Thesis (Ph.D.)--Brown University, 2008. / Vita. Advisor : Ian Dell'Antonio. Includes bibliographical references (leaves 122-124).

Thesis (Ph.D.)--Brown University, 2008. / Vita. Advisor : Peter H. Schultz. Includes bibliographical references.

This work is divided into two parts: a grey model for past Triton, Pluto, and Kuiper belt objects, and a nongrey model for current Titan's troposphere. Steady-state, planar models of early atmospheres for Triton, Pluto, and Kuiper belt objects are computed using a grey approach that tracks the transfer/distribution of heat via radiative transport. These objects are treated here together because they resemble one another in size, surface chemical composition, and exist in the same cold portion of the outer solar system. Beginning with present-day volatiles observed on the surfaces of Triton and Pluto (methane and molecular nitrogen), a trace of molecular hydrogen (present in most primordial atmospheres) is added. It is assumed that as the object is heated by solar, tidal, accretional, or radiogenic methods (this varies between the objects treated here) these chemical species then evaporate from the surface to create an atmosphere. Binary collisions among the molecules account for the sources of opacity, and absorption coefficients are provided by [21]. The grey atmosphere calculations require a mean opacity, and its results are sensitive to the type of mean opacity used. Thus a variety of methods (Planck, Rosseland, and Chandrasekhar mean opacities) are used to accommodate this dependence and the variations in optical depth. Surface temperatures are then calculated as a function of the heating rate, molecular hydrogen abundance, and mean opacity type. As a result of these modelling experiments, tidal heating is found to be crucial to the formation of a thick atmosphere on Triton, and albedo and gravitational acceleration strongly affect the formation of atmospheres on less massive objects such as Pluto and Kuiper belt objects. A nongrey, steady-state, planar model of Titan's current troposphere is developed to study the effect of varying methane mass fraction. Methods from stellar atmosphere modelling are used to solve the equation of transfer as a two-point boundary problem. To additionally satisfy radiative, hydrostatic, and local thermodynamic equilibrium, an iterative correction procedure is utilized since the correct temperature and density profiles as a function of altitude are not known a priori. The volatile composition is taken from observation: molecular nitrogen, methane, and molecular hydrogen. Again, binary collisions among the molecules account for the sources of opacity, and absorption coefficients are provided by [21]. The heating source for Titan is solar radiation absorbed and reradiated by the planet's surface in the infrared region of the spectrum, with a small amount of heat emanating from the stratosphere. The chemical species evaporate from the surface to create an atmosphere. Models of Titan's troposphere are calculated using different amounts of methane (within observational constraints) since the presence of methane is evolving in Titan's atmosphere due to photolytic processes. From model results it is shown that by solving the radiative transfer equation, subject to radiative, hydrostatic, and local thermodynamic equilibrium constraints, a model of Titan's troposphere with a maximum deviation of 8% from data [85] [170] can be obtained. The preliminary model of past Titan's troposphere is consistent with other analytic results [89].

The Voyager 1 Ultraviolet Spectrometer (UVS) observations are the only direct measurements we have of Titan's upper atmosphere. Previous analysis of the two UVS solar occultations yielded densities for N₂ CH₄ and C₂ as well as the thermospheric temperature. These results serve as the upper atmospheric boundary conditions in models of Titan's atmosphere; however, there are discrepancies between the observations and models, and the previous analysis itself is known to be internally inconsistent. We have undertaken a reanalysis of the UVS solar occultations to resolve these differences and to extract the maximum amount of information from the data. In so doing, we have developed a detailed model of the UVS detector and a new analysis method tailored to retrieving multiple species from an occultation of a finite-sized source such as the sun. Our analysis has yielded density profiles for nine species in Titan's upper atmosphere and a new measurement of the thermospheric temperature. We find higher N₂ densities and lower CH₄ and C₂ densities than those previously determined. We also find a thermospheric temperature of 150-155 K instead of 176-196 K as in the early analysis. Densities for C₂H₄, C₂H₆, C₄H₂, C₂N₂, HCN, and HC₃N are retrieved for the first time. Titan's atmosphere is one of the most interesting in the solar system. The composition and high degree of photochemical activity elicit comparisons to the early terrestrial atmosphere and considerations about the origins of life. Our results provide improved and expanded constraints for the atmospheric models and should provide scientists with a better view of Titan's upper atmosphere, which is important in planning for the upcoming Cassini mission.

