Solar System Dating and Neutrino Physics

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

2. is only function of T Homework • 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 • Dating the Solar System • Measure the ratio 206Pb/204Pb and 207Pb/204Pb in your sample, and, taking into account that 204Pb does not change, write

3. Microscopic physics • Relativistic corrections to electrons missing  Updated EoS (OPAL 2001) • 10% increase in 7Be + p cross section (Junghans et al. 2003) ppIII 1%  change in (8B) flux Updates since 2001 1/3 • Independent calculations of opacities: Opacity Project

4. Microscopic physics • Factor of 2 reduction in the 14N+p cross section (experimental result from LUNA collaboration) CN-cycle  CN cycle slowed down by similar amount  (13N) and (15O) ~ of previous theoretical value Updates since 2001 2/3 • Minor change (1%) in pp and also in hep cross sections (Park et al. 2003)

5. 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)

6. BS05 (updated microphysics, Grevesse & Sauval 1998 composition) (Bahcall, Serenelli & Basu 2005) Quantities to match Solar luminosity L8=3.842 1033erg s-1 0.4% Solar radius R8=6.9598 1010cm 0.1% Solar metals/hydrogen ratio (Z/X)8= 0.0229 Standard Solar Model (2005)

7. Standard Solar Model (2005) Difference in the sense: Sun - model

8. p-modes are acoustic modes  sound speed c is the key to wi Change in slope Radiat. transport  Convect. transport  change in temp. gradient dc/dr < 0  m gradient important: information about composition Standard Solar Model (2005)Sound speed

9. Standard Solar Model (2005)Internal structure

10. Distribution of neutrino fluxes Standard Solar Model (2005)Neutrino production

11. CN-cycle C+N (+O) = Const. Standard Solar Model (2005)Neutrino production

12. Standard Solar Model (2005)Neutrino production Neutrino fluxes on Earth (cm-2 s-1) FSNO(8B)=4.99±0.33x106 cm-2 s-1 No neutrino oscillation

13. Standard Solar Model (2005)Comparison with experiments

14. Standard Solar Model (2005)Solar neutrino spectra

15. For matter effects the “neutrino potential” is Standard Solar Model (2005)Electron and neutron density

16. Standard Solar Model (2005)Solar neutrinos and matter effects Solar neutrinos heavily affected by matter effects, but… Fogli, et al. 2006 (hep-ph/0506083)

17. … survival probability Pee depends on A(x)=2EV(x) and matter effect are important if A(x)  dm2 Fogli, et al. 2006 (hep-ph/0506083) Standard Solar Model (2005)Solar neutrinos and matter effects Vacuum oscillations for pp and 7Be Matter effects for 8B

18. 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)

19. Two main sources: • Spectral lines from solar photosphere/corona • Meteorites 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 !!!

20. What is good… • Much improved modeling • Different lines of same element give same abundance (e.g. CO and CH lines) • Sun has now similar composition to solar neighborhood 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)

21. New Solar Composition 4/4 What is not so good … Agreement between helioseismology and SSM very much degraded Was previous agreement a coincidence?

22. (Z/X)8 down from 0.0229 to 0.0165 (~30% decrease) Main effect: radiative opacity k goes down Consequence: smaller radiative gradient Stability criterion: location of convective boundaries is modified Standard Solar Model 2005Old and new metallicity

23. 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

24. Sound speed and density profiles are degraded Standard Solar Model 2005Old and new metallicity

25. Standard Solar Model 2005Old and new metallicity Central temperature lower by 1.2%  changes in neutrino fluxes FSNO(8B)=4.99±0.33x106 cm-2 s-1

26. 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

27. Using 1st approach, power-law dependences of fluxes are very good approximation (Bahcall & Ulrich 1988) In the more general case, if many inputs are varying Standard Solar Model Power law dependences aij can be calculated from (at least) 2 SSMs computed with xj+Dxj and xj-Dxj

28. Standard Solar Model Power law dependences Power laws: some instructive examples

29. 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

30. 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)

31. “Conservative”: 1-s defined as difference between GS98 and AGS05 central values (this is very conservative) • “Optimistic”: 1-s as given by AGS05 Conservative Optimistic 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 Standard Solar Model Monte Carlo Simulations Solar abundance dichotomy  two choices for central values and uncertainties

32. Standard Solar Model Monte Carlo Simulations Some results for helioseismology: RCZ and YSURF

33. GS98 - Conservative AGS05 - Optimistic Standard Solar Model Monte Carlo Simulations Some results for helioseismology: sound speed and density profiles

34. Standard Solar Model Monte Carlo Simulations Some results on neutrino fluxes: (8B) and (7Be)

35. Standard Solar Model Monte Carlo Simulations Some results on neutrino fluxes: (pp) and (pep)

36. GS98-Conservative Standard Solar Model Monte Carlo Simulations Some results on neutrino fluxes: other fluxes • Lognormal distributions reflect adopted composition uncertainties • 13N+15O 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?

37. Standard Solar Model Monte Carlo Simulations Fluxes uncertainties

38. The end.