The Standard Solar Model Aldo Serenelli Max Planck Institute for Astrophysics PHYSUN L'Aquila 16-17 October, 2008
Outline Overview of Standard Solar Model - BPS08 Two solar compositions SSM, solar compositions and helioseismology: The Solar Abundance Problem Neutrino fluxes and uncertainties
Standard Solar Model - Overview Input physics: Most up to date nuclear cross sections Radiative opacities Equation of state Input parameters: Solar properties: radius, luminosity, mass, age, surface composition Keep free parameters to a minimum: 3 (two fix the composition, the other the entropy jump in the upper convective zone)
Most up to date SSM. BPS08 Recent cross section determinations: 14N+p astro factor: S(0)= 1.57 ± 0.13 kev b (Marta el al. 2008) 4He+3He astro factor: S(0)= 0.56 ± 0.017 kev B (Confortola et al. 2007) Two standard solar compositions: central values and uncertainties Grevesse & Sauval (1998; GS98) & Asplund et al. (2005; AGS05) Other input as in Bahcall et al. (2006)
Different solar compositions Different total metallicity Z/X= 0.0229 (GS98) Z/X= 0.0165 (AGS05) GS98 8.52 0.06 7.92 0.06 8.83 0.06 8.08 0.06 7.58 0.03 7.56 0.02 7.20 0.04 6.40 0.06 7.50 0.03 AGS05 8.39 0.05 7.78 0.06 8.66 0.05 7.84 0.06 7.53 0.03 7.51 0.02 7.16 0.04 6.18 0.08 7.45 0.03 Abd= log nx/nh +12 C N O Ne Mg Si S Ar Fe 30-50% reduction
Different solar compositions: dominant effects Different total metallicity Z/X= 0.0229 (GS98) Z/X= 0.0165 (AGS05) GS98 8.52 0.06 7.92 0.06 8.83 0.06 8.08 0.06 7.58 0.03 7.56 0.02 7.20 0.04 6.40 0.06 7.50 0.03 AGS05 8.39 0.05 7.78 0.06 8.66 0.05 7.84 0.06 7.53 0.03 7.51 0.02 7.16 0.04 6.18 0.08 7.45 0.03 Abd= log nx/nh +12 C N O Ne Mg Si S Ar Fe Helioseismology lower opacity below CZ RCZ and cs profile lower core opacity higher hydrogen to keep L lower helium
Different solar compositions: dominant effects Different total metallicity Z/X= 0.0229 (GS98) Z/X= 0.0165 (AGS05) GS98 8.52 0.06 7.92 0.06 8.83 0.06 8.08 0.06 7.58 0.03 7.56 0.02 7.20 0.04 6.40 0.06 7.50 0.03 AGS05 8.39 0.05 7.78 0.06 8.66 0.05 7.84 0.06 7.53 0.03 7.51 0.02 7.16 0.04 6.18 0.08 7.45 0.03 Abd= log nx/nh +12 C N O Ne Mg Si S Ar Fe Helioseismology lower opacity below CZ RCZ and cs profile lower core opacity higher hydrogen to keep L lower helium Neutrino fluxes CNO fluxes depend linearly; affects pp and pep indirectly lower opacity lower T in core lower opacity largest individual contribution to lower 7Be and 8B
Helioseismology: Sound speed and density profiles GS98 AGS05 Helioseism. RCZ 0.713 0.728 0.713±0.001 YS 0.243 0.010 0.005 0.229 0.053 0.047 0.248±0.035 ----- < c> < >
Theoretical Uncertainties: MC simulation (Bahcall et al. 2006) EOS, rad. opacity, diffusion Cross sections Solar age and luminosity Solar composition (9 elements) GS98 and AGS05 compositions Optimistic uncertainties: 1- as given by AGS05 Conservative uncertainties: 1- difference between GS98 and AGS05 typically 2-3 times optimistic value
MC simulation. Helioseismology results I
MC simulation. Helioseismology results II GS98 Conservative uncertainties AGS05 Optimistic uncertainties
Solar core: Helioseismology with low-l modes Roxburgh & Vorontsov (2003) Large separation 1 [ ] R = 2 0 dr c S model: full solar model A B C: modified structure in convective envelope; same interior structure. Not true solar models
Solar core: Helioseismology with low-l modes WKB analysis of p-modes in outer layers R 1/ 2 1/ 2 1 r r A c r cos nl r dr ' c Different mode (n,l), same frequency same eigenfunction in outer layers