Aspects of the self consistent acceleration and transport of cosmic rays in astrophysical fluid flows and associated numerical methods are studied. Problems investigated are: (i) magnetohydrodynamic (MHD) wave interactions and instabilities in two-fluid models of cosmic ray modified shocks and flows; (ii) two dimensional, self consistent models of cosmic ray acceleration by the first order Fermi mechanism in supernova remnant shocks; (iii) new Riemann solver for the two-dimensional Euler equations and adaptive mesh refinement scheme for the coupled MHD and cosmic ray transport equations. The interaction of short wavelength MHD waves and instabilities in cosmic ray modified flows are investigated using asymptotic analysis and numerical simulations, with application to cosmic ray driven squeezing instabilities in supernova remnant shocks. In the linear wave regime, the waves are coupled by wave mixing due to gradients in the background flow; cosmic-ray squeezing instability effects, and damping due to the diffusing cosmic-rays. Numerical solutions of the fully nonlinear two-fluid cosmic ray MHD equations are compared with solutions of the wave mixing equations for oblique, cosmic ray modified shocks. A two-dimensional, self-consistent, adaptive mesh refinement numerical algorithm is developed for the solution of the ideal magnetohydrodynamic equations coupled to the kinetic transport equation for energetic charged particles. The method is used to simulate the evolution of the momentum distribution function of the cosmic rays accelerated at supernova remnant shocks. The numerical methods were tested on a variety of fluid dynamics and MHD problems, and previous models of cosmic ray modified supernova remnant shocks. A Riemann solver based on two-dimensional multi-state Riemann problems was developed. The scheme generalizes the traditional one-dimensional flux calculation to include contributions to the flux through the cell edges of the waves originating at cell corners. The multidimensional flux corrections increase the accuracy and stability of the scheme. An adaptive mesh refinement technique was used to study the Von Neumann paradox associated with the formation of three shocks, when a low Mach number, supersonic flow impinges on a thin wedge. For the first time, the region near the triple point has been resolved in a numerical solution of the Euler equations.

The properties of aerosol dust on Mars may be deduced from photometric observations of its atmosphere. By comparing sky images taken by the Imager for Mars Pathfinder to numerical models, the size distribution and reflective properties of the dust particles can be determined. The format, quality, and reduction of the IMP images is described herein, as is the computational radiative transfer model used, with its various parameters. After discovering and compensating for an imprecision in the pointing of the camera, models were successfully fit to the IMP solar aureole datasets. Key results include determining the particle size (reff = 1.6 ± 0.15 μm); quadratic parameters G and Θmin describing the phase function for internally scattered light as functions of wavelength; and the imaginary refractive index n i (and single scattering albedo o) of the aerosols as a function of wavelength (presented in Table 4.1). Preliminary indications of temporal variation in ni turn out to be due to an unplanned change in the time of day of the measurements, coupled with a limitation in the algorithm for correcting the aforementioned pointing imprecision. Excluding unreliable datasets leads to a set of particle properties which shows no significant variation over the first two months of the Pathfinder mission. A multispectral sky patch from MPF Sol 22 gives greater wavelength resolution, as well as showing the sensitivity of the results to variations in key model parameters. In addition, images from the Hubble Space Telescope are used to refine the surface reflectance used in the model. The final result is a model for the aerosol dust which is consistent with the IMP solar aureole observations and the HST observations. Evidence for a minor component of water ice is also discussed. Dust reflectances derived for comparison with ground spectra show a feature in the near infrared which is not present in most MPF spectra of bright surface regolith. This is an indication that there are components visible in the bright soil which are not present in the airborne dust.

