Self-refraction of supernova neutrinos: mixed spectra and three-flavor instabilities Alexander Friedland Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, NM 87545, USA (Dated: January 6, 2010; updated to match the PRL version on May 10, 2010) Neutrinos in a core-collapse supernova undergo coherent flavor transformations in their own back- ground. We explore this phenomenon during the cooling stage of the explosion. Our three-flavor calculations reveal qualitatively new effects compared to a two-flavor analysis. These effects are es- pecially clearly seen for the inverted mass hierarchy: we find a different pattern of spectral “swaps” in the neutrino spectrum and a novel “mixed” spectrum for the antineutrinos. A brief discussion of the relevant physics is presented, including the instability of the two-flavor evolution trajectory, the 3-flavor pattern of spectral “swaps,” and partial nonadiabaticity of the evolution. PACS numbers: 97.60.Bw, 14.60.Pq 1. Introduction and motivation . – Core-collapse su- pernovae play an essential role in the evolution of the Universe, from controlling the temperature of the gas and the rate of star formation in the galactic disk ( e.g. , [1]), to synthesizing and dispersing heavy elements ( e.g. , [2]). The ashes of ancient explosions have literally shaped the world around us. The struggle to understand and model the explosion mechanism has occupied researchers for the better part of the 20th century [3–12] and remains a very active topic (for review, see, e.g. , [13, 14]). Neutrinos, which are emitted during the first ∼ 10 sec after the onset of the collapse and arrive to us directly from the core of the star, could serve as a direct probe of the explosion mechanism. It is expected that, unlike su- pernova 1987a [15, 16], the next galactic supernova may yield O (10 $^{4}$) antineutrino (¯ ν$_{e}$ ) events and, furthermore, a similar number of neutrino ( ν$_{e}$ ) events, if a large liquid argon detector is constructed at DUSEL. With such high statistics, it should be possible to reconstruct the second- by-second evolution of the ν$_{e}$ and ¯ ν$_{e}$ spectra. The task is to understand how to “read” this signal, i.e. , how to extract signatures of various physical processes from it, and to optimize the detector design. One important process that needs to be thoroughly understood is the coherent flavor transformations of neu- trinos outside of the neutrinosphere. Compared to the well-studied case of solar neutrinos, in a supernova these transformations are much more involved. Not only neu- trinos and antineutrinos of all flavors are emitted, not only are there two mass splittings – “solar” and “atmo- spheric” – to worry about [17], but the physics of the transformations is significantly richer. For example, sev- eral seconds after the onset of the explosion, the flavor conversion probability is affected by the expanding shock front [18] and the turbulent region behind it [19]. The conversion process in such a “bumpy,” stochastic profile is qualitatively different from the adiabatic MSW effect in the smooth, fixed density profile of the Sun. Even more complexity is brought about by the coher- ent scattering of neutrinos off each other [20–36]. This neutrino “self-refraction” results in highly nontrivial fla- 2. Formulation of the problem . – The energy spec- tra of emitted neutrinos evolve as the explosion devel- ops. Since the self-refraction effect is nonlinear, differ- ent initial spectra may result in qualitatively different outcomes. Therefore, it is important to choose spec- tra that are (i) specific to the late phase and (ii) sim- ulated with sufficient accuracy. It has been shown [50] that the emerging spectra of the nonelectron neutrinos ( ν$_{x}$ ) are sensitive to several seemingly subdominant pro- cesses, such as ν$_{x}$e ± scattering, neutrino coannihilation, bremsstrahlung, and nucleon recoil. The addition of nu- cleon recoil, in particular, makes the ν$_{x}$ spectra softer and On the other hand, it is fair to say that the subject is still far from being exhausted and qualitatively new effects continue to be uncovered. This letter is another contribution to this effort. We explore the self-refraction phenomenon for the conditions typically present during the cooling stage of the protoneutron star (several sec- onds into the explosion) and show that a three-flavor analysis of this process reveals several new effects. Below we report the main results; a detailed discussion will be given elsewhere [49]. One may wonder whether all this complexity will im- pede the extraction of useful information from the future signal. In fact, the opposite is true: the new effects can imprint information about the inner workings of the ex- plosion on the signal. For example, by observing the sig- natures of the expanding shock and the post-shock region in the neutrino signal, we will learn about the develop- ment of the explosion during the crucial first 10 seconds. This information could be inaccessible in other ways. vor transformations [37–48] close to the neutrinosphere, typically within a few hundred kilometers from the cen- ter, where the density of streaming neutrinos is very high. Since the evolving flavor composition of the neutrino flux feeds back into the oscillation Hamiltonian, the prob- lem is nonlinear . Furthermore, as the interactions cou- ple neutrinos and antineutrinos of different flavors and energies, the oscillations are characterized by collective modes. This leads to very rich physics that has been the subject of intense interest over the last several years. arXiv:1001.0996v2 [hep-ph] 11 May 2010