Hartmann, D H

Kajino, T

Kimura, K

Takamura, A

Yokomakura, H

Yoshida, T

CERN Document Server

PoS(NIC-IX)196Can supernova neutrino nucleosynthesis constrainneutrino oscillation parameters?Takashi Yoshida∗National Astronomical Observatory of JapanE-mail: takashi.yoshida@nao.ac.jpToshitaka KajinoNational Astronomical Observatory of Japan and the Graduate University for Advanced StudiesDepartment of Astronomy, University of TokyoHidekazu Yokomakura, Keiichi KimuraDepartment of Physics, Nagoya UniversityAkira TakamuraDepartment of Mathematics, Toyota National College of TechnologyDieter H. HartmannDepartment of Physics and Astronomy, Clemson UniversityRecent neutrino experiment confirmed that neutrinos have finite masses and that neutrino oscil-lations occur. Supernova neutrinos also change their flavors propagating in the stellar materialsurrounding a proto-neutron star and, accordingly, change their spectral energy distributions. Thenucleosynthesis of light elements such as 7Li and 11B is significantly enhanced through the ν-process in supernova explosions. Yields depend on the energy spectra of the neutrinos emittedfrom the proto-neutron star, so that neutrino oscillations could be crucial for the estimated yieldsof 7Li, 11B, and other isotopes produced in supernovae. We evaluate the 7Li and 11B yields insupernovae taking into account changes of the neutrino energy spectra due to flavor oscillationsassuming large mixing angle solutions. We investigate their dependence on key parameters, suchas mass hierarchies and the mixing angle θ13. In the case of a normal mass hierarchy and anadiabatic resonance of 13-mixing, the 7Li yield is larger than that without neutrino oscillationsby a factor of ∼ 2. For other parameter cases and for the 11B yield in general, the enhancementis smaller. The increase of the 7Li/11B ratio is demonstrated for a normal mass hierarchy anda relatively large sin2 2θ13, where 13-mixing resonance is adiabatic and sin2 2θ13 < 0.1. Thus,the detection of 7Li/11B enhancements in stars showing signs of supernova enrichment suggest anormal mass hierarchy and relatively large value of sin2 2θ13.International Symposium on Nuclear Astrophysics — Nuclei in the Cosmos — IXJune 25-30 2006CERN, Geneva, Switzerland∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)196SN Nucleosynthesis with Neutrino Oscillations Takashi Yoshida1. IntroductionRecent observations of solar, atmospheric, and reactor neutrinos confirmed the existence offlavor oscillations (for a recent review see [1]). These experiments have precisely determined mostof the neutrino oscillation parameters, such as the squared-mass differences and mixing angles.However, definite constraints on two oscillation parameters have not been obtained; the mass hier-archy has not been determined and only upper limits of the mixing angle θ13 have been obtained.During a supernova (SN) explosion, a very large neutrino luminosity emanates from the cool-ing proto-neutron star (PNS). The resulting large neutrino irradiation of the stellar layers above thePNS induces significant modifications of the isotopic abundance patterns, which is referred to asthe ν-process. This process plays an important role for the production of, amongst several, thelight elements 7Li and 11B [2, 3, 4]. On the other hand, it has been shown that the neutrinos changetheir flavors in the O/C and He-rich layers and that this flavor change strongly depends on the masshierarchy and the mixing angle θ13 (e.g., [5]). This implies that the neutrino energy spectra changein these layers and that the extent of the spectral modifications depends on these two parameters.We have shown in [4] that the 7Li and 11B yields depend on the neutrino energy spectra. If theνe and ¯νe spectra change, the 7Li and 11B yields are affected because of the contribution fromcharged-current ν-process reactions. In this study, we investigate the effects of oscillations on 7Liand 11B production, and evaluate the dependence of these yields on assumed mass