Chapter three Sun

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Chapter three Suns model
Major contributions in building the Suns model
have been made by Eddington (1930s),
Hoyle (1950s),
Bahcall, Clayton (1980s) and others.
1. Rate of energy generation
W kg-1 (3.1)
where X is hydrogen mass factor
W kg-1 (3.2)
where ZN is nitrogen mass factor
These predict very rapid temperature dependence
for power output,
E ? T n
T n E ( W kg-1) PP 5 x 106 6 10-5 1 x
107 4.5 3 x 10-4 1.5 x 107 4 1.7 x 10-3 CNO 5 x
106 29 3 x 10-16 1 x 107 23 1 x 10-8 1.5 x
107 20 3 x 10-5
CNO rapidly overtakes PP, rates equal at 1.7 x
107 K
Suns central temperature is believed to be 1.56
x 107 K, hence importance of neutrino experiments
is to try to find which fusion reactions occur.
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2. Mystery of the missing solar neutrinos
2.1 The flux of neutrinos predicted
--But few of the details are open to observation
because the whole process is obscured by million
of kilometres of stellar matter
--But the cover-up is not complete
-- Neutrinos can escape almost without
interaction from the heart of a star.
--The neutrino flux from the Sun ?a direct window
to the interior and its nuclear reactions.
Estimate the flux of neutrinos
In the hydrogen burning process,
Then neutrinos must be released at a rate of
To escape from the Sun, each neutrino must travel
a distance
The probability of interaction during this escape
is
is the average interaction cross-section with an
electron or a nucleus
the average density of electrons and nuclei in
the sun is ,
Thus neutrinos do indeed escape almost
unhindered from the sun and arrive some eight
minutes later at the earth.
so we have P10-9.
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The neutrino flux at earth is
In Summary, the following fusion reactions give
neutrinos
Process Fv (1014 m-2s-1
) Emax(MeV) PPI p
p ? H12 e ? 6.0
0.42 PP II 7Be e- ? 7Li ? 0.47
0.86 PP III 8B ?
8Be e ? 5.8 10-4
15 CNO cycle13N ? 13C e ? 0.06
1.2 CNO cycle 15O? 15N
e ? 0.05
1.73
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2.2 Properties of neutrinos
a) Massless (or nearly so?) but they have
energy/ momentum
b) Speed of light (or very close)
c) Very weak interaction with matter, essentially
all leave the Sun.
If we can detect on Earth, we can measure
reaction rates of various stages of H ? He fusion
and hence temperature of fusion reaction. No
other technique could provide such a direct probe
of conditions in the Suns core.
2.3 Detecting neutrinos
a) First experiment
Site 1 mile down the abandoned Homestake gold
mine in South Dakota, USA, to minimise cosmic
rays
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Detect principle
37Cl ? ? 37Ar e
The number of Argon 37 atoms detected gives the
number of neutrino interactions in the chlorine
vat? the solar neutrino flux.
The chief drawback of this reaction is that only
neutrinos with Ev gt 0.81 MeV can be detected.
From the table in the previous slide, this high
threshold energy implies that neutrinos from the
primary P-P fusion reaction cannot be detected.
The neutrino from electron capture on 7Be only
just exceed the threshed and the probability of
capture in 37Cl is exceedingly low
Most of neutrinos from 8B decay have an energy
well above the threshold for detection.
Even though these neutrinos contribute a minor
component of the neutrino flux from the sun, they
are expected to dominate the capture rate in
37Cl.
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The actual capture rates depend on incident
neutrino flux, the number of target 37Cl nuclei
and the energy-averaged neutrino capture
cross-section.
For the neutrinos from 8B decay, the average
capture cross-section 37Cl is
and a target containing N(37Cl) nuclei should
give a capture rate of
Because of the low probability of neutrino
capture, a special unit called the solar neutrino
unit (SNU) is used in neutrino astrophysics
This is the capture rate per second per 10 -36
target nuclei
Therefore the capture rate of neutrinos from 8B
decay in the SUN should be 6.1 SNU
the capture rate of neutrinos from 7Be 1.1 SNU
From N13 0.1SNU and from O15 0.3SNU.
In total (7.9 ?2.6) SNU
Predicted capture rate of neutrinos
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Result
Data taken from 1969 until 1993 (24 years!!)
gives observed rate 2.55?0.2 SNU
The discrepancy (a deficit 69) between the
observed capture rate and the predicted capture
rate of solar neutrinos in 37Cl has and continues
to be a subject of debate in astrophysics.
b) SAGE and GALLEX collaborations began taking
data in late 1991..
A container with 12.2 tons of watered Gallium 71
which, after an interaction with a solar
neutrino, becomes Germanium 71
71Ga ? ? 71Ge e-
a radioactive isotope with a half-life of 11.43
days.
From May 1991 to September 1993 observation gave
a mean of 79-11 SNU while theory predicts 132
SNU. This is a neutrino deficit of 40. Why?
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2.4 Reason for the discrepancy ?
Possibilities
1). Temperature of centre of Sun is lower than
thought (15.2, not 15.6 x 106 K) Astrophysicists
claim standard model better than 3 accurate.
2). Nuclear reaction rates incorrect
If more of CNO, less of PP, we would see fewer
neutrinos
Nuclear physicists do not believe rates are
wrong, but CNO is VERY temperature sensitive
3). Neutrinos rest mass is not zero, so energy
carried off is different
An appealing possibility since it leads to much
more research and speculation!
4). Neutrino changes on the journey to Earth
3 types electron, muon, tau neutrinos
There is recent evidence for this.
5). Some other unsuspected problem with detectors
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2.5 Solutions
In 1998, a Kamiokande experiment on cosmic ray
--provided evidence that muon neutrinos can
transform to tau neutrinos as they travel through
the earth
If electron neutrinos behave similarly, one could
account for the low detection rate of solar
neutrinos on earth
-- because none of the solar neutrino experiments
would detect an electron neutrino emitted during
hydrogen burning if it changes to a muon or tau
neutrino as it propagates through the sun or the
earth
The detection of muon or tau neutrinos from the
sun would provide evidence for the transformation
of electron neutrinos to muon or tau neutrinos
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Recent experiment Two kilometers down in the
Sudbury Neutrino Observatory, sensors on the
interior of these studded panels detect dim
flashes when neutrinos interact with heavy water
inside this ball
The new data indicate that electron neutrinos
oscillate with other flavors as they make their
way to Earth.
Because detectors have been less sensitive to
muon and tau than to electron neutrinos, the
result was a systematic undercounting of solar
neutrinos
Science News, Vol. 159, No. 25, June 23, 2001, p.
388