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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 - PowerPoint PPT Presentation
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Trieste 23-25 Sept. 2002
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
• 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(v
eZZ2expESE1E
221
4
Stellar burning rates• The relevant quantity is:
Gamow peak
Tunnel effectexp[-b/E1/2]
Maxwel Boltzmannexp[-E/KT]
kTEkTESσv o
o3exp2/1
• 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
5
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 [K
evb]
3He(4He7Be
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)
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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/QK 210o
TOT
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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]
Neut
rino
flux
[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/
iSSM
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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….
23
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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 E2QK
i=different species of neutrinos
25
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 S17Junghans 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/SSSSopaZ/XgeaLS/SSSS
Nuclear TemperaturePi 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 2.5uncertaintycontribution [%]
2 7 2 10 4 3 0.6 8 5
total 12% 11%
• Contribution to uncertainty:
• Constrain on Tc from B, EXP :
%1NuclearNuclear
201
TT 2
EXPB
B2
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/S33
1/2
• 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