hierarchies andthe mixing angle θ13. We further discuss the possibility for constraining oscillation parameterswith light element synthesis in supernovae.2. Supernova nucleosynthesis model and neutrino parametersWe adopt the same stellar model as that described in [3, 4, 6, 7]. The SN progenitor is a 16.2M¯ star [8], and the explosion is followed numerically with a piecewise parabolic method [9].We set the explosion energy and the mass cut to be 1× 1051 ergs and 1.61 M¯, respectively. De-tailed explosive nucleosynthesis is calculated by postprocessing using a nuclear reaction networkincluding 291 species of nuclei [3].We adopt the following assumptions regarding neutrinos emitted from the PNS’s neutrinosphere. The luminosity decays exponentially with a decay time scale of 3 s and is equally parti-tioned by each flavor. The neutrino energy spectra obey Fermi-Dirac distributions. As the stan-dard model of this study, the total neutrino energy and the neutrino temperatures are set to beEν = 3×1053 ergs, Tνe = 3.2 MeV, T¯νe = 5 MeV, and Tνµ,τ = 6 MeV. We will discuss the effect ofuncertainties in the total neutrino energy and the neutrino temperatures [6, 7]. The ν-process crosssections are adopted from [10] except charged-current reactions of 4He and 12C: 4He(νe,e−p)3He,4He( ¯νe,e+n)3H, 12C(νe,e−p)11C, and 12C( ¯νe,e+n)11B. In this study, we focus on the change of therates of these reactions due to neutrino oscillations because the ν-process reactions of 4He and 12Care the most important for 7Li and 11B production. We adopt analytical approximations to the crosssections as a function of energy εν : σν(εν) = σ0(εν − εth)α , where εth is a threshold energy. Co-efficients are listed in [7]. We evaluate the rates of the charged-current reactions using the energydependent neutrino flux, the transition probabilities by neutrino oscillations, and the analyticallyapproximated cross sections (see [7, 11]).2PoS(NIC-IX)196SN Nucleosynthesis with Neutrino Oscillations Takashi Yoshida11.21.41.61.8210-610-410-2Yield ratios of 7Lisin22!13normalinverted(a)11.21.41.61.8210-610-410-2Yield ratios of 11Bsin22!13(b)normalinvertedFigure 1: Yield ratios of 7Li (a) and 11B (b) as a function of sin2 2θ13. Solid lines and dotted lines correspondto a normal mass hierarchy and an inverted mass hierarchy, respectively.Neutrino oscillation parameters are adopted from recent neutrino experiments. The squared-mass differences ∆m2i j ≡m2i −m2j are set to be ∆m221 = 7.9×10−5 eV2 and ∆m231 =±2.4×10−3 eV2where positive and negative values of ∆m231 correspond to a normal mass hierarchy, m1 <m2 <m3,and an inverted mass hierarchy, m3 < m1 < m2, respectively. The mixing angles θi j are set tobe sin2 2θ12 = 0.816, sin2 2θ23 = 1.0, and 0 ≤ sin2 2θ13 ≤ 0.1. The change of the spectra dueto neutrino oscillations is calculated with a Runge-Kutta method and using exact solutions of theoscillations given in [12, 13].3. ResultsWe demonstrate the effects of neutrino oscillations on the 7Li and 11B yields in SN ejecta. Fig-ure 1 shows the ratios of the 7Li (a) and 11B (b) yields when taking into account of spectral changesby oscillations to those without oscillations. When we do not consider neutrino oscillations, the7Li and 11B yields are 2.36×10−7M¯ and 6.26×10−7M¯.In a normal mass hierarchy, the 7Li yield increases by about a factor of 1.9 for sin2 2θ13 ≥ 2×10−3. In this range, almost all νe in the He-rich layer are the result of νµ ,τ conversions. Therefore,the effective neutrino temperature changes from 3.2 MeV to 6 MeV. This change in Tνe increases thereaction rate of 4He(νe,e−p)3He, and thus raises the yield of 7Be produced through 3He(α,γ)7Be.This large νe ↔ νµ,τ exchange is due to the fact that the resonance of mass eigenstates 1 and 3, i.e.,the 13-mixing resonance, is adiabatic. In the case of sin2 2θ13 ≤ 2×10−5, the 7Li yield is larger byonly a small factor of 1.1. This range corresponds to nonadiabatic resonance of the 13-mixing, andflavor exchange is less effective. With increasing sin2 2θ13, the