries, millisecond pulsars, and Type Ia supernovae than previously predicted. / Astronomy