EMPLOYING MODERN STATISTICS TO EXPLORE THE UNIVERSE WITH TYPE IA SUPERNOVAE by Anja Weyant B.S. in Physics, Carnegie Mellon University, 2008 Submitted to the Graduate Faculty of the Kenneth P. Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2014 UNIVERSITY OF PITTSBURGH DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Anja Weyant It was defended on April 22th 2014 and approved by William Michael Wood-Vasey, PhD, Assistant Professor Jeffrey Newman, PhD, Associate Professor Paul Shepard, PhD, Professor Larry Wasserman, PhD, Professor Andrew Zentner, PhD, Associate Professor Dissertation Director: William Michael Wood-Vasey, PhD, Assistant Professor ii EMPLOYING MODERN STATISTICS TO EXPLORE THE UNIVERSE WITH TYPE IA SUPERNOVAE Anja Weyant, PhD University of Pittsburgh, 2014 The Large Synoptic Survey Telescope (LSST) anticipates observing hundreds of thousands of well-measured Type Ia supernovae (SNe Ia). These stellar remnant explosions are exceptional in that they have a standardizeable light curve which allows for an accurate measurement of their luminosity. The standard nature of SNe Ia allow us to measure relative distances in the Universe with better than 6% precision in distance. With distance estimates in hand to large sets of galaxies through Type Ia Supernova (SN Ia) measurements, we can measure the expansion history of the Universe or create flow models of how galaxies (matter) near the Milky Way are moving. In this new regime of large datasets, weaknesses and limitations of the current techniques for estimating cosmological parameters and modeling local flows are becoming apparent. As statistical errors are reduced systematic uncertainties ranging from calibration to survey design and cadence to host galaxy contamination are dominating the error budget and lim- iting our ability to make improvements on cosmological measurements. Similarly, recent comparisons of flow models reveal systematic inconsistencies between different approaches. For my dissertation I have employed modern statistical methods to improve flow models in the local Universe by accounting for the non-uniform distribution of data across the sky and demonstrated how Approximate Bayesian Computation can tackle complicated likelihood functions in supernova cosmology. I also present the first results of a new near-infrared SN Ia survey called "SweetSpot" whose focus is on improving our ability to standardize the total luminosity of SNe Ia. iii TABLE OF CONTENTS PREFACE ......................................... xiii 1.0 INTRODUCTION .................................1 1.1 Measuring Properties of the Universe.....................2 1.1.1 The Luminosity Distance.......................2 1.1.2 Friedmann Equation..........................5 1.1.3 Fluid Equation.............................6 1.1.4 Equation of State............................7 1.1.5 Luminosity Distance and the Matter-Energy Content of the Universe8 1.2 The Local Peculiar Velocity Field....................... 11 1.3 Type Ia Supernovae as Standard Candles................... 12 1.3.1 Progenitor Scenarios.......................... 15 1.3.2 Observational tests of progenitor systems............... 16 1.3.2.1 Pre-explosion data....................... 16 1.3.2.2 Event Rates.......................... 17 1.3.2.3 Remnants............................ 18 1.3.2.4 Observed Event Properties.................. 19 1.3.3 Standardizing SN Ia Light Curves................... 20 1.4 Current limitations of SN Ia Data Sets.................... 22 1.5 Dissertation Overview............................. 24 2.0 AN UNBIASED METHOD OF MODELING THE LOCAL PECU- LIAR VELOCITY FIELD WITH TYPE IA SUPERNOVAE ...... 26 2.1 Introduction................................... 26 iv 2.2 Non-parametric Analysis of a Scalar Field.................. 33 2.2.1 Weighted Least Squares Estimator.................. 35 2.2.2 Coefficient Unbiased Estimator.................... 36 2.2.2.1 Estimating h(x)........................ 37 2.3 Determining Tuning Parameter via Risk Estimation............. 38 2.3.1 Risk Estimation for WLS....................... 38 2.3.2 Risk Estimation for CU........................ 39 2.4 Application to Simulated Data......................... 40 2.4.1 Simulated Data............................. 40 2.4.2 Recovered Peculiar Velocity Field from WLS............. 42 2.4.3 Recovered Peculiar Velocity Field from CU.............. 45 2.5 Application to Observed SN Ia data...................... 52 2.5.1 SN Ia Data............................... 52 2.5.2 WLS and CU Regressions on SN Ia Data............... 59 2.6 Dependence of CU and WLS on Bulk Flow Direction............ 66 2.7 Conclusion.................................... 72 2.8 acknowledgments................................ 