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Nuclear reactions and solar neutrinos

Trieste 23-25 Sept. 2002. Episode III. Nuclear reactions and solar neutrinos. Nuclear reactions and solar neutrinos. The basis of Nuclear Astrophysics The spies of nuclear reactions in the Sun The luminosity constraint The pp chain -pp neutrinos -Be neutrinos -B neutrinos

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Nuclear reactions and solar neutrinos

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  1. Trieste23-25 Sept. 2002 Episode III Nuclear reactions and solar neutrinos

  2. Nuclear reactions and solar neutrinos • The basis of Nuclear Astrophysics • The spies of nuclear reactions in the Sun • The luminosity constraint • The pp chain -pp neutrinos -Be neutrinos -B neutrinos • What have we learnt about the sun from solar neutrino experiments?

  3. Cross sections of astrophysical interest • The Gamow formula: • exp is the penetration probability through barrier, determined by Coulomb interaction • S is the astrophysical factor, determined by nuclear physics, depending on the process involved ( strong, e.m, weak)

  4. Maxwel Boltzmann exp[-E/KT] Gamow peak Tunnel effect exp[-b/E1/2] Stellar burning rates • The relevant quantity is: • where f(E) is the velocity distribution • The main contribution arises from nuclei near the Gamow peak, generally larger than kT: Eo  ( 1/2Z1Z2T)2/3 » 10-20 KeV Gamow Energy

  5. a Stellar burning rates vs temperature • The strong energy dependence of the cross section translates into a strong dependence of the rate on the temperature. • This dependence is usually parametrized by a power law: • e.g. : p+p -> d+e++nea=4 3He(3He,2p)3He a =16 7Be(p,g)8B a =13 • This dependence which will be crucial for the determination of neutrino fluxes a=dlog<sv>/dlogT

  6. 3He(4He,g)7Be S [Kevb] Determination of the astrophysical S- factor • Nuclear physics is summarized in S(E), which (in absence of resonances) is a smooth function of E. • The measurement near the Gamow peak is generally impossible, one has to extrapolate data taken at higher energies. Sun

  7. The lowest energies frontier • Significant effort has been devoted for lowering the minimal detection energy • Since counting rates become exponentially small, cosmic ray background is a significant limitation. • This has been bypassed by installing acelerators deep underground*. *Fiorentini, Kavanagh and Rolfs (1991)

  8. LUNA result* • LUNA at LNGS has been able to measure 3He+3He at solar Gamow peak. 2 events/month ! S(0)=5.32 (1± 6%)MeVb *PRL 82(1999) 5205

  9. The spies of nuclear reactions in the Sun • The real proof of the occurrence of nuclear reactions is in the dectection of reaction products. • For the Sun, only neutrinos can escape freely from the production region. • By measuring solar neutrinos one can learn about the deep solar interior (and about neutrinos…)

  10. = if L and Le are conserved ? 2ne The luminosity constraint • The total neutrino flux is immediately derived from the solar constant Ko: • If one assumes that Sun is powered by transforming H into He (Q=26,73MeV): 4p+2e- -> 4He + ? • Then one has 2ne for each Q of radiated energy, and the total neutrino produced flux is:

  11. Towards neutrino energy spectra • To determine Ftot we did not use anything about nuclear reactions and solar models. • In order to determine the energy distribution of solar neutrinos one has to know the producing reactions rate and their efficiency in the Sun

  12. 8B 8Be*+ e+ +e 2 The pp-chain 99,77% p + p  d+ e+ + e 0,23% p + e - + p d + e 86% d + p 3He + ~210-5 % 14% 3He + 4He 7Be +  13,98% 0,02% 7Be + e-7Li + e 7Be + p 8B +  3He+3He+2p 7Li + p ->+ 3He+p+e++e pp I pp II pp III hep

  13. Main components of solar neutrinos name: reaction: spectrum: [MeV] abundance: [cm -2 s-1] uncertainty: (1s) production zone: pp p+pd+e++e £0.42 5.96.1010 1% 0.1 Ro 7Be 7Be+e-7Li+e 0.861 (90%) 0.383 (10%) 4.82.109 10% 0.06 Ro 8B 8B8Be+e++e £15 5.15 .106 18% 0.05 Ro from: Bahcall et al ApJ 555(2001) 990

  14. A group photo (1) Neutrino flux [cm-2 s-1 ] Neutrino Energy [Mev]

  15. A group photo (2) The fraction of neutrino produced inside the sun within dR

  16. Remarks: • The production efficiency of the different neutrinos depends on: 1) Nuclear inputs (cross sections) 2)Astrophysical inputs (Lum.,opacity, age,Z/X…) which affect physical conditions of the medium where they are produced: particle density and (most relevant) temperature • Uncertianties on the predicted neutrino fluxes depend thus on nuclear physics and astrophysics (Z/X, opacity age, Lum….). To a good approximation these latter can be reabsorbed in the solar temperature. • Remarks: uncertianties on fluxes are correlated, since they depend on uncertianties on the same physical parameters, i.e. one cannot tune the parameters in order to deplete Be-neutrinos without changing B-neutrinos

  17. Dependence on Tc • By building different solar models, with varied inputs parameters (within their uncertainties) and by using a power law parametrization, one finds (approximately): FBe~ Tc 10 FB ~ Tc 20 Fpp~ Tc-0.7 • Be neutrinos strong depends on Tc, due to Gamow factor in 3He+4He • B neutrinos has the strongest dependence due both to 3He+4He and (mainly) to 7Be+p • For the conservation of total flux, pp neutrinos decrease with increasing Tc

