Nuclear reactions and solar neutrinos
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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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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
15
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