Neutrinos in Supernova Evolution and Nucleosynthesis Gabriel Martínez Pinedo The origin of cosmic elements: Past and Present Achievements, Future Challenges, Barcelona, June 12 15, 2013 M.-R. Wu, T. Fischer, GMP, Y.-Z. Qian, arxiv:1305.2382 [astro-ph.he] Nuclear Astrophysics Virtual Institute
Introduction Sterile neutrinos and Supernova Summary Core-collapse supernova "! H.-Th. Janka, et al, PTEP 01A309 (2012)
Multidimensional simulations M. Liebendörfer et al. (2012) B. Müller, H.-Th. Janka & Marek, ApJ 756, 84 (2012) 3D supernova models with ELEPHANT 500 450 400 350 Radius [km] 300 250 200 150 15Ms, 432, LS EOS 15Ms, 600, LS EOS 100 11Ms, 600, LS EOS 40Ms, 432, LS EOS 50 15Ms, 432, TM1 EOS 15Ms, 432, DD2 EOS 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time After Bounce [s] Lνe [1052 erg/s] 3.0 2.5 2.0 1.5 1.0 400 600 800 11.2-1D 15.0-1D 15.0-2D 11.2-2D 11.2-3D 15.0-3D 3 o 2 o 1.5 o 1 o 0.5 o Lνe [1052 erg/s] 3.0 2.5 2.0 1.5 1.0 15.0-3D 11.2-2D 11.2-1D 11.2-3D 15.0-1D 15.0-2D 400 600 800 3 o 2 o 1.5 o 1 o 0.5 o 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 200 400 600 800 1000 Ṁ[M /s] texp [ms] F. Hanke, A. Marek, B. Müller & H.-Th. Janka, ApJ 755, 138 (2012)
Three-flavor neutrino parameters ν e ν µ ν τ 1 0 0 c 13 0 s 13 e iδ c 12 s 12 e iλ 2 0 = 0 c 23 s 23 0 1 0 s 12 c 12 e iλ 2 0 0 s 23 c 23 s 13 e iδ 0 c 13 0 0 e iλ 3 ν 1 ν 2 ν 3 U e1 U e2 U e3 = U µ1 U µ2 U µ3 U τ1 U τ2 U τ3 ν 1 ν 2 ν 3 normal hierarchy (m 3 ) 2 (m 2 ) 2 inverted hierarchy (m 1 ) 2 ( m 2 ) sol ( m 2 ) atm ν e ν µ ν τ ( m 2 ) atm m 2 sol = m 2 21 = (7.50 ± 0.20) 10 5 ev 2 m 2 atm = m 2 32 = (2.43 ± 0.13) 10 3 ev 2 θ 12 = 34.4 ± 1.3 θ 23 = 45 ± 4 θ 13 = 8.8 ± 0.8 ( m 2 ) sol (m 2 ) 2 (m 1 ) 2 (m 3 ) 2 At least two massive neutrinos: m 2 > 8.7 10 3 ev (Normal hierarchy) m 1 > 0.05 ev (Inverted hierarchy) Tritium decay m β = ( k U ek 2 m 2 k) 1/2 < 2 ev
Vacuum Oscillations As m 2 21 m2 32 the 3-flavor oscillation problem can be reduced to a two-flavor problem. In this case the probability that a ν e of energy E is observed as ν e after traveling a distance L is: P(ν e ν e ) = 1 sin 2 (2θ) sin 2 m2 21 L 4E For solar neutrinos (E νe 10 MeV) the oscillation length becomes: λ osc = 4πE m 2 21 300 km As the distance Sun-Earth and the radius of Earth are much larger than the oscillation length we can average the oscillation probability to get: P(ν e ν e ) = 1 1 2 sin2 (2θ) 0.57 around 40% (independently of energy) of Solar neutrinos should oscillate to other flavors.
Observations neutrinos Sun W. C. Haxton, R. G. Hamish Robertson & A. Serenelli, arxiv:1208.5723 [astro-ph.sr] Different detectors are sensitive to different neutrino energies Oscillation probability depends on neutrino energy
Matter effects As neutrinos travel through the Sun they scatter mainly with electrons. ν e have a much larger cross section that ν µ,τ. The evolution is governed by a combination of matter and vacuum hamiltonians (Mikheyev & Smirnov 1985, 1986; Wolfenstein 1978): H = H vac + H matter with H matter in the flavor basis: ( ) 2GF n H matter = e 0, n e Electron number density 0 0 The neutrino effective mass and mixing angle depends on the local value of the electron density.
MSW mechanism W. C. Haxton, R. G. Hamish Robertson & A. Serenelli, arxiv:1208.5723 [astro-ph.sr] (x) /2 H> e> (x) v H> > m i 2 2E The density at the resonance is: L> > L> e> ρ r = m u m 2 21 cos 2θ 2 2G F E (x c ) 0 that has to be smaller than the sun core density: ρ core 160 g cm 3. Hence, only neutrinos with: E m u m 2 21 cos 2θ 2 1.5 MeV 2G F ρ core will be affected by the MSW mechanism.