resonance of the 13-mixing changesfrom nonadiabatic to adiabatic and the 7Li yield increases. There are no resonances of antineutrinosin a normal mass hierarchy. Thus, the increase in the rates of charged-current ¯νe reactions is smalland does not depend on sin2 2θ13.In an inverted mass hierarchy, the 7Li yield increases by a factor of 1.3 in the range ofsin2 2θ13 ≥ 2× 10−3. In this range, the 13-mixing resonance is adiabatic and, therefore all ¯νe3PoS(NIC-IX)196SN Nucleosynthesis with Neutrino Oscillations Takashi Yoshida0.710-6 10-4 10-2N(7 Li) / N(11B)sin22θ130.80.90.6normalinvertedno oscillations1.0Figure 2: Abundance ratio of 7Li to 11B as a function of sin2 2θ13. Dark and medium shaded regions cor-respond to a normal mass hierarchy and an inverted mass hierarchy, respectively. The lightly shaded regionis the case where the effect of neutrino oscillations is ignored. Solid, dotted, and dashed lines correspond tothe standard neutrino spectra in our study (see the text).in the He-rich layer result from conversion of ¯νµ,τ . This change raises the temperature T¯νe from 5MeV to 6 MeV and the rate of 4He( ¯νe,e+n)3H. However, the difference between T¯νe and T¯νµ,τ issmaller than that between Tνe and Tνµ,τ , so that the increase in the rate of 4He( ¯νe,e+n)3H is smallerthan that of 4He(νe,e−p)3He. In sin2 2θ13 ≤ 2× 10−5, the 7Li yield is larger by a factor of 1.1.When the 13-mixing resonance is nonadiabatic, the change of the energy spectra by oscillationsdoes not depend on the mass hierarchies.The dependence of the 11B yield on sin2 2θ13 is similar to that of 7Li. However, the 11B yieldis larger by a factor of 1.3 even in a normal mass hierarchy and adiabatic 13-mixing resonance.Furthermore, the 11B yield ratio is insensitive to mass hierarchies. Most of 11B is produced from4He by way of 7Li through 7Li(α,γ)11B. In a normal mass hierarchy and adiabatic 13-mixingresonance, the 11B yield increases by the enhancement of the 7Li yield by way of 7Be. However,most of 7Li produced through 7Be does not capture α-particles. In an inverted mass hierarchyand adiabatic 13-mixing resonance, the increase in the 11B yield is due to the enhancement of 7Liproduction by way of 3H. However, small difference of T¯νe and T¯νµ,τ makes the enhancement of 7Liand 11B yields small. A part of 11B is produced through the ν-process from 12C, especially in theO-rich layers. The reaction rates of 12C(νe,e−p)11C and 12C( ¯νe,e+n)11B increase in the cases ofnormal and inverted mass hierarchies, respectively. However, the 11B yield produced from 12C inthe He-rich layer is small even with neutrino oscillations.We have shown in [4] that the 7Li and 11B yields depend on neutrino temperatures and that wehave an uncertainty of a factor of 2.2 in the yields. This factor is larger than the enhancement of the7Li yield due to neutrino oscillations. Although the temperature dependence is similar among the7Li and 11B yields, the enhancement of the yield by neutrino oscillations is different between 7Liand 11B. Thus, we consider the dependence of the 7Li/11B abundance ratio on mass hierarchies andsin2 2θ13. Figure 2 shows the 7Li/11B abundance ratio with the relation of sin2 2θ13 in normal andinverted mass hierarchies. In this figure, we consider the uncertainties of the total neutrino energy4PoS(NIC-IX)196SN Nucleosynthesis with Neutrino Oscillations Takashi Yoshidaand the temperature of νµ,τ at the neutrino sphere [6] and the uncertainties of the temperaturesof νe and ¯νe [7]. When we do not consider neutrino oscillations, the 7Li/11B abundance ratio is0.58− 0.63. In sin2 2θ13 ≤ 1× 10−5, the 7Li/11B is 0.63− 0.71. In a normal mass hierarchy andadiabatic 13-mixing resonance (sin2 2θ13 ≥ 2×10−3), the 7Li/11B is larger than 0.83 by taking intoaccount uncertainties of neutrino temperatures. Thus, if a large 7Li/11B ratio is detected in starswhose atmosphere exhibits a clear signature of a strong contribution of SN ejecta, a normal masshierarchy and relatively large sin2 2θ13 (2×10−3≤ sin2 2θ13≤ 0.1) are