We have developed a two-dimensional heliospheric model that includes galactic and anomalous cosmic rays as well as pickup ions. Cosmic rays are described via their number density in phase space, rather than pressure, as every preceding 2-D model has done. Cosmic-ray pressure is included in the total energy budget, allowing us to compute dynamical effects of the energetic particles on the solar wind. We include the magnetic field as well in order to consistently compute cosmic-ray diffusion coefficients. To accommodate' lower-energy cosmic rays with their short diffusion length, we implemented an adaptive mesh refinement code featuring improved spatial resolution near the termination shock. Our simulations show that galactic cosmic rays could substantially change the solar wind flow in the outer heliosphere. In particular, the solar wind is deflected towards the ecliptic plane during the positive solar cycle, resulting in faster wind near the current sheet. This is a result of large latitudinal gradients in the cosmic-ray pressure, caused by the difference in cosmic-ray drift patterns over latitude. We also found that anomalous cosmic rays have a minor effect on the solar wind. Their pressure is not sufficient to modify the termination shock significantly, a conclusion based on comparing model cosmic-ray spectra with observations. However, anomalous cosmic-ray acceleration occurs somewhat differently than thought before, and shock drift effects are not prominent. The spectra of these particles have an enhancement near the cutoff, that is not caused by shock drifts.

The success of the Hubble Space Telescope created a great interest in the next generation of space telescopes. To address this need, the University of Arizona (UA) has designed and built several lightweight prototype mirrors ranging in size from 0.5 m to 2 m in diameter. These mirrors consist of three key components: a thin, lightweight glass substrate holds the reflective surface; the surface accuracy is maintained by an array of position actuators; and the stiffness is maintained by a lightweight carbon-fiber/epoxy support structure. The UA mirrors are different from conventional mirrors in that they are actively-controlled: their figure may be changed after they leave the optics shop. This dissertation begins with an overview of the technical issues for placing large optics in space, and I also discuss the current state-of-the-art in active mirror design. Chapters 3 and 4 discuss ways to design mirrors such that the optical performance is maximized while the mass is minimized. Chapter 3 looks at the best way to distribute the mass between the reflective substrate and the actuators, and Chapter 4 looks at the optimum geometries for structured mirrors. The second half of this work looks at the practical aspects of controlling active mirrors. Chapter 5 discusses the University of Arizona's 2 m NMSD prototype mirror. Specifically, I review the system that I developed to measure and control the mirror. I also provide some details on using a least-squares solution to solve for the actuator commands. Chapter 6 discusses the UA ultralightweight 0.5 m prototype mirror. I describe the techniques that I developed for attaching loadspreaders to the reflective surface, the metrology system, and a software package used to remotely-control the mirror.