Solar Neutrinos and MSW mechanism Neutrinos with E 1.5 MeV will be affected by the MSW mechanism: P(ν e ν e ) = 1 2 1 cos(2θ) 0.32 2 Neutrinos with E 1.5 MeV will follow vacuum oscillations P(ν e ν e ) = 1 1 2 sin2 (2θ) 0.57 Bellini et al, Phys. Rev. Lett 108, 051302 (2012)
What about sterile neutrinos? For active-sterile neutrino oscillations m 2 as 1 ev and the resonances appear at densities relevant for supernova physics [Nunokawa, Peltoniemi, Rossi & Valle, PRD 56, 1704 (1997)]
Evidence for sterile neutrinos m 2 = 0.44 ev 2, sin 2 2θ 14 = 0.13 Short baseline reactor neutrino oscillation experiments show a dissappearance of neutrinos at distances 10 100 m (Reactor anomaly). observed / no osc. expected 1.1 1 0.9 0.8 0.7 ILL m 2 = 1.75 ev 2, sin 2 2θ 14 = 0.10 m 2 = 0.9 ev 2, sin 2 2θ 14 = 0.057 Bugey3,4 Rovno, SRP SRP Rovno Krasn Gosgen Bugey3 Gosgen Krasn Gosgen Krasn Bugey3 10 100 distance from reactor [m] Gallium solar neutrino experiments have been tested with radioactive 51 Cr or 37 Ar sources resulting in a deficit with respect to theoretically expected value 10 0 (Gallium anomaly) θ 14 9 Kopp, Machado, Maltoni, Schwertz, JHEP05 10 1 95 CL (2013) 050 10 3 10 2 10 1 ev 2 m 41 2 10 1 SBL reactors All Ν e disapp U e4 2 LBL reactors Solar KamL C 12 Gallium
MSW mechanism For the case of active (electron neutrinos)-sterille neutrinos. The ν e -ν e entry of the hamiltonian matrix is: Hmatter ee = 2G F n b (c e vy e + cv p Y p + c n vy n ) = 3 ( 2G F n b Y e 1 ) 3 And the MSW resonance for neutrinos will appear when: m 2 cos 2θ = 3 ( 2 2E ν 2 G Fn b Y e 1 ) = Vν eff 3 e, and for antineutrinos: m 2 cos 2θ = 3 2 2E ν 2 G Fn b ( Y e 1 ) = V ν eff 3 e,
Supernova profiles Y e 0.6 0.5 0.4 0.3 0.2 0.1 0.0 R νe R sh (a) 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10-1 100 1000 10-2 r (km) 2 2G F n b E ν / δm 2 V eff ν e (b) δm 2 cos2θ 2E ν 0 R νe R IR R sh R OR r
Neutrino conversion at the resonance For neutrinos we have: ν L = ν e, ν H = ν s (Before res.), ν L = ν s, ν H = ν e (After res.) For antineutrinos we have: ν L = ν s, ν H = ν e (Before res.), ν L = ν e, ν H = ν s (After res.) Both ν e and ν e can be converted to sterile neutrinos as they cross the resonance at Y e 1/3.
Survival probability Survival Probability P ee 1 0.8 0.6 0.4 0.2 0 L-Z formula Numerical integration 0 10 20 30 40 50 E(MeV) We define E 0.5 as the energy for which the probability is 0.5. Neutrinos with lower energies are converted to sterile neutrinos
Evolution resonance radius and E 0.5 r (km) 200 150 100 50 (a) R IR R sh R νe (b) E 0.5 (MeV) 0 40 30 20 10 0 (c) 10 100 t pb (ms) (d) 0 100 200 300 t pb (ms) 8.8 M (left) 11.0 M (right)
8.8 M (left) 11.0 M (right) Consequences q' νn / q νn 1 0.8 0.6 0.4 0.2 0 (a) ν e ν e (b) L ν (10 51 erg/s) E ν (MeV) 40 30 20 10 0 20 15 10 5 (c) (e) (d) (f) λ νe p / λ ν e n 1.5 1 0.5 0 10 100 t pb (ms) (g) (h) 0 100 200 300 t pb (ms)
Dependence mixing angle and δm 2 Countours of ratios of heating rates. 10 10-4 δm 2 (ev 2 ) 1 0.9 0.5 0.05 0.99 0.1 0.01 0.1 1 sin 2 2θ Supernova can help to constrain the mixing parameters
Summary There is growing evidence for the existence of sterile neutrinos with masses in the ev range If confirmed, active-sterile oscillations due to the MSW mechanism will occur in the region between neutrinosphere and supernova shock. The oscillations will affect supernova dynamics (reducing heating rates) and nucleosynthesis (affecting the Y e profile of matter). It is necessary to include a self-consistent treatment of oscillations in supernova simulations. They will help to constrain the allowed parameter space.