Graduate Funding Information Center

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1 Graduate Funding Information Center UNC-Chapel Hill, The Graduate School Graduate Student Proposal Sponsor: North Carolina Space Grant Program Title: North Carolina Space Grant Graduate Research Fellowship Department: Physics & Astronomy Funding Type: Fellowship Year: 2015 INTELLECTUAL PROPERTY STATEMENT All materials comprising the Successful Proposal Collection are provided by the Graduate Funding Information Center as a service to the Carolina community. All proposals contained in this database are the property of their original authors and protected by copyright laws and, subject to applicable laws, may not be reproduced, modified, republished, distributed, transmitted, or otherwise exploited in any manner without explicit permission. The proposals may be downloaded provided that they are used only as a personal reference tool and are not fully or partially plagiarized. Plagiarism is a violation of the UNC-Chapel Hill Honor Code as well as possible grounds for rejection of grant funding by sponsors. The Graduate Funding Information Center would like to thank all UNC-Chapel Hill graduate students who have shared their winning fellowship proposals with their colleagues. We would also like to encourage any graduate student who has won a fellowship, grant, or other award to consider contributing the proposal(s) to the Successful Proposal Collection. gfic@unc.edu.

2 In your own words describe the research project that you will be conducting. The description should include but not be limited to a description of the research, start and end dates, intended results, and how you will be working with your research mentor for the term of the award. (750 words or less): Fitting Realistic, Parameterized Models of Structured, Off-Axis, Ultra-Relativistic Jets to Real Gamma-Ray Burst Afterglow Data: Probing the Biggest Bangs since the Big Bang Itself Building on previous analyses of Gamma ray burst (GRB) afterglow brightness profiles, this research seeks to incorporate angle-dependent energy functions into the standard synchrotron emission model. This advancing model will generate a variety of light curves by varying the amount by which the GRB jet is directed away from our line of sight, the angular dependence of the internal energy structure, and the overall energy normalization. By comparing the model s output with existing observations of GRBs, we hope to learn how the internal engine of GRBs functions on a granular level, providing insight into a number of peculiar afterglow events and possibly having implications for all GRB analysis. GRBs are the most energetic events in the post-big Bang universe. The collimated pulse of gamma rays that follows the collapse of a super-massive star is the ephemeral observation of material not immediately consumed by the resulting black hole being ejected at relativistic speed. The spectral flux is approximated by a series of smoothly broken power-laws in frequency and time with indices that vary across specific break frequencies. Initial observations of these flux values, coupled with redshift measurements, indicate isotropic energies more than one thousand times that of a typical supernova - the amount of energy produced by the sun over its entire lifetime discharged in seconds. Fortunately, the emission is narrowly beamed, reducing the assumed isotropic equivalent energy. As this relativistic jet interacts with the interstellar medium (ISM) it rapidly decelerates, resulting in an afterglow of longer-wavelength radiation. Theoretically, the afterglow is understood as synchrotron emission from shocks in an expanding spherical shell. Evidence of jetted emission is observed via breaks in the afterglow light curves, after which the flux rapidly decays. These jet breaks are understood to result from either the sideways spreading or sideways beaming of the emission as the jet slows. While the standard model encompasses the majority of GRB afterglows, there are subclasses with features yet to be fully understood. The light curves of slow-risers build more gradually and peak later than most GRBs. While some propose that this behavior is the result of a jet in its pre-deceleration phase seen on-axis, this assumes a far lower energy output than average and fails to address the observed diversity in peak times and temporal indices for the rising component. Instead, we believe slow-risers are the result of a non-uniform jet viewed off-axis, allowing for a great deal of variation with viewing angle across the jet surface. As the afterglow evolves, the jet expands and we receive emission from different areas on its surface. If the jet is structured, the amount of emission will change across the jet surface, allowing for the early rising component as our sight line moves from outer regions toward the more energetic jet center. My master s project involved analysis of the slow-riser GRB and required the use of time-varying energy components. This prompted an investigation into the angular structure of GRB brightness profiles. Building on existing theory, I modified these profiles to incorporate energy structures that vary arbitrarily with the angle away from the jet emission axis, allowing for the production of simulations and synthetic light curves for a sample set of jet structures.

