The standard solar model and solar neutrinos

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The standard solar model and solar neutrinos
Trieste 23-25 Sept. 2002

• 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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Episode I
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Main solar observables and typical scales

• Observables
• Mass, Luminosity, Radius, Age,
• Metal content of the photosphere
• The typical scales
• Helioseismic data
• Rotation
• Magnetic fields

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Who measured the solar mass?
Galileo
Einstein
Cavendish
Smirnov
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Solar mass
1s error

• 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

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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
• Lo4pd2Ko 3.844(1 0.4) 1033 erg/s

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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
• Ro6.9598(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
• t4.57(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)photo0.0245(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
  l1/(ne sTh)
• 1/(1024 cm-3 10-24 cm2) 1 cm
• (photon escape time 2 104 yr)
• e Lot 10-4 Moc2
• typical nuclear energy scale

astrophyscists use opacity k l1/(r k)
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The birth of Nuclear Astrophysics

• Eddington Nature (1920)
• 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

e Lot 10-4 Moc2

• 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 well-being
  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 kTgtgt e2/r e2n1/3
• perfect gas reasonable
• However KTltlt 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.
• gt 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)

used the Gamow factor to derive the rate at which
nuclear reactions would proceed at the high
temperatures believed to exist in the interiors
of stars.
However, von Weizsäcker did not investigate the
rate at which energy would be produced in a star
by the CNO cycle nor did he study the crucial
dependence upon stellar temperature.
KTltlt e2/rnuc
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The gross solar structure

• Hot nucleus
• R lt 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 (Dw/w 10-3 - 10-4)
• 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 gtoscillation 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
  0.5see next lesson)

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Solar rotation

• Solar surface does not rotate uniformely T24
  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 ltlt
  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
• Anyhow also a 106G field give
  an energy contribution ltlt KT

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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
• gtBirth of nuclear Astrophysics
• New Solar observables oscillation frequencies
• gtBirth of Helioseismology
  

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See you tomorrow...
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Inversion method

• Calculate frequencies wi as a function of u gt
  wi wi(uj) jradial coordinate
• Assume Standard Solar Model as linear deviation
  around the true sun
• wiwi, sun Aij(uj-uj,sun)
• Minimize the difference between the measured Wi
  and the calculated wi
• In this way determine Duj uj -uj, sun