  18. Spp S33 S34 S17 L Z/X opa age pp 0.14 0.03 -0.06 0 0.73 -0.08 0.008 -0.07 Be -0.97 -0.43 0.86 0 3.4 0.58 -0.08 0.69 B -2.59 -0.40 0.81 1 6.76 1.3 2.6 1.28 N -2.53 0.02 -0.05 0 5.16 1.9 -0.1 1.01 O -2.93 0.02 -0.05 0 5.94 2.0 -0.12 1.27 T -0.14 - - - 0.34 0.08 0.14 0.08 For the sake of precision • All physics cannot be exactly summarized in a single parameter Tc • By using a power law parametrization Fi~Pi bP=Sij, L,Z/X, opa,age • and by varying the SSM inputs around their uncertainties, one has:

  19. ….anyhow • pp, Be and B neutrinos are mainly determined by the central temperature almost independently of the way we use to vary Tc. Fi/FiSSM Tc/TcSSM

  20. Recent experimental data on B-n • Superkamiokande (n+e--> n +e- ): F(B)SK= 2.32(1±3.5%) 106 cm-2 s-1 (ne,nm,nt) • SNO - CC (ne+d-> n+n+e+ ): F(B)SNO=1.75 (1±8.0%) 106 cm-2 s-1(ne) • Combined*: F(B)EXP= 5.20 (1±18%) 106 cm-2 s-1 flux of total active neutrinos produced in the Sun • agreement with recent SNO - NC (n+d-> n+p+n): • F(B)NC= 6.42 (1±25%) 106 cm-2 s-1 • SSM: 5.15 (1 ±18%) 106 cm-2 s-1 * see. Fogli, Lisi,Montanino, Villante PRD 1999; Fogli, Lisi, Montanino, Palazzo PRD 2001

  21. What have we learnt on the Sun from solar neutrinos? (1) • The measurement of the (total active) B-neutrino flux, from SK and SNO provides a confirmation to the 1% level of the “central” solar temperature (i.e the temperature at the B-neutrinos production zone, »0.05 Ro)* • Gallium expts (GALLEX and SAGE) have provided the proof the Sun is powered by nuclear reactions (pp-low energy neutrinos have been detected) * Fiorentini and B.R. PLB 526 (2002) 186

  22. What have we learnt on the Sun from solar neutrinos? (2) • These are wonderful confirmations of the SSM, but no quantitative improvement of our knowledge of the solar interior • Future experiment, where individual neutrino fluxes will be measured, and the knowledge of neutrinos survival, will allow the dream of learning on the Sun from neutrinos….

  23. Episode IV... next year?

  24. Remarks • So far we neglegcted the energy carried by neutrinos. The general formula for the luminosity constraint is: • Actually the average neutrino energies <E>~ 0.3 MeV can be neglected for an approximate estimate. i=different species of neutrinos

  25. (p,) (p,) 13C 14N 17O (p,) CN 1,49% NO 0,01% (e+,e) (e+,e) 17F 13N 15O (e+,e) (p,) (p,) 12C 15N 16O (p,) (p,) CNO be-cycle • This cycle is responsible for only 1.5% of the solar luminosity The overall conversion of 4p into He is achid with the aid of 12C, the total energy release is 26.7 MeV • This cycle is governed by the slowest reaction: 14N+p

  26. CN-neutrinos F 17F17O+e++e £2 5.63 .106 25% 0.05 Ro name: reaction: spectrum: [MeV] abundance: [cm -2 s-1] uncertainty (1s) production zone: N 13N13C+e++e £1.2 5.48.108 19% 0.05 Ro O 15O15N+e++e £1.7 4.80 .108 22% 0.05Ro

  27. Junghans et al PRL 88 (2002) 041101 Status of S17 Junghans 19+4-2 eVb* (1967) (1983) (2001) (2002) * racomanded value in Adelberger 1998 compilation, (1s)

  28. Sterile neutrinos? • We have seen: F(8B)EXP=5.20 (1±18%) 106 cm-2 s-1 F(8B)SSM=5.15 (1±18%) 106 cm-2 s-1 • very good agreement between EXP and SSM • similar errors affects both determinations • we can derive an upper bound for sterile neutrinos: F(8B)sterile< 2.5 106 cm-2 s-1 (at 2s) • if sterile neutrinos exist, F(8B)EXP is a lower limit

  29. B-neutrinos and “Tc” • Power laws: • Contribution to uncertainty: 12% • Constrain on Tc from FB, EXP : 11%

  30. Helioseismology and Be-neutrinos • Helioseismology can provide information also on the nuclear cross sections of 3He+3He -> a +2p 3He+4He -> 7Be +g • These govern Be-neutrino production, through a scaling law: F(Be) a S34/S331/2 • Can one measure F(Be) by means of Helioseismology?

  31. S34 /S34 S34/S34SSM S33/S33SSM • S34 is costrained at 25% level S33/S33SSM stay in 0.64-1.8 • Since F(Be) a S34/S331/2 • =>F(Be) is determined to within 25% • Also u=P/r satisfies the same scaling relation • u = u (S34/S331/2 ) <-> F(Be) • n(Be) waste more energy than n(pp) . If their production is larger, more H->He is burnt for the same e.m. energy and the molecular weight increases • Since T does not depend on S34 or S33 , sound speed decreases when n(Be) is increased.

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