1. Standard Solar Model Calculation of Neutrino Fluxes Aldo Serenelli Institute for Advanced Study NOW 2006 Conca Specchiulla 11-Sept-2006

2. John N. Bahcall (1934-2005)

3. Standard Solar Model: What is done… What is done… Initial 1M  =1.989  10 33 g, homogeneous composition Evolve it during t  =4.57  10 9 yrs Match present Sun: L  = 3.842  10 33 erg s -1 R  = 6.96  10 10 cm (Z/X)  = 0.0229/0.0165 (note differing values!!) Free parameters… Convection prescription: 1 parameter (  MLT ) Initial solar composition: X+Y+Z=1  2 free parameters, e.g. X, Z Basic assumptions: spherical symmetry no rotation no magnetic fields

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

5. SSM - BS05(OP,GS98) Bahcall, Serenelli & Basu (2005) Most updated input physics including Grevesse & Sauval (1998; GS98) solar composition: ( Z/X ) ,today = 0.0229 --- 0.012 --- 0.001 <c><c> 0.2485 ±0.00350.243Y SURF 0.713±0.0010.713R CZ Helios.BS05 0.74040.34610.7087X SurfaceCenter Present day values Initial 0.01700.02020.0188Z 0.24260.63370.2725Y

6. SSM - BS05(OP,GS98) 5.84x10 6 (1±0.52) 17 F 2.31x10 8 (1+0.33-0.29) 15 O 3.05x10 8 (1+0.31-0.28) 13 N 5.69x10 6 (1±0.16) 8B8B 4.84x10 9 (1±0.10) 7 Be 7.93x10 3 (1±0.16) hep 1.42x10 8 (1±0.02) pep 5.99x10 10 (1±0.01) pp BS05(OP,GS98) Neutrino fluxes on Earth (cm -2 s -1 )  SNO  8 B )= 4.94x10 6 (1±0.08) cm -2 s -1 Neutrino production profiles together with electron and neutron density profiles needed for oscillation studies: e.g. 8 B s affected by MSW effect, pp and 7 Be s only by vacuum oscillations

7. SSM – New Solar Composition 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 0.05 0.22 0.04 0.05 0.24 0.17 0.14 0.13 Reduction [dex] 0.03 0.08 0.04 0.02 0.03 0.06 0.05 0.06 0.05 Quoted uncert.[dex] Fe Ar S Si Mg Ne O N C Element ( Z/X ) ,today = 0.0165 (old 0.0229) 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. SSM – BS05(OP,AGS): Helioseismology Sound speed and density profiles are degraded, particularly outer half 0.2485 ±0.0040.2290.243 Y SURF ---0.0440.012 ---0.0050.001 <c><c> 0.713±0.0010.7280.713 R CZ ASG05Helioseism.GS98

9. SSM – BS05(OP,AGS): Neutrino fluxes Central temperature lower by ~ 1% Lower CNO abundances directly affect CNO fluxes 3.25x10 6 5.84x10 617 F 1.44x10 8 2.31x10 815 O 2.00x10 8 3.05x10 813 N 4.51x10 6 5.69x10 68B8B 4.34x10 9 4.84x10 9 7 Be 8.25x10 3 7.93x10 3 hep 1.45x10 8 1.42x10 8 pep 6.06x10 10 5.99x10 10 pp AGS05GS98  SNO  8 B )= 4.94x10 6 cm -2 s -1 ↑ 1% ↑ 2% ↑ 4% ↓ 10% ↓ 20% ↓ 33% ↓ 38% ↓ 44%

10. SSM – Uncertainties Composition uncertainties: two approaches to define 1-  0.05 0.22 0.04 0.05 0.24 0.17 0.14 0.13 (Very) Conservative 1-  Change [dex] 0.03 0.08 0.04 0.02 0.03 0.06 0.05 0.06 0.05 Optimistic 1-  Quoted uncert.[dex] Fe Ar S Si Mg Ne O N C Element 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. SSM – Uncertainties: MC Monte Carlo simulations: 2 sets with 5000 SSMs each, 9 individual elements, 7 nuclear rates, age, luminosity, diffusion, rad. opac. & EOS GS98 - Conservative AGS05 - Optimistic Helioseismology mostly affected by uncertainties in composition

12. SSM – Uncertainties: MC Some cross section uncertainties: S 11 (0.6%) - S 33 (6.0%) - S 34 (9.4%) S 17 (3.8%) - S 1,14 (8.4%) 3.25x10 6 5.84x10 617 F 1.44x10 8 2.31x10 815 O 2.00x10 8 3.05x10 813 N 4.51x10 6 5.69x10 68B8B 4.34x10 9 4.84x10 9 7 Be 8.25x10 3 7.93x10 3 hep 1.45x10 8 1.42x10 8 pep 6.06x10 10 5.99x10 10 pp AGS05GS98 Will neutrino experiments discriminate between GS98 & AGS05 compositions?

13. SSM – Uncertainties: MC Bahcall, Serenelli, Basu (2006) Using “improved” (LUNA) optimisitc uncertainties SSM predictions (GS98 and AGS05) for 7 Be and 13 N- 15 O differ by approx. 1.2  and 1.9   It will be a difficult task!! LUNA S 34 ~5.5% ~8-9% Difficult to reduce: composition dominates

14. Conclusions 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?

15. SSM – Production profiles of neutrino fluxes Solar model gives the internal structure: T(r),  (r), X i (r), n e (r), n n (r)  compute local neutrino production per unit mass, e.g. for pp neutrinos and the production per unit radius

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

17. SSM – Neutrino oscillations Fogli, et al. 2006 (hep-ph/0506083) Survival probability P ee depends on A(x)=2EV(x) and matter effect are important if A(x)  m  Vacuum oscillations for pp and 7 Be Matter effects for 8 B