suggested. Rebull et al. [14]measured the 11B/10B ratio in HD76932 using the Goddard High-Resolution Spectrograph with theHubble Space Telescope and inferred a ratio of 11B/10B ∼ 4− 10. Since SNe produce 11B ratherthan 10B, stars that exhibit a large 11B/10B ratio may provide direct evidence for the ν-process.Future observations of 7Li and 11B abundances in such stars might constrain mass hierarchies andthe mixing angle θ13.There are alternative astrophysical approaches to constraining neutrino mass hierarchies andthe mixing angle θ13. One such method involves detection of the diffuse supernova neutrino back-ground (DSNB). Although the DSNB has not yet been detected, improved detection methods andlarger detectors may soon lead to the detection of ¯νe in the DSNB [15]. In the case of an in-verted mass hierarchy and an adiabatic 13-mixing resonance, the ¯νe flux significantly differs fromwhat one would find for other oscillation parameters [16, 17, 18]. Another approach involves highredshift galaxy surveys. Since neutrinos with finite masses affect structure formation in the earlyUniverse, future galaxy surveys with higher precision may constrain the total mass of the neu-trino mass eigenstates (mν ,tot = m1 +m2 +m3) [19, 20]. Combining these approaches even morestringently constrains the mass hierarchy and θ13.It has been recently discussed the effect on neutrino oscillations from the contribution ofneutrino-neutrino interactions in deep region just above a proto-neutron star. In such a deep re-gion, the neutrino flux is so large that the neutrino-neutrino interactions may play an importantrole in the change of neutrino spectra in addition to the neutrino oscillations. The analysis of theneutrino oscillations with the neutrino-neutrino interactions has been conducted in several limitedcases [21, 22], and the effect on the neutrino spectra has been investigated [11]. We would liketo investigate the nucleosynthesis including this effect when more definite characteristics of theneutrino-neutrino interactions on neutrino spectra are found quantitatively.4. SummaryWe investigated the effects of neutrino oscillations on the 7Li and 11B production through theν-process in a SN model corresponding to SN 1987A. The 7Li and 11B yields taking into accountneutrino oscillations are larger than the corresponding yields without oscillations. In a normal masshierarchy and sin2 2θ13 ≥ 2×10−3, corresponding to adiabatic 13-mixing resonance, the 7Li yieldincreases by a factor of 1.9. On the other hand, the 11B yield increases by a factor of 1.3. In othercases of neutrino oscillation parameters, the enhancement of the 7Li and 11B yields is smaller. Ina normal mass hierarchy and sin2 2θ13 ≥ 2× 10−3, the enhancement of 7Li/11B is obtained eventaking account of uncertainties of neutrino temperatures and the total neutrino energy. Thus, thedetection of a 7Li/11B enhancement in stars displaying evidence for a definite SN suggest a normalmass hierarchy and relatively large sin2 2θ13. The answer to the question whether SN neutrino5PoS(NIC-IX)196SN Nucleosynthesis with Neutrino Oscillations Takashi Yoshidanucleosynthesis can constrain neutrino oscillation parameters is affirmative, but the effects aresubtle so that one requires high quality abundance measurements for a large sample of stars inorder to use this approach in a meaningful way.References[1] R. D. McKeown and P. Vogel, Phys. Rep. 394 (2004) 315.[2] S. E. Woosley, D. H. Hartmann, R. D. Hoffman, and W. C. Haxton, Astrophys. J. 356 (1990) 272.[3] T. Yoshida, M. Terasawa, T. Kajino, and K. Sumiyoshi, Astrophys. J. 600 (2004) 204.[4] T. Yoshida, T. Kajino, and D. H. Hartmann, Phys. Rev. Lett. 94 (2005) 231101.[5] K. Takahashi, M. Watanabe, K. Sato, and T. Totani, Phys. Rev. D64 (2001) 093004.[6] T. Yoshida, T. Kajino, H. Yokomakura, K. Kimura, A. 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Can Supernova Neutrino Nucleosynthesis Constrain Neutrino Oscillation Parameters?

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