UC San Diego UC San Diego Electronic Theses and Dissertations Title Neutrino flavor transformation in core-collapse supernovae Permalink https://escholarship.org/uc/item/9p60h8bw Authors Cherry, John F. Cherry, John F. Publication Date 2012 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO Neutrino Flavor Transformation in Core-Collapse Supernovae A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by John F. Cherry Jr. Committee in charge: Professor George M. Fuller, Chair Professor Bruce Driver Professor Brian Keating Professor Michael Norman Professor Nolan Wallach 2012 Copyright John F. Cherry Jr., 2012 All rights reserved. The dissertation of John F. Cherry Jr. is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2012 iii DEDICATION To my parents, who made this all possible. iv EPIGRAPH Codeine... bourbon. —Tallulah Bankhead v TABLE OF CONTENTS Signature Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Epigraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Vita and Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Abstract of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . xx Chapter 1 Neutrinos in Supernovae . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Engine of the Explosion . . . . . . . . . . . . . . . . 1 Chapter 2 Neutrino Flavor Transformation . . . . . . . . . . . . . . . . . 6 2.1 Neutrino Masses and Mixing . . . . . . . . . . . . . . . . 6 2.2 Neutrinos in Vacuum . . . . . . . . . . . . . . . . . . . . 8 2.3 Schro¨dinger-like Formalism . . . . . . . . . . . . . . . . . 10 2.4 Isospin Formalism . . . . . . . . . . . . . . . . . . . . . . 12 Chapter 3 Simulation Methodology . . . . . . . . . . . . . . . . . . . . . 15 3.1 Physical Setup . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Theory of Calculation . . . . . . . . . . . . . . . . . . . . 20 3.3 Integration Algorithm . . . . . . . . . . . . . . . . . . . . 22 Chapter 4 Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . 26 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Neutronization Burst Signal . . . . . . . . . . . . . . . . 32 4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 33 4.2.2 Sensitivity to Neutrino Mass-Squared Differences 39 4.2.3 Variation of θ13 . . . . . . . . . . . . . . . . . . . 41 4.3 Density Fluctuation Effects . . . . . . . . . . . . . . . . . 45 4.3.1 Neutrino Flavor Transformation With and With- out Matter Fluctuations . . . . . . . . . . . . . . 46 4.3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . 52 vi 4.3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . 59 4.4 Luminosity Variation Effects . . . . . . . . . . . . . . . . 69 ′ 4.4.1 Analysis of Flavor Evolution of the νe s . . . . . . 69 4.4.2 Dependence on Lν . . . . . . . . . . . . . . . . . 70 4.4.3 Spectral Swap Formation . . . . . . . . . . . . . . 74 4.4.4 Expected Signal . . . . . . . . . . . . . . . . . . . 76 Chapter 5 The Neutrino Halo . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1 Issues with Neutrino Scattering . . . . . . . . . . . . . . 89 5.1.1 Direction Changing Scattering . . . . . . . . . . . 89 5.1.2 The Safety Criterion . . . . . . . . . . . . . . . . 91 5.1.3 Implicit Calculation of the Halo . . . . . . . . . . 94 5.2 Flavor Transformation During the Accretion and SASI phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2.1 Flavor Transformation is now a Boundary Value Problem . . . . . . . . . . . . . . . . . . . . . . . 100 5.2.2 Multi-dimensionality . . . . . . . . . . . . . . . . 101 5.2.3 Multi-composition . . . . . . . . . . . . . . . . . . 103 5.2.4 Dispersion and Interference . . . . . . . . . . . . . 104 5.2.5 Compounding Unknowns . . . . . . . . . . . . . . 105 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 vii LIST OF FIGURES Figure 2.1: The precession of NFIS si about the effective external field Hi. 14 Figure 3.1: A cartoon illustration of the neutrino emission from the sur- face of a protoneutron star. Neutrinos emerge from the neutri- nosphere, a hard spherical shell with radius Rν. The neutrino emission trajectories are characterized by ϑ, the angle relative to the normal of the neutrinosphere surface at the location where they are emitted. Both neutrinos i and j stream outward until their trajectories intersect at a distance r from the center of the protoneutron star, with intersection angle θij. This inter- section angle sets the strength of the neutrino-neutrino neutral current forward scattering interaction that these neutrinos both experience at this location. . . . . . . . . . . . . . . . . . . . . 