Standard Solar Model Calculation of Neutrino Fluxes

1. Standard Solar Model Calculation of Neutrino Fluxes Aldo Serenelli Institute for Advanced Study NOW 2006 Conca Specchiulla11-Sept-2006

2. John N. Bahcall (1934-2005)

3. Basic assumptions: spherical symmetry no rotation no magnetic fields What is done… • Initial 1M8=1.9891033g, homogeneous composition • Evolve it during t8=4.57 109yrs • Match present Sun:L8=3.842 1033erg s-1 • R8=6.96 1010cm • (Z/X)8= 0.0229/0.0165(note differing values!!) Free parameters… • Convection prescription: 1 parameter (aMLT) • Initial solar composition:X+Y+Z=1 2 free parameters, e.g.X, Z Standard Solar Model: What is done…

4. For helioseismology… • Sound speed profilec(r) • Density profiler(r) • Depth of the convective envelopeRCZ • Surface helium abundanceYS • 8 Neutrino fluxes: total flux and internal distribution. Only 8B directly measured so far (negligible contribution to solar energetics) Standard Solar Model: predictions • Nuclear and gravothermal (negligible) energy contributions to solar luminosity“luminosity constraint” • Chemical elements internal distributionselectron and neutron density profiles

5. Initial Present day values Center Surface X 0.7087 0.3461 0.7404 Y 0.2725 0.6337 0.2426 Z 0.0188 0.0202 0.0170 BS05 Helios. RCZ 0.713 0.713±0.001 YSURF 0.243 0.2485 ±0.0035 <dc> 0.001 --- <dr> 0.012 --- • Most updated input physics including • Grevesse & Sauval (1998; GS98) solar composition: (Z/X)8,today= 0.0229 SSM - BS05(OP,GS98)Bahcall, Serenelli & Basu (2005)

6. Neutrino fluxes on Earth (cm-2 s-1) BS05(OP,GS98) pp 5.99x1010(1±0.01) pep 1.42x108 (1±0.02) hep 7.93x103 (1±0.16) 7Be 4.84x109 (1±0.10) 8B 5.69x106 (1±0.16) FSNO(8B)=4.94x106 (1±0.08) cm-2 s-1 13N 3.05x108 (1+0.31-0.28) 15O 2.31x108 (1+0.33-0.29) 17F 5.84x106 (1±0.52) SSM - BS05(OP,GS98) Neutrino production profiles together with electron and neutron density profiles needed for oscillation studies: e.g. 8B ns affected by MSW effect,pp and 7Be ns only by vacuum oscillations

7. Results from the “Asplund group” summarized in Asplund, Grevesse & Sauval (2005; AGS05): improved modeling of solar atmospherelarge reduction in volatile elements: C, N, O, Ne, Ar (Z/X)8,today= 0.0165 (old 0.0229) Element Reduction [dex] Quoted uncert.[dex] C 0.13 0.05 N 0.14 0.06 O 0.17 0.05 Ne 0.24 0.06 Mg 0.05 0.03 Si 0.05 0.02 S 0.04 0.04 Ar 0.22 0.08 Fe 0.05 0.03 SSM – New Solar Composition • Main effect: lower radiative opacity • Shallower convective envelope and low surface helium • Sound speed and density profiles in disagreement with Helioseismology • Flatter T-gradient in core (somewhat lower central T)

8. Sound speed and density profiles are degraded, particularly outer half GS98 ASG05 Helioseism. RCZ 0.713 0.728 0.713±0.001 YSURF 0.243 0.229 0.2485 ±0.004 <dc> 0.001 0.005 --- <dr> 0.012 0.044 --- SSM – BS05(OP,AGS): Helioseismology

9. GS98 AGS05 ↑ 1% pp 5.99x1010 6.06x1010 ↑ 2% pep 1.42x108 1.45x108 hep 7.93x103 8.25x103 ↑ 4% 7Be 4.84x109 4.34x109 ↓ 10% 8B 5.69x106 4.51x106 FSNO(8B)=4.94x106 cm-2 s-1 ↓ 20% ↓ 33% 13N 3.05x108 2.00x108 ↓ 38% 15O 2.31x108 1.44x108 17F 5.84x106 3.25x106 ↓ 44% • Central temperature lower by ~ 1% • Lower CNO abundances directly affect CNO fluxes SSM – BS05(OP,AGS): Neutrino fluxes

10. Composition uncertainties: two approaches to define 1-s Element (Very) Conservative 1-s  Change [dex] Optimistic 1-s  Quoted uncert.[dex] C 0.13 0.05 N 0.14 0.06 O 0.17 0.05 Ne 0.24 0.06 Mg 0.05 0.03 Si 0.05 0.02 S 0.04 0.04 Ar 0.22 0.08 Fe 0.05 0.03 SSM – Uncertainties Two approaches to compute SSM uncertainties: Monte Carlo simulations (Bahcall, Serenelli & Basu 2006) and Power-Law dependences (improved treatment of composition in Bahcall & Serenelli 2005)

11. Helioseismology mostly affected by uncertainties in composition GS98 - Conservative AGS05 - Optimistic Monte Carlo simulations: 2 sets with 5000 SSMs each, 9 individual elements, 7 nuclear rates, age, luminosity, diffusion, rad. opac. & EOS SSM – Uncertainties: MC

12. Some cross section uncertainties: S11 (0.6%) - S33 (6.0%) - S34 (9.4%) S17 (3.8%) - S1,14 (8.4%) GS98 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 Will neutrino experiments discriminate between GS98 & AGS05 compositions? SSM – Uncertainties: MC

13. LUNA S34 ~5.5% ~8-9% Difficult to reduce: composition dominates SSM – Uncertainties: MC Bahcall, Serenelli, Basu (2006) Using “improved” (LUNA) optimisitc uncertainties SSM predictions (GS98 and AGS05) for 7Be and 13N-15O differ by approx. 1.2s and 1.9sIt will be a difficult task!!

14. SSM with “high” (old; GS98) metallicity in excellent agreement with helioseismology and neutrino experiments • New solar abundance determinations (AGS05) result in disagreement between SSM and helioseismology. Additional works with different approaches (Basu & Antia 2006, Basu et al. 2006, Pinsonneault & Delhaye 2006) also rule out new composition (but measurements are there!!!) • Neutrino flux(es) agreement still excellent (SNO measurement right in the middle of both SSM predictions) • Is the SSM paradigm not good enough for helioseismology? Need for independent group doing solar abundances at similar level of sophistication • Will future neutrino experiments shed light on the solar core composition? Conclusions

15. Solar model gives the internal structure:T(r), r(r), Xi(r), ne(r), nn(r) • compute local neutrino production per unit mass, e.g. for pp neutrinos SSM – Production profiles of neutrino fluxes and the production per unit radius

16. Fogli, et al. 2006 (hep-ph/0506083) Combining with the electron (or neutron) density profile SSM – Neutrino potential Construct the “neutrino potential” for matter effects:

17. Fogli, et al. 2006 (hep-ph/0506083) Survival probabilityPeedepends onA(x)=2EV(x) and matter effect areimportant ifA(x)  dm2 SSM – Neutrino oscillations Vacuum oscillations for pp and 7Be Matter effects for 8B