Standard Solar Models I Aldo Serenelli Institute for Advanced Study, Princeton

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Standard Solar Models IAldo SerenelliInstitute
for Advanced Study, Princeton
SUSSP61 Neutrino Physics - St. Andrews, Scotland
8th to 23rd, August, 2006
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• John N. Bahcall (1934-2005)

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Plan

• Lecture 1
• Motivation Solar models Solar neutrinos
  connection
• Stellar structure equations
• Standard Solar Models (SSM) - setting up the
  problem
• Overview of helioseismology
• History of the SSM in 3 steps

• Lecture 2
• SSM 2005/2006
• New Solar Abundances troubles in paradise?
• Theoretical uncertainties power-law dependences
  and Monte Carlo simulations
• Summary

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Motivation

• The Sun as a paradigm of a low-mass star.
  Standard test case for stellar evolution. Sun is
  used to callibrate stellar models
• Neutrinos from the Sun only direct evidence of
  solar energy sources (original proposal for the
  Homestake experiment that led to the Solar
  Neutrino Problem)
• Neutrino oscillations onstraints in the
  determination of LMA solution. However, SNO and
  SK data dominate ? importance of SSM minor

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Motivation

• Transition between MSW effect and vacuum
  oscillations at 5 MeV. 99.99 of solar
  neutrinos below 2 MeV additional neutrino
  physics at very low energies?
• Direct measurements of 7Be (pep, pp?) (Borexino,
  KamLAND, SNO) key to astrophysics. Check the
  luminosity constraint
• Future measurement of CNO fluxes? Answer to Solar
  Abundance Problem?

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What is inside a Standard Solar Models?Stellar
structure Basic assumptions

• The Sun is a self-gravitating object
• Spherical symmetry
• No rotation
• No magnetic field

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Stellar structure Hydrostatic equilibrium 1/2
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Stellar structure Hydrostatic equilibrium 2/2
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Stellar structure Mass conservation
We already used the relation
leading to
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Stellar structure Energy equation 1/2
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Stellar structure Energy equation 2/2
In a standard solar model we include nuclear and
neutrino contributions (thermal neutrinos are
negligible) e en en
(taking en gt 0)
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Stellar structure Energy transportRadiative
transport 1/2
Mean free path of photons lph1/kr (k opacity, r
density) Typical values ?k?0.4cm2g-1, ?r?1.4 g
cm-3 ? lph?2cm lph /R8?3?10-11 ? transport as a
diffusion process
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Stellar structure Energy transportRadiative
transport 2/2
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Stellar structure Energy transportConvective
transport 1/3
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Stellar structure Energy transportConvective
transport 2/3
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Stellar structure Energy transportConvective
transport 3/3
Using definition of
and
we can write
and, if there is convection FFradFconv
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Stellar structure Composition changes 1/4
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Stellar structure Composition changes 2/4
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Stellar structure Composition changes 3/4
Nuclear reactions (2 particle reactions, decays,
etc.)
here
?(v) is the relative velocity distrib. and s(v)
is cross section
Sun main sequence star ? hydrogen burning
low mass ? pp chains (99), CNO (1) Basic
scheme 4p ? 4He 2b 2ne 25/26 MeV
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Interlude on hydrogen burning pp chains
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Interlude on hydrogen burning CNO cycle
CNO cycle is regulated by 14Np reation (slowest)
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Stellar structure Composition changes 4/4
Composition changes
(5)
i1,..,N
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Stellar structure Complete set of equations
Microscopic physics equation of state, radiative
opacities, nuclear cross sections
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Standard Solar Model What we do 1/2
Solve eqs. 1 to 5 with good microphysics,
starting from a Zero Age Main Sequence
(chemically homogeneous star) to present solar age
Fixed quantities Fixed quantities Fixed quantities
Solar mass M81.989?1033g 0.1 Keplers 3rd law
Solar age t84.57 ?109yrs 0.5 Meteorites
Quantities to match Quantities to match Quantities to match
Solar luminosity L83.842 ?1033erg s-1 0.4 Solar constant
Solar radius R86.9598 ?1010cm 0.1 Angular diameter
Solar metals/hydrogen ratio (Z/X)8 0.0229 Photosphere and meteorites
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Standard Solar Model What we do 2/2
3 free parameters

• Convection theory has 1 free parameter aMLT
  determines the temperature stratification where
  convection is not adiabatic (upper layers of
  solar envelope)
• 2 of the 3 quantities determining the initial
  composition Xini, Yini, Zini (linked by
  XiniYiniZini1). Individual elements grouped in
  Zini have relative abundances given by solar
  abundance measurements (e.g. GS98, AGS05)

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Standard Solar Model Predictions

• Eight neutrino fluxes production profiles and
  integrated values. Only 8B flux directly measured
  (SNO) so far

• Chemical profiles X(r), Y(r), Zi(r) ? electron
  and neutron density profiles (needed for matter
  effects in neutrino studies)

• Thermodynamic quantities as a function of
  radius T, P,
• density (r), sound speed (c)

• Surface helium Ysurf (Z/X and 1XYZ leave 1
  degree of freedom)

• Depth of the convective envelope, RCZ

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The Sun as a pulsating star - Overview of
Helioseismology 1/4
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The Sun as a pulsating star - Overview of
Helioseismology 2/4

• Doppler observations of spectral lines
  velocities of a few cm/s are measured

• Differences in the frequencies of order mHz
  very long observations are needed. BiSON network
  (low-l modes) has data collected for ? 5000 days
• Relative accuracy in frequencies 10-5

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The Sun as a pulsating star - Overview of
Helioseismology 3/4

• Solar oscillations are acoustic waves (p-modes,
  pressure is the restoring force) stochastically
  excited by convective motions
• Outer turning-point located close to temperature
  inversion layer. Inner turning-point varies,
  strongly depends on l (centrifugal barrier)

Credit Jørgen Christensen-Dalsgaard
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The Sun as a pulsating star - Overview of
Helioseismology 4/4
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History of the SSM in 3 steps

• Step 1. Predictions of neutrino fluxes by the
  SSM to high (factor 2.5/3) w.r.t. to
  radiochemichal experiments solar neutrino
  problem. 8B flux too sensitive to central
  temperature ?(8B)?T20-25. Problem with SSM?
  Specultive solutions of all kinds. This lasted
  about 30 years.

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History of the SSM in 3 steps
RCZ0.714 / 0.713 0.001 YSUP0.244 / 0.249
0.003
F(8B) (5.05 0.91) x 106 cm-2 s-1 FSK(8B)
(2.32 0.09) x 106 cm-2 s-1 (only sensitive to
ne)
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History of the SSM in 3 steps

• Step 3. SNO direct measurement of the ?(8B)
  flux.