17 Figure 4.1: Left panel: electron neutrino survival probability Pν eνe (color/shading key at top left) for the inverted mass hierarchy is shown as a function of cosine of emission angle, cos ϑR, and neutrino en- ergy, E in MeV, plotted at a radius of r = 5000 km. Right: mass basis (key top right, inset) emission angle-averaged neu- trino energy distribution functions versus neutrino energy, E. The dashed curve gives the initial νe emission angle-averaged energy spectrum. Movies of this simulation can be found at the URL in Ref. [1]. Each frame of the movie shows a represen- tation of the neutrino survival probability in various different bases at a fixed radius above the core. Each successive frame is 1 km further out from the initial radius of rinit = 900 km out to the final radius r = 5000 km. . . . . . . . . . . . . . . . . . . . 35 Figure 4.2: Emission angle-averaged neutrino energy distribution functions versus neutrino energy plotted in the neutrino mass basis for the 3 × 3 multi-angle calculation of neutrino flavor evolution. Results shown at a radius of r = 5000km. In this simulation, a small (10%) admixture of all other species of neutrinos and anti-neutrinos are included. . . . . . . . . . . . . . . . . . . . . 36 viii Figure 4.3: Left panel: electron neutrino survival probability Pν eνe (color/shading key at top left) for the normal mass hierarchy is shown as a func- tion of cosine of emission angle, cos ϑR, and neutrino energy, E in MeV, plotted at a radius of r = 5000 km. Right: mass basis (key top right, inset) emission angle-averaged neutrino energy distribution functions versus neutrino energy, E. The dashed curve gives the initial νe emission angle-averaged energy spec- trum. Movies of this simulation can be found at the URL in Ref. [1]. Each frame of the movie shows a representation of the neutrino survival probability in various different bases at a fixed radius above the core. Each successive frame is 1 km further out from the initial radius of rinit = 900 km out to the final radius r = 5000 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Figure 4.4: This calculation of the flavor evolution of neutrinos in the in- 2 verted mass hierarchy was conducted with values of ∆m = ⊙ −5 2 2 −3 2 7.6× 10 eV and ∆m = −2.4× 10 eV . Left panel: elec- atm tron neutrino survival probability Pν eνe (color/shading key at top left) for the inverted mass hierarchy is shown as a function of cosine of emission angle, cos ϑR, and neutrino energy, E in MeV, plotted at a radius of r = 5000 km. Right: mass basis (key top right, inset) emission angle-averaged neutrino energy distribution functions versus neutrino energy, E. The dashed curve gives the initial νe emission angle-averaged energy spectrum. 39 Figure 4.5: This calculation of the flavor evolution of neutrinos in the nor- 2 mal mass hierarchy was conducted with values of ∆m = 7.6× ⊙ −5 2 2 −3 2 10 eV and ∆m = 2.4×10 eV . Left panel: electron neu- atm trino survival probability Pν eνe (color/shading key at top left) for the normal mass hierarchy is shown as a function of cosine of emission angle, cos ϑR, and neutrino energy, E in MeV, plot- ted at a radius of r = 5000 km. Right: mass basis (key top right, inset) emission angle-averaged neutrino energy distribu- tion functions versus neutrino energy, E. The dashed curve gives the initial νe emission angle-averaged energy spectrum. . . 40 Figure 4.6: Emission angle-averaged electron neutrino flux Φν (key top right, inset) for the normal neutrino mass hierarchy is shown as a func- tion of neutrino energy E in MeV. The dashed curve gives the initial νe emission angle-averaged neutrino flux. The shaded re- gion gives the predicted flux in a single-angle calculation, and the thick line shows the flux predicted by the multi-angle cal- culation. These calculations of electron neutrino flux are done 2 −5 2 2 −3 2 using ∆m = 7.6×10 eV and ∆m = −2.4×10 eV and ⊙ atm θ13 = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 ix