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

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Standard Solar Models IIAldo SerenelliInstitute
for Advanced Study, Princeton
SUSSP61 Neutrino Physics - St. Andrews, Scotland
8th to 23rd, August, 2006
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Homework

• Dating the Solar System

• Ratio 238U/235U known and constant (in space,
  not in time) in solar system material
• Primordial isotopic composition of lead (Pb)
  known from meteoritic samples with very low
  abundances of U or Th

• Measure the ratio 206Pb/204Pb and 207Pb/204Pb in
  your sample, and, taking into account that 204Pb
  does not change, write

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Updates since 2001 1/3

• Independent calculations of opacities Opacity
  Project

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Updates since 2001 2/3

• Minor change (1) in pp and also in hep cross
  sections (Park et al. 2003)

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Updates since 2001 3/3
Solar composition

• Large change in solar composition mostly
  reduction in C, N, O, Ne. Results presented in
  many papers by the Asplund group. Summarized in
  Asplund, Grevesse Sauval (2005)

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Standard Solar Model (2005)
Initial Present day values Present day values
Initial Center Surface
X 0.7087 0.3461 0.7404
Y 0.2725 0.6337 0.2426
Z 0.0188 0.0202 0.0170
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Standard Solar Model (2005)
BS05 Helios. BP00
RCZ 0.713 0.7130.001 0.714
YSURF 0.243 0.2485 0.0035 0.244
ltdcgt 0.001 --- 0.001
ltdrgt 0.012 --- 0.005
Difference in the sense Sun - model
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Standard Solar Model (2005)Sound speed
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Standard Solar Model (2005)Internal structure
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Standard Solar Model (2005)Neutrino production
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Standard Solar Model (2005)Neutrino production
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Standard Solar Model (2005)Neutrino production
Neutrino fluxes on Earth (cm-2 s-1)
BS05 BP00
pp 5.99x1010 5.95x1010
pep 1.42x108 1.40x108
hep 7.93x103 9.3x103
7Be 4.84x109 4.77x109
8B 5.69x106 5.05x106
13N 3.05x108 5.48x108
15O 2.31x108 4.80x108
17F 5.84x106 5.63x106
Cl(SNU) 8.12 7.6
Ga(SNU) 126.1 128
FSNO(8B)4.990.33x106 cm-2 s-1
No neutrino oscillation
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Standard Solar Model (2005)Comparison with
experiments
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Standard Solar Model (2005)Solar neutrino spectra
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Standard Solar Model (2005)Electron and neutron
density
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Standard Solar Model (2005)Solar neutrinos and
matter effects
Solar neutrinos heavily affected by matter
effects, but
Fogli, et al. 2006 (hep-ph/0506083)
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Standard Solar Model (2005)Solar neutrinos and
matter effects
Vacuum oscillations for pp and 7Be Matter effects
for 8B
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New Solar composition 1/4Troubles in paradise?

• Large change in solar composition mostly
  reduction in C, N, O, Ne. Results presented in
  many papers by the Asplund group. Summarized in
  Asplund, Grevesse Sauval (2005)

Authors (Z/X)8 Main changes (dex)
Grevesse 1984 0.0277
Anders Grevess 1989 0.0267 DC-0.1, DN0.06
Grevesse Noels 1993 0.0245
Grevesse Sauval 1998 0.0229 DC-0.04, DN-0.07, DO-0.1
Asplund, Grevesse Sauval 2005 0.0165 DC-0.13, DN-0.14, DO-0.17, DNe-0.24, DSi-0.05 (affects meteor. abd.)
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New Solar Composition 2/4

• Volatile elements (do not aggregate easily into
  solid bodies) e.g. C, N, O, Ne, Ar only in solar
  spectrum
• Refractory elements, e.g. Mg, Si, S, Fe, Ni both
  in solar spectrum and meteorites meteoritic
  measurements more robust

Abundances from spectral lines a lot of modeling
required !!!
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New Solar Composition 3/4

• Improvements in the modeling 3D model
  atmospheres, MHD equations solved, NLTE effects
  accounted for in most cases
• Improvements in the data better selection of
  spectral lines. Previous sets had blended lines
  (e.g. oxygen line blended with nickel line)

