Dissertation Supernova Neutrino Spectra and Applications to Flavor Oscillations by Mathias Thorsten Keil arXiv:astro-ph/0308228v1 13 Aug 2003 Institut f¨ur Theoretische Physik T30, Univ.-Prof. Dr. Manfred Lindner Supernova Neutrino Spectra and Applications to Flavor Oscillations Mathias Thorsten Keil Vollst¨andiger Abdruck der von der Fakult¨at f¨ur Physik der Technischen Universit¨at M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. F. v. Feilitzsch Pr¨ufer der Dissertation: 1. Univ.-Prof. Dr. M. Lindner 2. Univ.-Prof. Dr. M. Drees Die Dissertation wurde am 27.05.2003 bei der Technischen Universit¨at M¨unchen eingereicht und durch die Fakult¨at f¨ur Physik am 25.06.2003 angenommen. Summary We study the flavor-dependent neutrino spectra formation in the core of a supernova (SN) by means of Monte Carlo simulations. Several neutrino detectors around the world are able to detect a high-statistics signal from a galactic SN. From such a signal one may extract information that severely constrains the parameter space for neutrino oscillations. Therefore, reliable predictions for flavor-dependent fluxes and spectra are urgently needed. In all hydrodynamic simulations the treatment of νµ,τ andν ¯µ,τ is rather schematic, with the exception of the most recent Garching-Group simulation, where the interaction processes were updated partly based on our results. The interactions commonly included in traditional simulations are iso-energetic scattering on nucleons Nν νN, scattering on electrons and positrons ± ± → + − e ν νe , and electron-positron pair annihilation e e νµ,τ ν¯µ,τ . In our Monte→ Carlo simulations we vary the static stellar background→ models in ad- dition to systematically switching on and off our set of interaction processes, ± i.e., recoil and weak magnetism in Nν νN, scattering on e and νe/¯νe, + − → e e and νeν¯e annihilation into νµ,τ ν¯µ,τ pairs, and neutrino bremsstrahlung off nucleons NN NNνν¯. As νµ,τ andν ¯µ,τ sources, NN NNνν¯ and ν ν¯ ν ν¯ dominate.→ The latter process has never been→ studied before e e → µ,τ µ,τ in the context of SNe and turns out to be always more important than the traditional e+e− annihilation process by a factor of 2–3. For energy transfer, the most important reactions are Nν νN with recoil, and scattering on ± → e . Weak magnetism has a very small effect and scattering on νe andν ¯e is negligible. The charged current reactions e−p ν n and e+n ν¯ p dominate for ν → e → e e andν ¯e. In comparing our numerical results for all flavors we find the standard < hierarchy of mean energies ǫ < ǫ ∼ ǫ , with, however, very similar h νe i h ν¯e i h νµ,τ i values for νµ,τ andν ¯e. The luminosities of νµ,τ andν ¯e can differ by up to a factor of 2 from L L . The Garching Group obtains similar results ν¯e ≈ νe from their self-consistent simulation with the full set of interactions. These results are almost orthogonal to the previous standard picture of exactly equal luminosities of all flavors and differences in mean energies of up to a factor of 2. Existing concepts for identifying oscillation effects in a SN neutrino signal need to be revised. We present two methods for detecting the earth-matter effect that are rather independent of predictions from SN simulations. An earth-induced flux difference can be measured by the future IceCube detector in Antarctica and a co-detector like Super- or Hyper-Kamiokande. At a single detector with high energy resolution the Fourier transform of the inverse- energy spectrum can reveal the modulations of the spectrum. Both methods are sensitive to the small mixing angle θ13 and the neutrino mass hierarchy. i ii F¨ur meine Eltern iii iv Acknowledgments Many people contributed to this dissertation with their advice, support, pa- tience, and kindness. I express my gratitude to everyone who helped making this work come true. Foremost I am indebted to my advisor, Georg Raffelt, not only for propos- ing the project and thereby getting me into Astroparticle Physics, but even more for his great support and advice in so many ways. I benefited very much from our close and very inspiring collaboration. Also for the proofreading and uncountable valuable suggestions on the manuscript I am very grateful. The numerical part of this work was only possible with the code that Hans-Thomas Janka had developed and kindly introduced me to. I enjoyed the collaboration with Thomas and appreciate his patience with my ques- tions and his exhaustive answers on all kinds of code- and supernova-related questions. Thomas and his Garching Supernova Group, i.e., Robert Buras and Markus Rampp, contributed very valuable results from their hydrody- namic simulations. I also thank Robert for our many long discussions and his valuable suggestions on parts of the manuscript. With Amol Dighe I had a wonderful collaboration on the neutrino- oscillation part. But also for all other questions and discussions I found Amol’s door wide open. In addition, I thank Amol for improving parts of the manuscript by his