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 What have we learnt about the sun from solar neutrino experiments?

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)

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

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++ne a=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 a=dlog<sv>/dlogT

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

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)

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

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…)

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 + ? = if L and L e are conserved 2ne ? Then one has 2ne for each Q of radiated energy, and the total neutrino produced flux is:

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

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 ->+ 8B  8Be*+ e+ +e 2 3He+p+e++e pp I pp II pp III hep

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

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

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

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

Dependence on Tc FBe~ Tc 10 FB ~ Tc 20 Fpp~ Tc-0.7 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

For the sake of precision All physics cannot be exactly summarized in a single parameter Tc By using a power law parametrization Fi~Pi b P=Sij, L,Z/X, opa,age and by varying the SSM inputs around their uncertainties, one has: 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

….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

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

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

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….

Episode IV... next year?

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

CNO be-cycle This cycle is responsible for only 1.5% of the solar luminosity 17F 16O 17O (p,) (p,) (e+,e) 13C 13N 15N 12C 15O 14N CN 1,49% NO 0,01% 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

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

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

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

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

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?

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.