Solar core: Helioseismology with low-l modes WKB analysis of p-modes in outer layers R 1/ 2 1/ 2 1 r r A c r cos nl r dr ' c Different mode (n,l), same frequency same eigenfunction in outer layers nl n l / 2 O nl small separation ratios
Solar core: Helioseismology with low-l modes WKB analysis of p-modes in outer layers R 1/ 2 1/ 2 1 r r A c r cos nl r dr ' c Different mode (n,l), same frequency same eigenfunction in outer layers nl n l / 2 O nl small separation ratios R dc dr nl nl n 1 l 2 4l 6 2 4 nl 0 dr r Weighed towards the center
Solar core: Helioseismology with low-l modes Roxburgh & Vorontsov (2003): ratio of small to large separation ratios depend only on interior structure Separation ratios: r02 - r13 d n r 02 n = 02 = n, 0 n 1,2 1 n 1 n,1 n 1,1 r 13 n = d 13 n = n,1 n 1,3 0 n 1 n, 0 n 1,0
Solar core: Helioseismology with low-l modes The Sun as a Star: low-l modes from Birmingham Solar Oscillations Network (BiSON) (Chaplin et al. 2007; Basu et al. 2007) 4752 days of data low-l l=0, 1, 2, 3 n= 8, 10,..., 26
Solar core: Helioseismology with low-l modes Effect of metalicity arise in the core R dc dr nl nl n 1 l 2 4l 6 2 4 nl 0 dr r
Solar core: Helioseismology with low-l modes Effect of metalicity arise in the core R dc dr nl nl n 1 l 2 4l 6 2 4 nl 0 dr r Low-Z models not compatible with low-l frequencies Conservative abundances: too conservative assume smaller uncertainties for SSM
Solar core: Helioseismology with low-l modes: Results for MC simulation <r02> GS98 <r02> AGS05 <r13> c: molecular weight averaged inner R<0.2R GS98 c= 0.723±0.003 AGS05 c= 0.723±0.003 Precise measurement of molecular weight in solar core. No room for mixing in the core? <r13>
Solar core: Helioseismology with low-l modes <r02> GS98 <r02> AGS05 <r13> Z = surface metallicity GS98 Z=0.0191±0.003 AGS05 Z= 0.0224±0.003 Surface metallicity: consistent with high(er) value (GS98); larger dispersion: diffusion uncertainties <r13>
BPS08. Neutrino fluxes and uncertainties 14N+p: S(0)= 1.57 ± 0.13 kev b 7% 4He+3He: Smaller composition uncertainties (as given by GS98 and AGS05) S(0)= 0.56 ± 0.017 kev B 5.7%
BPS08. Neutrino fluxes and uncertainties 14N+p: S(0)= 1.57 ± 0.13 kev b 7% 4He+3He: Smaller composition uncertainties (as given by GS98 and AGS05) S(0)= 0.56 ± 0.017 kev B 5.7% GS98 AGS05 pp 5.97(1±0.006) 6.04(1±0.005) pep 1.41(1±0.011) 1.45(1±0.010) hep 7.90(1±0.15) 8.22(1±0.15) 7 Be 5.07(1±0.058) 4.55(1±0.058) 5% 8B 5.94(1±0.11) 4.72(1±0.11) 4% 13N 2.88(1±0.15) 1.89(1±0.14) 5% 15O 2.15(1±0.17) 1.34(1±0.16) 8% 17 F 5.82(1±0.18) 3.25(1±0.16) Changes w.r.t. BP05
BPS08. Neutrino fluxes and uncertainties Similar fluxes Lower uncertainties
BPS08. Neutrino fluxes and uncertainties pp BS05(cons) BPS08 Non-Comp. Comp. 1% 0.6% 0.5% 0.2% pep 1.7% 1.1% 1% 0.5% hep 15.5% 15.5% 15.4% 0.7% 7 Be 10.5% 5.8% 5.3% 2.1% 8B 16% 11% 10% 4.7% 13N 30% 15% 8.8% 12.8% 15O 31% 17% 11.5% 12.5% 17F 50% 18% 8.9% 16% Dominant sources of uncertainty CNO elements dominate error for CNO fluxes Iron dominates for all other fluxes, particularly 8B (opacity in the core)
BPS08. Neutrino fluxes and uncertainties pp BS05(cons) BPS08 Non-Comp. Comp. 1% 0.6% 0.5% 0.2% pep 1.7% 1.1% 1% 0.5% hep 15.5% 15.5% 15.4% 0.7% 7 Be 10.5% 5.8% 5.3% 2.1% 8B 16% 11% 10% 4.7% 13N 30% 15% 8.8% 12.8% 15O 31% 17% 11.5% 12.5% 17F 50% 18% 8.9% 16% Dominant sources of uncertainty CNO elements dominate error for CNO fluxes Iron dominates for all other fluxes, particularly 8B (opacity in the core) 13N, 15O: S114 8% uncertainty Cross sections affecting individual fluxes: hep, S17
