Solar System Small-Body Demographics with the Palomar Transient Factory Survey

Observational studies of our solar system's small-body populations (asteroids and comets) offer insight into the history of our planetary system, as these minor planets represent the left-over building blocks from its formation. The Palomar Transient Factory (PTF) survey began in 2009 as the latest wide-field sky-survey program to be conducted on the 1.2-meter Samuel Oschin telescope at Palomar Observatory. Though its main science program has been the discovery of high-energy extragalactic sources (such as supernovae), during its first five years PTF has collected nearly five million observations of over half a million unique solar system small bodies. This thesis begins to analyze this vast data set to address key population-level science topics, including: the detection rates of rare main-belt comets and small near-Earth asteroids, the spin and shape properties of asteroids as inferred from their lightcurves, the applicability of this visible light data to the interpretation of ultraviolet asteroid observations, and a comparison of the physical properties of main-belt and Jovian Trojan asteroids. Future sky-surveys would benefit from application of the analytical techniques presented herein, which include novel modeling methods and unique applications of machine-learning classification. The PTF asteroid small-body data produced in the course of this thesis work should remain a fertile source of solar system science and discovery for years to come.

Demographic studies of extrasolar planets

Uncovering the demographics of extrasolar planets is crucial to understanding the processes of their formation and evolution. In this thesis, we present four studies that contribute to this end, three of which relate to NASA's Kepler mission, which has revolutionized the field of exoplanets in the last few years.

In the pre-Kepler study, we investigate a sample of exoplanet spin-orbit measurements---measurements of the inclination of a planet's orbit relative to the spin axis of its host star---to determine whether a dominant planet migration channel can be identified, and at what confidence. Applying methods of Bayesian model comparison to distinguish between the predictions of several different migration models, we find that the data strongly favor a two-mode migration scenario combining planet-planet scattering and disk migration over a single-mode Kozai migration scenario. While we test only the predictions of particular Kozai and scattering migration models in this work, these methods may be used to test the predictions of any other spin-orbit misaligning mechanism.

We then present two studies addressing astrophysical false positives in Kepler data. The Kepler mission has identified thousands of transiting planet candidates, and only relatively few have yet been dynamically confirmed as bona fide planets, with only a handful more even conceivably amenable to future dynamical confirmation. As a result, the ability to draw detailed conclusions about the diversity of exoplanet systems from Kepler detections relies critically on understanding the probability that any individual candidate might be a false positive. We show that a typical a priori false positive probability for a well-vetted Kepler candidate is only about 5-10%, enabling confidence in demographic studies that treat candidates as true planets. We also present a detailed procedure that can be used to securely and efficiently validate any individual transit candidate using detailed information of the signal's shape as well as follow-up observations, if available.

Finally, we calculate an empirical, non-parametric estimate of the shape of the radius distribution of small planets with periods less than 90 days orbiting cool (less than 4000K) dwarf stars in the Kepler catalog. This effort reveals several notable features of the distribution, in particular a maximum in the radius function around 1-1.25 Earth radii and a steep drop-off in the distribution larger than 2 Earth radii. Even more importantly, the methods presented in this work can be applied to a broader subsample of Kepler targets to understand how the radius function of planets changes across different types of host stars.

A Model For Residential Adoption of Photovoltaic Systems

The rapid rise in the residential photo voltaic (PV) adoptions in the past half decade has created a need in the electricity industry for a widely-accessible model that estimates PV adoption based on a combination of different business and policy decisions. This work analyzes historical adoption patterns and finds fiscal savings to be the single most important factor in PV adoption, with significantly greater predictive power compared to all other socioeconomic factors including income and education. We can create an application available on Google App Engine (GAE) based on our findings that allows all stakeholders including policymakers, power system researchers and regulators to study the complex and coupled relationship between PV adoption, utility economics and grid sustainability. The application allows users to experiment with different customer demographics, tier structures and subsidies, hence allowing them to tailor the application to the geographic region they are studying. This study then demonstrates the different type of analyses possible with the application by studying the relative impact of different policies regarding tier structures, fixed charges and PV prices on PV adoption.