3 The North Carolina Space Grant Graduate Research Fellowship would support the continued development of a structured jet emission model. During the summer of 2015 I will optimize the afterglow surface integration method and incorporate the model fully into our genetic algorithm-based modeling software. I will detail the results of this investigation, and the resulting structured jet model, in a theoretical paper. I will then begin fitting the model to the afterglow of GRB , for which we have a data set with high signal to noise and broad spectral coverage, as well as other slow-riser data sets. Proper testing and optimization of our structured jet emission model as well as the modeling campaign that will result will comprise the bulk of my dissertation, which I will begin writing following the summer research campaign. [name redacted] Throughout I will work directly with Dr., who has been available to answer questions and prompt discussion during the completion of my masters and development of my dissertation projects. We keep in contact through a combination of regularly scheduled meetings and impromptu brainstorming sessions. This level of collaboration, especially during periods when we do not have teaching requirements, has been instrumental to the great research progress I have made over the last year. Obtaining summer funding will allow this progress to continue. Identify which NASA Mission Directorate that your research supports and describe how your research will contribute to the mission of that Directorate. (250 words or less): The goal of NASA s Astrophysics Science Mission Directorate is discovering how the universe works, exploring how the universe began and evolved, and searching for Earth-sized planets. Gamma-ray Bursts (GRBs) are some of the most distant observable astrophysical phenomenon and they provide a window into the early universe and high redshift GRBs uniquely probe the age of re-ionization of the Universe. In addition, since GRBs are ubiquitous with star-formation, we can learn a great deal from careful study of their afterglows and measurements of metallicity, absorption, and extinction values tell us a great deal about their host galaxies. Development of a new theoretical afterglow model will help answer two of the big questions proposed by NASA s Astrophysics Science Mission Directorate: 1) How do matter, energy, space, and time behave under the extraordinarily diverse conditions of the cosmos? and 2) How did the Universe originate and evolve to produce the galaxies, stars, and planets we see today? Modeling and analysis of GRB afterglows, especially during their early stages, provides insight into the processes governing matter and energy during the formation of a black hole. Furthermore, this project is directly in line with four out of the five Swift mission objectives, namely to: determine the origin of gamma-ray bursts, classify gamma-ray bursts and search for new types, determine how the blast wave evolves and interacts with the surroundings and use gamma-ray bursts to study the early universe. In addition, we seek to answer these objectives by making extensive use of Swift-XRT data. Describe your career and research interests in space and aerospace-related science. (400 words or less):

4 A career in Astrophysics requires careful consideration of analytical problems without ever losing sight of the larger physical framework encompassing them. This bimodal thinking process drew me to a graduate program in Physics & Astronomy. I have a strong interest in solving theoretical problems through detailed statistical modeling and analysis and hope to continue this type of work throughout my academic and professional career. Following my analysis of GRB , a well-sampled slow-riser, I spent time developing a new theoretical framework for understanding the angular structure in GRB jets. Further testing, implementation of this work into our existing modeling software, and its application to observation data set will result in my PhD in The modeling of large and complex data sets requires a number of computational, statistical, and analytical skills which will serve me in any number of areas of study. I hope to use these skills to continue answering big questions in astronomy and elsewhere. In addition, I hope to continue as a Teaching Assistant for the Introductory Astronomy Labs at UNC. These labs are allowed access to the telescopes on the Skynet Robotic Telescope Network. Researchquality tools have dramatically increased enrollment numbers and student enthusiasm. My involvement in this aspect of science education is a particular point of pride and is part of a larger desire to engage in public outreach and education. I have fostered this goal by hosting public guest nights at the [name redacted] and presenting at various public demonstrations with the Physics & Astronomy Department s outreach program including [name redacted] at the [name redacted] the past two years. Upon completion of my PhD I will continue my involvement in scientific education and research, with the ultimate goal of a teaching career. In my limited time at UNC I have seen the impact of bringing research-quality tools to younger students and the general public. I hope to gain the experience to one day found an organization similar to The Algebra Project, a 501(c)(3) national, nonprofit organization that uses mathematics as a tool to organize communities around the goal to ensure quality public school education for every child. With the recent rise in the quality and availability of as well as remote access to smaller and networked telescopes, I believe structures like Skynet can be tools for significant growth in communities lacking the resources of a large university or research institution. My goal is to create a program which raises the confidence of young people in STEM subject areas as a path toward improving the overall quality of and access to public education. Describe any relevant work or co-op experience, academic awards, leadership positions in student organizations, and/or honors. (400 words or less): I have been involved with a number of research and teaching related positions in my working career. During my first work experience as a swimming lesson instructor I gained a great deal of experience in a variety of methods of teaching and student interaction. While this was not related to science education, the years of instruction motivated my desire for a career in education by showing me the positive impact I could have on student learning. As an undergraduate, I held a position in data monitoring for the [name redacted], a space-based NASA project. This position was an adjunct to the research I was involved in to search for, monitor, and study gamma-ray pulsars using the Large Area Telescope (LAT) aboard the [name redact

