Nuclear reactions and solar neutrinos

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Trieste 23-25 Sept. 2002
Episode III
Nuclear reactions and solar neutrinos
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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

• 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)

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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 ? (? 1/2 Z1Z2T)2/3 10-20 KeV Gamow
Energy
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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. pp -gt dene a4
• 3He(3He,2p)3He a 16
• 7Be(p,g)8B a 13
• This dependence which will be crucial for the
  determination of neutrino fluxes

adlogltsvgt/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.

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 3He3He at
  solar Gamow peak.

2 events/month !
S(0)5.32 (1 6)MeVb
PRL 82(1999) 5205
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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 (Q26,73MeV)
• 4p2e- -gt 4He

?

• Then one has 2ne for each Q of radiated energy,
  and the total neutrino produced flux is

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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

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The pp-chain
99,77 p p ? d e ?e
0,23 p e - p ? d ?e
2?10-5
86
d p ? 3He ?
14
3He 4He ?7Be ?
0,02
13,98
7Be e- ? 7Li ?e
7Be p ? 8B ?
3He3He??2p
7Li p -gt??
3Hep??e?e
pp I
pp III
pp II
hep
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Main components of solar neutrinos
pp pp?de?e 0.42 5.96 .1010
1 0.1 Ro
7Be 7Bee-?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 (1s) production zone
8B 8B?8Bee?e 15 5.15 .106
18 0.05 Ro
from Bahcall et al ApJ 555(2001) 990
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A group photo (1)
Neutrino flux cm-2 s-1
Neutrino Energy Mev
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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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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)

Fpp Tc-0.7
FB Tc 20
FBe Tc 10

• Be neutrinos strong depends on Tc, due to Gamow
  factor in 3He4He
• B neutrinos has the strongest dependence due both
  to 3He4He and (mainly) to 7Bep
• For the conservation of total flux, pp neutrinos
  decrease with increasing Tc

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For the sake of precision

• All physics cannot be exactly summarized in a
  single parameter Tc
• By using a power law parametrization
  FiPi b PSij, L,Z/X, opa,age
• and by varying the SSM inputs around their
  uncertainties, one has

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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.

Fi/FiSSM
Tc/TcSSM
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Recent experimental data on B-n

• Superkamiokande (ne--gt n e- )
• F(B)SK 2.32 (1 3.5) 106 cm-2 s-1
  (ne,nm,nt)
• SNO - CC (ned-gt nne )
• F(B)SNO1.75 (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 (nd-gt npn)
• 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
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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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Episode IV...
next year?
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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 ltEgt 0.3
  MeV can be neglected for an approximate estimate.

idifferent species of neutrinos
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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
  14Np

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CN-neutrinos
F 17F?17Oe?e 2 5.63 .106
25 0.05 Ro
N 13N?13Ce?e 1.2 5.48.108
19 0.05 Ro
O 15O?15Ne?e 1.7 4.80 .108
22 0.05Ro
name reaction spectrum MeV abundance cm -2
s-1 uncertainty (1s) production zone
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Status of S17
Junghans et al PRL 88 (2002) 041101
Junghans
194-2 eVb
(1983)
(2001)
(2002)
(1967)
racomanded value in Adelberger 1998
compilation, (1s)
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Sterile neutrinos?

• We have seen
• F(8B)EXP5.20 (1 18) 106 cm-2 s-1
• F(8B)SSM5.15 (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)sterilelt 2.5 106 cm-2 s-1 (at 2s)
• if sterile neutrinos exist, F(8B)EXP is a lower
  limit

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B-neutrinos and Tc

• Power laws

• Contribution to uncertainty

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• Constrain on Tc from FB, EXP

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Helioseismology and Be-neutrinos

• Helioseismology can provide information also on
  the nuclear cross sections of
• 3He3He -gt a 2p
• 3He4He -gt 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?

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S34 /S34
S33/S33SSM
S34/S34SSM

• S34 is costrained at 25 level

S33/S33SSM stay in 0.64-1.8

• Since F(Be) a S34/S331/2
• gtF(Be) is determined to within 25

• Also uP/r satisfies the same scaling relation
• u u (S34/S331/2 ) lt-gt F(Be)
• n(Be) waste more energy than n(pp) . If their
  production is larger, more H-gtHe 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.