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New Solar Composition 4/4
What is not so good Agreement between
helioseismology and SSM very much degraded
Was previous agreement a coincidence?
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Standard Solar Model 2005Old and new metallicity
BS05(GS98) BS05(ASG05) Helioseism.
RCZ 0.713 0.728 0.7130.001
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Standard Solar Model 2005Old and new metallicity
Towards the center temperature (radiative)
gradient smaller ? initial helium must be lower
to match present day Sun ? SSM prediction for
YSURF too low
BS05(GS98) BS05(ASG05) Helioseism.
RCZ 0.713 0.728 0.7130.001
YSURF 0.243 0.229 0.2485 0.0035
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Standard Solar Model 2005Old and new metallicity
BS05(GS98) BS05(ASG05) Helioseism.
RCZ 0.713 0.728 0.7130.001
YSURF 0.243 0.229 0.2485 0.0035
ltdcgt 0.001 0.005 ---
ltdrgt 0.012 0.044 ---
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Standard Solar Model 2005Old and new metallicity
Central temperature lower by 1.2 ? changes in
neutrino fluxes
BS05(GS98) BS05(AGS05)
pp 5.99x1010 6.06x1010
pep 1.42x108 1.45x108
hep 7.93x103 8.25x103
7Be 4.84x109 4.34x109
8B 5.69x106 4.51x106
13N 3.05x108 2.00x108
15O 2.31x108 1.44x108
17F 5.84x106 3.25x106
Cl(SNU) 8.12 6.6
Ga(SNU) 126.1 118.9
FSNO(8B)4.990.33x106 cm-2 s-1
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Standard Solar Model Uncertainties

• 1st approach compute SSM varying one input at
  the time ? compute dependences of desired
  quantity on each input (composition, nuclear
  cross sections, etc.). Draw back estimation of
  total uncertainty is a bit fuzzy

• 2nd approach do a Monte Carlo simulation using
  a (large) bunch of SSMs where all inputs are
  varied randomly and simultaneously ? better
  overall estimates of uncertainties. However input
  uncertainties are hard wired. Individual
  contributions to total uncertainties are hidden

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Standard Solar Model Power law dependences
aij can be calculated from (at least) 2 SSMs
computed with xjDxj and xj-Dxj
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Standard Solar Model Power law dependences
Power laws some instructive examples
S11 S1,14 L8 (Z/X)8
pp 0.14 -0.02 0.73 -0.07
7Be -0.97 0.0 3.40 0.69
8B -2.59 0.01 6.76 1.28
13N -2.53 0.85 5.16 1.01
15O -2.93 1.00 5.94 1.27
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Standard Solar Model Power-law dependences

• One word of warning for very interested people
  flux dependences on metallicity (details in
  Bahcall Serenelli 2005)
• Better treat elements individually than (Z/X) ?
  uncertainty estimations for fluxes can get
  smaller, specially for ?(8B)
• Uncertainty in Z/X dominated by C, N, O, Ne but
  fluxes depend more strongly on Si, S, Fe (these
  have small uncertainties as abundances are
  determined in meteorites) ? smaller uncertainties
  in the fluxes
• Total uncertainty for ?(8B) goes from 23 (using
  total uncertainty of Z/X) to 13 using individual
  element uncertainties and power-law dependences

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Standard Solar Model Monte Carlo Simulations
2nd approach compute a large numbers of SSM by
varying individual inputs independently and
simultaneously. Originally done by Bahcall
Ulrich (1988)
An update 10000 SSMs (in 2 groups of 5000) using
21 variable input parameters 7 cross sections,
age, luminosity, diffusion velocity, 9 individual
elements, EoS and opacities. Details can be found
in Bahcall, Serenelli Basu (2006)
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Standard Solar Model Monte Carlo Simulations
Solar abundance dichotomy ? two choices for
central values and uncertainties
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Standard Solar Model Monte Carlo Simulations
Some results for helioseismology RCZ and YSURF
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Standard Solar Model Monte Carlo Simulations
Some results for helioseismology sound speed and
density profiles
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Standard Solar Model Monte Carlo Simulations
Some results on neutrino fluxes ?(8B) and ?(7Be)
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Standard Solar Model Monte Carlo Simulations
Some results on neutrino fluxes ?(pp) and ?(pep)
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Standard Solar Model Monte Carlo Simulations
Some results on neutrino fluxes other fluxes

• Lognormal distributions reflect adopted
  composition uncertainties

• 13N15O mean and most probable values from GS98
  and AGS05 distributions differ by 3.5sOPT and
  2.6sOPT respectively
• Will neutrino experiments be able to determine
  the metallicity in the solar interior?

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Standard Solar Model Monte Carlo Simulations
Fluxes uncertainties
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The end.