73 3.0 LIKELIHOOD-FREE COSMOLOGICAL INFERENCE WITH TYPE IA SUPERNOVAE: APPROXIMATE BAYESIAN COMPUTATION FOR A COMPLETE TREATMENT OF UNCERTAINTY ....... 74 3.1 Introduction................................... 75 3.1.1 Classical Estimation of Cosmological Parameters from SN Ia Data. 76 3.2 General Problem Formulation......................... 79 3.2.1 A Simple Example........................... 81 3.3 Approximate Bayesian Computation..................... 89 3.3.1 ABC Rejection Samplers........................ 89 3.3.2 Adaptive ABC Algorithms....................... 92 3.3.3 Example: Revisited........................... 95 3.4 SMC ABC Cosmology with SDSS-II Supernovae............... 99 3.4.1 Simulation Setup............................ 99 v 3.4.2 SMC ABC Implementation...................... 102 3.4.3 Results and Discussion......................... 106 3.4.4 Type IIP Contamination........................ 109 3.5 Future Work................................... 112 3.6 Conclusions................................... 113 3.7 Acknowledgements............................... 114 4.0 SWEETSPOT: NEAR-INFRARED OBSERVATIONS OF THIRTEEN TYPE IA SUPERNOVAE FROM A NEW NOAO SURVEY PROB- ING THE NEARBY SMOOTH HUBBLE FLOW ............. 115 4.1 Introduction................................... 115 4.2 The Observation and Processing of the SN Ia Sample............ 118 4.2.1 Observations and Sample Selection.................. 118 4.2.2 Image Processing and Coaddition................... 121 4.2.3 Photometry and Calibration...................... 122 4.3 SN Ia Sample from the Literature....................... 130 4.4 Analysis..................................... 133 4.5 Results...................................... 143 4.5.1 Near-Infrared SN Ia Hubble Diagram................. 143 4.5.2 Absolute H-band Magnitude of a SN Ia................ 143 4.6 Discussion.................................... 147 4.6.1 NIR SN Ia as Standard Candles.................... 147 4.6.2 Absolute Brightness.......................... 148 4.7 SweetSpot: A 3-Year Survey Program with WHIRC............. 149 4.8 Conclusion.................................... 152 4.9 Acknowledgments................................ 152 5.0 CONCLUSIONS .................................. 154 APPENDIX A. CHAPTER 1 APPENDICES .................. 157 A.1 Bias on WLS coefficients............................ 157 A.2 Bias on CU Coefficients............................ 158 A.3 Risk Estimation................................. 159 vi A.4 Smoothing Matrix for CU Regression..................... 160 APPENDIX B. NON-PARAMETRICALLY SMOOTHING THE SIMU- LATED AND OBSERVED DATA ....................... 161 APPENDIX C. BIBLIOGRAPHY ......................... 162 vii LIST OF TABLES 1 SN Ia Data..................................... 54 2 Summary of Results................................ 62 3 Paired t-test results................................ 64 4 Summary of Dipole Results............................ 65 5 Probability of the 95% confidence interval containing the truth........ 68 6 SN Ia Properties.................................. 119 7 SN Ia Sample Summary I............................. 120 8 SN Ia Sample Summary II............................ 121 9 Photometric Calibration Terms.......................... 125 10 2MASS Calibration Stars............................. 127 11 SN Ia Light Curves................................ 128 12 H-band Maximum Apparent Magnitude for Current Sample.......... 136 viii LIST OF FIGURES 1 Supernova brightness corrected for light curve shape as a function of redshift (Hubble diagram) using a recent compilation of SNe Ia from Conley at al. (2011)........................................9 2 Cosmological constraints from Conley at al. (2011) including statistical and systematic uncertainty............................... 10 3 Quasi-bolometric light curve and spectra from 2003du.............. 14 4 2D distribution of 1000 simulated data points.................. 41 5 2D simulated peculiar velocity field in km/s, described by Equation 2.36.... 41 6 Estimated risk for WLS (black-solid) and CU (red-dashed)........... 43 7 Recovered velocity field (top), standard deviation (middle), and residuals (bot- tom) in km/s for WLS for one realization of the data (left) and the combined results of 100 realizations of the data (right)................... 44 8 Results for WLS forcing the tuning parameter to be J=8 created in an identical manner to the plots presented in Figure7..................... 45 9 Estimated risk for the sampling density with a minimum at l=4........ 46 10 Typical recovered sampling density for one realization of the data using the tuning parameter I=4 (top)............................ 47 11 Recovered velocity field (top), standard deviation (middle),