Transcript Il Sole: 1a puntata - Istituto Nazionale di Fisica Nucleare

Trieste 23-25 Sept. 2002
The standard solar model
and solar neutrinos
• Episode I:
Solar observables and typical scales
• Episode II:
Standard and non-standard solar models
• Episode III:
Nuclear reactions and solar neutrinos
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2
Main solar observables and
typical scales
• Observables:
Mass, Luminosity, Radius, Age,
Metal content of the photosphere
• The typical scales
• Helioseismic data
Rotation
Magnetic fields
3
Who measured the solar mass?
Galileo
Einstein
Cavendish
Smirnov
4
Solar mass
• Astronomy only deals with the extremely well
determined Gaussian constant:
GNMo=(132 712 438  5) 1012 m3/s2
• Astrophysics needs Mo, since:
- opacity is determined by
Ne  Np  Mo/mp  1057
- energy content/production of the star
depends on Np.
• Cavendish, by determining GN provided a
measurement of Mo
• The (poor) accuracy on GN (0.15%)reflects on Mo
Mo= 1.989 (1  0.15%) 1033 gr  1057mp
5
Solar Luminosity
• The solar constant Ko: amount of energy, per
unit time and unit area, from the Sun that
reaches the Earth, measured ^ to the direction to
the Sun, without atmosphere absorption .
• Is not a constant, but varies with time (0.1% in a
solar cycle). The value averaged over 12 years of
the solar irradiance (and over diffent satellite
radiometers) gives the solar luminosity:
Lo=4pd2Ko =3.844(1  0.4%) 1033 erg/s
6
Solar Radius
• The distance from the center of the sun
to its visible surface (the photosphere)
• Difficult to define the edge of the sun
• Different methods and different
experiments:
Ro=6.9598(1 0.04%) 1010 cm
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Solar Age
• Method: radioactive dating of oldest
objects in the solar system
(chondrite meteorites)
• Problems:
– relationship between the
age of the meteorite and the
age of the sun
– what is the the zero time
for the sun?
• The age of the sun referred to
Zero Age Main Sequence point
t=4.57(1  0.4%) Gyr
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Solar Metal abundance
• Spectroscopic measurements of the solar
photosphere yield the relative
abundances (in mass) of “Metals“ to H
(Z/X)photo=0.0245(1  6%)
• Most abundant: O, C, N, Fe
• Results are generally consitent with
the meteoritic abundances
• A remarkable exception: the solar Li
content is depleted by 100 with respect
to meteorites
Note: Hydrogen abundance X~ 0.75
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A remark: Helium abundance
• Helium was discovered in the Sun
(1895), its abundance cannot be
accurately measured there
• Until a few years ago, as determination
of present photospheric He abundance
was taken the result of solar models
• Helioseismology provides now an
indirect measurement…..
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Typical scales
• r =3Mo/(4pRo3) 1.5 g/cm3
• P =GMo2/Ro4 1016 dine/cm2
• vs u1/2 = (P/r) 1/2  800 Km/s
• photon mean free path*:
l=1/(ne sTh)
 1/(1024 cm-3 10-24 cm2)  1 cm
(photon escape time 2 104 yr)
Enuc 1MeV
nuc 