<p> <b>Context:</b> The majority (~85%) of the matter in the universe is composed of dark matter, a mysterious particle that does not interact via the electromagnetic force yet does interact with all other matter via the gravitational force. Many direct detection experiments have been devoted to finding interactions of dark matter with baryonic matter via the weak force. It is still possible that dark matter interacts with itself via a strong scale force and has a self-scattering cross-section of ~0.5 cm²g^-1. In fact such a strong scale scattering force could resolve several outstanding astronomical mysteries: a discrepancy between the cuspy density profiles seen in &Lambda;CDM simulations and the cored density profiles observed in low surface brightness galaxies, dwarf spheroidal galaxies, and galaxy clusters, as well as the discrepancy between the significant number of massive Milky Way dwarf spheroidal halos predicted by &Lambda;CDM and the dearth of observed Milky Way dwarf spheroidal halos. <b>Need:</b> While such observations are in conflict with &Lambda;CDM and suggest that dark matter may self-scatter, each suffers from a baryonic degeneracy, where the observations might be explained by various baryonic processes (e.g., AGN or supernove feedback, stellar winds, etc.) rather than self-interacting dark matter (SIDM). If dark matter lags behind the effectively collisionless galaxies then this is clear evidence that dark matter self-interacts. The expected galaxy-dark matter offset is typically >25 kpc (for cross-sections that would explain the other aforementioned issues with &Lambda;CDM), this is larger than the scales of that are plagued by the baryonic degeneracies. <b>Task:</b> To test whether dark matter self-interacts we have carried out a comprehensive survey of the dissociative merging galaxy cluster DLSCL J0916.2+2951 (also known as the Musket Ball Cluster). This survey includes photometric and spectroscopic observations to quantify the position and velocity of the cluster galaxies, weak gravitational lensing observations to map and weigh the mass (i.e., dark matter which comprises ~85% of the mass) of the cluster, Sunyaev-Zel'dovich effect and X-ray observations to map and quantify the intracluster gas, and finally radio observations to search for associated radio relics, which had they been observed would have helped constrain the properties of the merger. Using this information in conjunction with a Monte Carlo analysis model I quantify the dynamic properties of the merger, necessary to properly interpret constraints on the SIDM cross-section. I compare the locations of the galaxies, dark matter and gas to constrain the SIDM cross-section. This dissertation presents this work. <b>Findings:</b> We find that the Musket Ball is a merger with total mass of 4.8^+3.2_-1.5&times;10¹⁴M_sun. However, the dynamic analysis shows that the Musket Ball is being observed 1.1^+1.3_-0.4 Gyr after first pass through and is much further progressed in its merger process than previously identified dissociative mergers (for example it is 3.4^+3.8_-1.4 times further progressed that the Bullet Cluster). By observing that the dark matter is significantly offset from the gas we are able to place an upper limit on the dark matter cross-section of &sigma;_SIDMm^-1_DM &lt; 8 cm²g^-1. However, we find an that the galaxies appear to be leading the weak lensing (WL) mass distribution by 20.5" (129 kpc at z=0.53) in southern subcluster, which might be expected to occur if dark matter self-interacts. Contrary to this finding though the WL mass centroid appears to be leading the galaxy centroid by 7.4" (47 kpc at z=0.53) in the northern subcluster. <b>Conclusion:</b> The southern offset alone suggests that dark matter self-interacts with ~83% confidence. However, when we account for the observation that the galaxy centroid appears to trail the WL centroid in the north the confidence falls to ~55%. While the SIDM scenario is slightly preferred over the CDM scenario it is not significantly so. <b>Perspectives:</b> The galaxy-dark matter offset measurement is dominated by random errors in each cluster. Thus measuring this offset in other dissociative mergers holds the promise of reducing our uncertainty and enabling us to: 1) state confidently whether dark matter self-interacts via a new dark sector force, or 2) constrain the dark matter cross-section to such a degree that SIDM cannot explain the aforementioned mysteries. To this end we have established the Merging Cluster Collaboration to observe and simulate an ensemble of dissociative merging clusters. We are currently in the process of analyzing six dissociative mergers with existing data, and carrying out multi-wavelength observations of a new sample of 15 radio relic identified dissociative mergers. (Abstract shortened by UMI.)</p>

<p>In this dissertation, we describe observational and theoretical work related to the large-scale clustering of matter in the universe. Such work is crucial in constraining models of the Universe in future surveys and is one of the most powerful probes of the nature of dark energy. In Chapter \ref{magnification}, we present work performed using the Deep Lens Survey (DLS) to measure the growth of structure over cosmic time using weak lensing magnification. This is the first time such a measurement has been performed and represents a significant step forward for this relatively new probe of large-scale structure (LSS) which is known to be complementary to other weak lensing measurements. Later in Chapter \ref{conclusions}, we discuss steps needed for magnification become a competitive, precision probe of cosmology. Chapter \ref{covariance} presents a model for the emulation cosmology dependent error covariances in LSS probes. Estimating these covariances are necessary in order to compare models to the data and require a large amount of computational time to create the simulations required. Tools to reduce the number of simulations required and model the cosmology dependence are needed. We utilize a novel decomposition of LSS error covariances that allows for construction of a emulator that fulfills both of these criteria. In order for future surveys to reach their goals, methods to model measurement error and new probes of LSS complementary to those planned are required. The conclusions of this dissertation in Chapter \ref{conclusions} address the future outlook for this work and research that must be done between now and when the next set of survey data is available. Many systematic errors need to be addressed in magnification before it can be considered a precision cosmology tool. For the error covariances, additional methods to reduce the required number of simulations to estimate the matrices are required. In the Appendix, we present a high level description of an open sourced software package that we developed and implemented over the course of these two projects.