BPS08. Neutrino fluxes and uncertainties pp BS05(cons) BPS08 Non-Comp. Comp. 1% 0.6% 0.5% 0.2% pep 1.7% 1.1% 1% 0.5% hep 15.5% 15.5% 15.4% 0.7% 7 Be 10.5% 5.8% 5.3% 2.1% 8B 16% 11% 10% 4.7% 13N 30% 15% 8.8% 12.8% 15O 31% 17% 11.5% 12.5% 17F 50% 18% 8.9% 16% Dominant sources of uncertainty CNO elements dominate error for CNO fluxes Iron dominates for all other fluxes, particularly 8B (opacity in the core) 13N, 15O: S114 8% uncertainty Cross sections affecting individual fluxes: hep, S17 Diffusion: lowers Xc increase in Tc. Larger effect for CNO fluxes (increase in Zc). 2%, 4%, 5%, 5.7% 6% (7Be, 8B, CNO) Opacity: increased sensitivity with increased T dependence. 3.2%, 7%, 4%, 5%, 6% (7Be, 8B, CNO)
Effects of Opacity Adopted uncertainty: 2.5% characteristic of OP OPAL difference in radiative core (Badnell et al. 2005) 3.2%, 7%, 4%, 5%, 6% (7Be, 8B, CNO) Difference oscillates. If 1- defined as difference SSM(OP) SSM(OPAL), uncertainties are reduced: 1%, 2.4%, 1.3%, 2.1%, 2.2% (7Be, 8B, CNO) First approach a bit more conservative
BPS08 vs Experiment
Solar composition problem: attempted solutions Increased opacity below CZ (Bahcall et al. 2004) increase of order 10-12% to compensate for lower metallicity and recover location of RCZ and sound speed profile Difference too high? Frequency separation ratios don't fit BiSON data. May need + opacity in central regions as well
Solar composition problem: attempted solutions Increased opacity below CZ (Bahcall et al. 2004) increase of order 10-12% to compensate for lower metallicity and recover location of RCZ and sound speed profile Difference too high? Frequency separation ratios don't fit BiSON data. May need + opacity in central regions as well Increase neon abundance (Antia & Basu 2005; Bahcall et al. 2005) 0.4 dex increase needed gives right helioseismology Probably too large enhancement
Solar composition problem: attempted solutions Increased opacity below CZ (Bahcall et al. 2004) increase of order 10-12% to compensate for lower metallicity and recover location of RCZ and sound speed profile Difference too high? Frequency separation ratios don't fit BiSON data. May need + opacity in central regions as well Increase neon abundance (Antia & Basu 2005; Bahcall et al. 2005) 0.4 dex increase needed gives right helioseismology Probably too large enhancement Changes to mixing processes. Target increase contrast between surface and interior composition: enhanced diffusion, metal free accretion No satisfactory solution: Need too much ad-hoc tuning or additional processes
Solar composition problem: one word on abundances Caffau et al. (2008): solar oxygen abundance 8.76±0.05 (intermediate between GS98 and AGS05). Hydro-3D models. Przybilla et al. (2008): oxygen and neon abundances in B-type stars consistent with GS98 values but carbon lower than AGS05. Spread in abundances very low.
Conclusions Most recent cross section determinations affect somewhat fluxes and reduce significantly fluxes uncertainties; particularly S34 Two sets of solar abundances lead to contradictory results. Solar atmosphere models and solar interior models in disagreement Low-l modes used to provide direct information on the solar core Low-l modes used to show that conservative uncertainty errors are too conservative observational errors adopted in BPS08 reduced fluxes uncertainties No satisfactory solution to solar abundance problem within the framework of the SSM (or outside, to the best of my knowledge) Can solar neutrino experiments help discriminate between solar compositions?
The End
1 [ ] R dr = 2 0 c R r cos nl 1 /2 1 /2 1 r r A c r 2 nl n l /2 BL dr ' c 2 nl 2 BL nl 2 B= [ R c R 1 dc dr 2 dr r 4 R 0 ] R dc dr nl nl n 1 l 2 4l 6 2 4 nl 0 dr r