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Trieste 23-25 Sept. 2002

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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?

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Cross sections of astrophysical interest

• 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)

• The Gamow formula:

)E(veZZ2

expESE1

E2

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4

Stellar burning rates• The relevant quantity is:

Gamow peak

Tunnel effectexp[-b/E1/2]

Maxwel Boltzmannexp[-E/KT]

kT

EkTESσv o

o

3exp2/1

• 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

E)σ(E)v(E)f(dEσv

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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++e =4 3He(3He,2p)3He =16 7Be(p,)8B =13

• This dependence which will be crucial for the determination of neutrino fluxes

Tv

=dlog<v>/dlogT

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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.

S [

Kevb

]

3He(4He7Be

Sun

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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)

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LUNA result*• LUNA at LNGS has been able to measure

3He+3He at solar Gamow peak.

*PRL 82(1999) 5205S(0)=5.32 (1 6%)MeVb

2 events/month !

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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…)

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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 2e for each Q of radiated energy, and the total neutrino produced flux is:

• = if L and L e are conserved2e?

s/cm/104.62/Q

K 210oTOT

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Towards neutrino energy spectra

• To determine tot 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

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The pp-chainThe pp-chain99,77%

p + p d+ e+ + e

0,23%p + e - + p d +

e

3He+3He+2p

3He+p+e+

+e

~210-5

%86%

14%

0,02%13,98%3He + 4He 7Be +

7Be + e- 7Li + e7Be + p 8B

+

d + p 3He +

7Li + p ->+

pp I pp I pp IIIpp III pp IIpp II hephep

8B 8Be*+ e+ +e

2

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Main components of solar neutrinos

pp p+pd+e+

+e

0.42

5.96 .1010

1%

0.1 Ro

7Be7Be+e-

7Li+e

0.861 (90%)0.383 (10%)

4.82 .109

10%

0.06 Ro

name:reaction:spectrum:[MeV]abundance:[cm -2 s-1]uncertainty

:(1)production

zone:

8B8B8Be+e+

+e

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5.15 .106

18%

0.05 Rofrom: Bahcall et al ApJ 555(2001) 990

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A group photo (1)

Neutrino Energy [Mev]

Neutr

ino fl

ux [

cm-2 s

-1 ]

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A group photo (2)

The fraction of neutrino produced inside the sun within dR

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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

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ppTc

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):

• 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

B Tc BeTc

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Spp S33 S34 S17 L Z/X opa age

pp 0.14 0.03 -0.06 0 0.73 -0.08 0.008 -0.07Be -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 1.28N -2.53 0.02 -0.05 0 5.16 1.9 -0.1 1.01O -2.93 0.02 -0.05 0 5.94 2.0 -0.12 1.27T -0.14 - - - 0.34 0.08 0.14 0.08

• All physics cannot be exactly summarized in a single parameter Tc

• By using a power law parametrization

iPi P=Sij, L,Z/X, opa,age

• and by varying the SSM inputs around their uncertainties, one has:

For the sake of precision

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….anyhow

• pp, Be and B neutrinos

are mainly determined

by the central

temperature almost

independently of the

way we use to vary Tc.

Tc/TcSSM

i/

iSS

M

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• agreement with recent SNO - NC (d->

n+p+):(B)NC= 6.42 (1±25%) 106 cm-2 s-1

• SSM: 5.15 (1 ±18%) 106 cm-2 s-1

flux of total active neutrinos produced in the Sun

Recent experimental data on B-• Superkamiokande (e--> e- ):(B)SK= 2.32(1±3.5%) 106 cm-2 s-1 e

• SNO - CC (ed-> n+n+e+ ):

(B)SNO=1.75 (1±8.0%) 106 cm-2 s-1 e

• Combined*:(B)EXP= 5.20 (1±18%) 106 cm-2 s-1

* see. Fogli, Lisi,Montanino, Villante PRD 1999; Fogli, Lisi, Montanino, Palazzo PRD 2001

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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

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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….

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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.

ii

io E2Q

K

i=different species of neutrinos

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CNO be-cycle• This cycle is responsible for only

1.5% of the solar luminosity

17F

16O

17O

(p,)

(p,)

(p,)

(p,)

(e+,e)

13C

13N

15N12C

15O

14N

(p,)

(p,)

(e+,e)

(p,)

(e+,e) CN1,49%

NO0,01%

• This cycle is governed by the slowest reaction: 14N+p

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CN-neutrinos N13N13C+e+

+e

1.2

5.48.108

19%

0.05 Ro

O15O15N+e+

+e

1.7 4.80 .108

22%

0.05Ro

name:reaction:spectrum:[MeV]abundance

:[cm -2 s-1]uncertainty(1)production

zone:

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Status of S17

Junghans et alPRL 88 (2002) 041101

Junghans

19+4-2 eVb*

* racomanded value in Adelberger 1998 compilation, (1)

(1983) (2001) (2002)(1967)

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Sterile neutrinos?

• We have seen:(8B)EXP=5.20 (1±18%) 106 cm-2 s-1

(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:

(8B)sterile< 2.5 106 cm-2 s-1 (at 2)

• if sterile neutrinos exist, (8B)EXP is a lower

limit

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B-neutrinos and “Tc” • Power laws:

20

ce7170.8134

0.40-33B

6.21.31.2817

6.76o

59.2ppe717

0.8134

0.40-33B

T/SSSS

opaZ/XgeaLS/SSSS

Nuclear Temperature

Pi S33 S34 Se7 S17 Spp Lo age z/x opa Pi / Pi [%] 6.1 9.4 2 9 1.7 0.4 0.4 6.1 2.5

uncertaintycontribution [%]

2 7 2 10 4 3 0.6 8 5

total 12% 11%

• Contribution to uncertainty:

• Constrain on Tc from B, EXP :

%1Nuclear

Nuclear

201

TT

2

EXPB

B

2

c

c

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Helioseismology and Be-neutrinos

• Helioseismology can provide information also on the nuclear cross sections of

3He+3He -> +2p3He+4He -> 7Be +

• These govern Be-neutrino production, through a scaling law:

(Be) S34/S331/2

• Can one measure (Be) by means of Helioseismology?

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S34 is costrained at 25% level S33/S33SSM stay in 0.64-1.8

Since (Be) S34/S331/2

(Be) is determined to within 25%

S34 /S34 S33/S33SSMS34/S34

SSM