5 with members of the [name redacted] at the [name redacted]. The benefits of this experience were two-fold. First, as my initial experience with academic research, it allowed me to develop a number of data analysis as well as theoretical research skills. I also saw first-hand how research is conducted at the university level and the ways in which I could contribute to the group. In addition, I gained experience working with data in real-time and learned a number of computational skills that are relevant today. This familiarity with remote satellite and data control has been beneficial in my understanding and use of the Skynet Robotic Telescope Network at University of North Carolina at Chapel Hill. In recent years, I have had the privilege of being involved with the [name redacted] program. This program takes 18 mostly undergraduate students but also a few high [name redacted] school students and members of the general public on an intense, one-week workshop at the in [name redacted]. This experience gives me the opportunity not only to be an instructor in a research setting but also to broaden the scope of my astronomy knowledge and experience to include radio astronomy topics. List and any past or present financial aid (scholarships, grants, loans, etc.) (250 words or less): In my current position at the University of North Carolina at Chapel Hill I am being supported as a Teaching and Research Assistant in the Department of Physics and Astronomy. This position includes financial aid in the form of Tuition Remission to cover the entirety of my tuition for the academic year as well as a monthly stipend. I have also received support in the form of a Direct Subsidized Stafford Loan to cover student fees and other living expenses. Furthermore, I was the recipient of a NC Space Grant Graduate Research Fellowship during the summer of How will this award impact you personally and professionally? (250 words or less): The support of the NC Space Grant Graduate Research Fellowship Program will allow me to spend time developing my research skills. It will directly support the project I am undertaking, the research that will result in the completion of my Ph.D. Progress in my professional career will be contingent upon my ability to not only fund, but make progress in my field of research. This award will allow me to contribute a great deal to gamma-ray burst (GRB) research and help re-shape the theoretical picture of GRB afterglows. The work I will be doing is crucial for furthering theoretical understanding of GRBs and the NC Space Grant will allow me to focus on that task unimpeded. Have you previously received a Space Grant award? If so please describe the program and your experience. (750 words or less):

6 The goal of my 2014 NASA NC Space Grant Summer Research Fellowship Project, titled Development of a Structured Jet Model for Gamma-ray Burst Afterglows, was to develop a theoretical framework for analyzing the degree to which gamma-ray burst emission may be structured and to assess various models of such structure. While a few basic models for jet structure exist they have not been widely applied to actual afterglow observations and when they have fail to account for many observed nuances of the afterglow emission. To this end we sought to develop realistic models of GRB afterglow structure, i.e. functional forms for variation of energy across the surface of an expanding relativistic blast wave or jet, and a method to fit these models to observations of a particular subclass of afterglows known as slow risers, which exhibit shallower rising temporal indices and peak later than the majority of afterglows. This necessitated a deeper understanding of the emitting surface of a gamma-ray burst in order to properly account for the variations in light emission due to changes in underlying structure or energy output. I began the summer with a review of the relevant research on GRB afterglow images. This is the theoretical framework for understanding the zone of emission contributing to the light we see from a GRB at a given moment in time. By calculating the proper arrival time of photons from the surface of a relativistically expanding shock wave, i.e. a GRB, we are able to build an equal arrival time surface. This surface, when viewed in the emitting frame of the photons, turns out to be somewhat egg shaped. This geometric picture of the emitting region is useful as it allows us to calculate the GRB image or brightness profile as a function of scaled distance from the GRB central axis. In doing so we can learn the distribution of intensity over this surface, which turns out to be disc-like in some cases and tends toward a ring in others. The major result from this analysis is a geometric picture which can be tied to physical quantities such as the energy, Lorentz factor, and radius (or distance) of the emitting shell. This geometric picture can be further used as an integration surface over which we can apply various models of jet structure. Following my review of the background theory I was able to reconstruct and re-derive the important results outlined above. I then began to test a few simple models of GRB jet structure, e.g. a Gaussian profile where the energy is highest along the central axis and drops smoothly as you move away from it. I then developed a system to integrate the full GRB brightness profile over the entire disc or ring weighted by this Gaussian energy structure. In doing so I gained a great deal of intuition for the geometry of GRB emitting surfaces and images and made an important realization about the subtle effects an angle-dependent energy structure has on the emitting region, and hence region of integration, of a GRB. I learned that the energy functions cannot be used as a weighting on the existing brightness profiles, but needed to be fully integrated to the theoretical framework. The tremendous progress made while working on my NC Space Grant Summer Research Project gave me the necessary momentum to outline and fully investigate a dissertation project. Using the knowledge I gained over the summer I have spent this academic year deriving brightness profiles that incorporate energy structures which vary arbitrarily with angle away from the line of sight to the GRB and the resulting equal arrival time surface (EATS), i.e. the locus of points from which photons arriving at a given observer time are emitted. This has allowed me to produce a number of insightful animations and synthetic lightcurves using the basic simulation and visualization framework I developed over the summer. I have produced examples for a handful of physical parameters which can be viewed on my web page:. [website redacted]

7 The NC Space Grant Summer Research Fellowship allowed me to focus solely on preparation for my prelim and gave me the opportunity to devote myself fully to developing the theoretical framework that will be the foundation for my dissertation project. With the support of this fellowship I made tremendous progress over the summer and it was arguably the most productive period of my graduate career.