proofreading and suggestions. Also for discussions with Michael Kachelrieß, Sergio Pastor, Dimitry Semikoz, and Ricard Tom´as I am very grateful. As important as the support at the institute were all those friends and my family who supported and encouraged me throughout all the years, even when I was far away. For their love and support in any possible way I owe my deepest thanks to my parents as well as my brother and sister. Christoph even fitted some proofreading into his busy conference schedule, thank you. For your love, support, and encouragement, your patience, your smiles, and everything you did for me, words cannot express my gratitude and love for you, Meike. v Parts of this dissertation have already been published as: M. T. Keil, G. G. Raffelt, and H. T. Janka, • “Monte Carlo study of supernova neutrino spectra formation,” Astrophys. J. in press, astro-ph/0208035. R. Buras, H. T. Janka, M. T. Keil, G. G. Raffelt, and M. Rampp, • “Electron-neutrino pair annihilation: A new source for muon and tau neutrinos in supernovae,” Astrophys. J. 587 (2003) 320 [astro-ph/0205006]. M. T. Keil, G. G. Raffelt, and H. T. Janka, • “Supernova Neutrino Spectra Formation,” Nucl. Phys. B Proc. Suppl. 118 (2003) 506. G. G. Raffelt, M. T. Keil, R. Buras, H. T. Janka, and M. Rampp, • “Supernova neutrinos: Flavor-dependent fluxes and spectra,” astro-ph/0303226. A. S. Dighe, M. T. Keil, and G. G. Raffelt, • “Detecting the neutrino mass hierarchy with a supernova at IceCube,” JCAP, in press (2003), hep-ph/0303210. A. S. Dighe, M. T. Keil, and G. G. Raffelt, • “Identifying earth matter effects on supernova neutrinos at a single detector,” hep-ph/0304150. vi Contents 1 Introduction 1 2 The Core-Collapse Paradigm 7 2.1 TheLifeofaStar:BalancingForces. 7 2.2 TheDeathofaMassiveStar:CoreCollapse . 10 2.3 Reincarnation: A Proto-Neutron Star Emerges . 11 2.4 Self-Consistent Simulations . 13 2.5 Flavor-Dependent Neutrino Emission . 16 3 Neutrino Interactions 21 3.1 Beta-Processes .......................... 21 3.2 Neutrino-NucleonScattering . 23 3.3 WeakMagnetism ......................... 26 3.4 Bremsstrahlung .......................... 27 3.5 Pair Annihilation . 28 3.6 Scattering on Electrons and Electron Neutrinos . 32 3.7 OtherReactions.......................... 34 4 Setting the Stage for Neutrino Transport 35 4.1 CharacterizingProto-NeutronStars . 35 4.2 Proto-Neutron-StarProfiles . 36 4.3 OpticalDepthvs.ThermalizationDepth . 39 4.4 Thermalization Depths in Our Stellar Models . 42 5 Characterizing Non-Thermal Neutrino Spectra 49 5.1 GlobalParameters ........................ 49 5.2 AnalyticFits ........................... 51 6 Relative Importance of Neutral-Current Reactions 57 6.1 MonteCarloSetup ........................ 57 6.2 Accretion-PhaseModelI . 59 vii 6.3 SteepPowerLaw ......................... 62 6.4 ShallowPowerLaw ........................ 64 6.5 Summary ............................. 64 7 Comparison of All Flavors 67 7.1 ResultsfromOurMonteCarloStudy . 67 7.2 PreviousLiterature ........................ 74 7.3 SpectralShape .......................... 79 7.4 Summary ............................. 80 8 Detecting Oscillations of SN Neutrinos 85 8.1 Oscillations of SN Neutrinos . 85 8.2 Detecting Oscillations With Two Distant Detectors . 89 8.2.1 The Basic Principle . 89 8.2.2 TheSNSignalatIceCube . 89 8.2.3 The Oscillation Signal at Ice Cube . 93 8.2.4 Super- or Hyper-Kamiokande and IceCube . 99 8.3 Detecting the Earth-Matter Effect at a Single Detector . 101 8.4 Summary .............................102 9 Discussion and Summary 105 A Abbreviations 109 B Monte Carlo Code 111 B.1 GeneralConcept .........................111 B.2 StructureoftheCode. .113 viii Chapter 1 Introduction The physics of neutrino oscillations has received tremendous attention dur- ing the past years and today oscillations are thought to be established. A large number of experiments has contributed to our present knowledge of the mixing schemes and parameters. For several of the mixing parameters the allowed ranges are known. Within the next few decades the magnitude of the small mixing angle θ13 and the question whether the neutrino mass hierarchy is normal or inverted will remain open and can be settled only by future precision measurements at dedicated long-baseline oscillation exper- iments (Barger et al. 2001, Cervera et al. 2000, Freund, Huber, & Lindner 2001) or the observation of a future galactic supernova (SN). Along with the interest in neutrino oscillations developed the branch of neutrino astronomy. For the early experiments Raymond Davis Jr. and Masatoshi Koshiba received last year’s Physics Nobel Prize “for pioneering contributions to astrophysics, in particular for the detection of cosmic neu- trinos” (Nobel e-Museum, 2002). Current and planned experiments will be able to record some 10,000–100,000 neutrinos from a future galactic SN and therefore would provide valuable information on SN physics and neutrino properties (Barger, Marfatia, & Wood 2001, Minakata et al.