2
•  =Lot  10-4 Moc2
1GeV
mc
typical nuclear energy scale
E chem 1eV
 chem 

2
1GeV
mc
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*astrophyscists use “opacity” k: l=1/(r k)
The birth of Nuclear Astrophysics
Eddington: Nature (1920)
 =Lot  10-4 Moc2
“Certain physical investigations in the past year make it
probable to my mind that some portion of sub-atomic
energy is actually being set free in a star. … If five per
cent of a star's mass consists initially of hydrogen atoms,
which are gradually being combined to form more
complex elements, the total heat liberated will more
than suffice for our demands, and we need look no
further for the source of a star's energy…”
•In the same paper: “If indeed the sub-atomic energy in
the stars is being freely used to maintain their great
furnaces, it seems to bring a little nearer to fulfilment
our dream of controlling this latent power for the wellbeing of the human race - or for its suicide”
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Can nuclear reaction occur into the sun?
The temperature scale
• We have found P and r scales
• Need equation of state for T.
• Take Perfect gas and assume it is all
hydrogen (ionized):
kT= P/(2np)=P mp/(2r)
1 keV (T  1.2 107 K)
• Note: kT>> e2/r  e2n1/3
perfect gas reasonable
• However: KT<< e2/rnuc  1MeV
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Nuclear Astrophysics grows
• Rutherford: kT too small to overcome Coulomb
repulsion at nuclear distance. Nuclear fusion in star
cannot occur according to classical physics
• Gamow (1928): discovery of tunnel effect.
=> Nuclear reactions in star can occur below the
Coulomb barrier (Atkinson, Houtermans, Teller)
• von Weizsäcker (1938) : discovered a nuclear cycle,
(CNO) in which hydrogen nuclei could be burned
using carbon as a catalyst.
• Bethe (1938): worked out the basic nuclear
processes by which hydrogen is burned (fused) into
helium in solar (and stellar) interiors (pp chain)14
The gross solar structure
• Hot nucleus
R < 0.1 Ro
M  0.3 Mo
(nuclear reaction)
• Radiative zone
0.1  0.7 Ro
M  2/3 Mo
• Convection zone
0.7  1 Ro
M  1/60 Mo
As temperature drops, opacity
increases and radiation is not
efficient for energy transport
• Photosphere: deepest layer of
the Sun that we can observe
directly
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Helioseismology
•Birth: in 1960 it turns out that the solar
surface vibrates with a period T  5 min,
and an “amplitude” of about 1Km/s
•Idea: reconstructing the properties of
the solar interior by studying how the
solar surface vibrates
(like one studies the deep Earth ’s structure through
the hearthquake or just like you can tell something
about a material by listening to the sounds that it
makes when something hits it)
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Procedure (1)
• By using Doppler effect,
one measures the
oscillation frequencies
with a very high accuracy
(w/w  10-3 - 10-4)
l v v o
 
sinwt
l
c
c
• Most recent measurements
come from apparatus on
satellite: Soho (SOlar and
Heliospheric Observatory)
http://sohowww.nascom.nasa.gov/
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Procedure (2)
• The observed oscillations are
decomposed into discrete
modes (p-modes)
• At the moment 104 p-modes are
available
• Only p-modes observed so far
=>oscillation driven by pressure
involve solar structure only down
to 0.1R
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Helioseismic inferences
By comparing the measured frequencies with the
calculated ones (inversion method) one can determine:
• The transition from radiation to
convection:
Rb =0.711 (1 ± 0.14%) R
• The present He abundance at
solar surface:
Yphoto= 0.249 (1± 1.4%)
• The sound speed profile (with
accuracy of order 0.5%…see next
lesson)
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Solar rotation
• Solar surface does not rotate
uniformely: T=24 days (30 days) at
equator (poles). And the solar interior?
• Helioseismology
(after 6 years of
data taking) shows
that below the
convective region
the sun rotates in a
uniform way
• Note: Erot =1/2 m wrotR2  0.02 eV
Erot << KT
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Magnetic field
• From the observation of sunspots
number a 11 year solar cycle has
been determined
(Sunspots= very intense magnetic
lines of force (3KG) break through
the Sun's surface)
• the different rotation between
convection and radiative regions could
generate a dynamo mechanism and B= 104- 105
G near the bottom of the convective zone.
• A primordial 106G field trapped in the radiative
zone is proposed by some authors
B2
10 erg

10
cm
4p
• Anyhow also a 106G field give
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an energy contribution << KT
u  nKT  1015
3
erg
cm 3
Summary
• Main Solar observables: M,R,age, L, (Z/X)photo
• We can derive the typical scale of several
physical quantities
(need EOS for
T)
• Only nuclear energy can substain sun/stars
=>Birth of nuclear Astrophysics
• New Solar observables: oscillation
frequencies
=>Birth of Helioseismology
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Inversion method
• Calculate frequencies wi as a function of
u =>
wi  wi(uj)
j=radial coordinate
• Assume Standard Solar Model as linear
deviation around the true sun:
wiwi, sun + Aij(uj-uj,sun)
• Minimize the difference between the
measured Wi and the calculated wi

2
 W i  wi
 
 W
i
i





2
• In this way determine uj =uj -uj, sun
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