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

2. Homework Dating the Solar System Ratio 238 U/ 235 U 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 206 Pb/ 204 Pb and 207 Pb/ 204 Pb in your sample, and, taking into account that 204 Pb does not change, write is only function of T

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

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

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. Standard Solar Model (2005) BS05 (updated microphysics, Grevesse & Sauval 1998 composition) (Bahcall, Serenelli & Basu 2005) Quantities to match R  =6.9598  10 10 cm 0.1% Solar radius (Z/X)  = 0.0229Solar metals/hydrogen ratio L  =3.842  10 33 erg s -1 0.4% Solar luminosity InitialPresent day values CenterSurface X0.70870.34610.7404 Y0.27250.63370.2426 Z0.01880.02020.0170

7. Standard Solar Model (2005) BS05Helios.BP00 R CZ 0.7130.713±0.0010.714 Y SURF  0.2485 ±0.00350.244 <c><c> 0.001---0.001 0.012---0.005 Difference in the sense: Sun - model

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

9. Standard Solar Model (2005) Internal structure

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

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

12. Standard Solar Model (2005) Neutrino production BS05BP00 pp5.99x10 10 5.95x10 10 pep1.42x10 8 1.40x10 8 hep7.93x10 3 9.3x10 3 7Be4.84x10 9 4.77x10 9 8B5.69x10 6 5.05x10 6 13N3.05x10 8 5.48x10 8 15O2.31x10 8 4.80x10 8 17F5.84x10 6 5.63x10 6 Cl(SNU)8.127.6 Ga(SNU)126.1128 Neutrino fluxes on Earth (cm -2 s -1 ) No neutrino oscillation  SNO  8 B)=4.99±0.33x10 6 cm -2 s -1

13. Standard Solar Model (2005) Comparison with experiments

14. Standard Solar Model (2005) Solar neutrino spectra

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

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

17. Standard Solar Model (2005) Solar neutrinos and matter effects 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

18. New Solar composition 1/4 Troubles 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)  Main changes (dex) Grevesse 19840.0277 Anders & Grevess 19890.0267  C=-0.1,  Grevesse & Noels 19930.0245 Grevesse & Sauval 19980.0229  C=-0.04,  N=-0.07,  O=- 0.1 Asplund, Grevesse & Sauval 2005 0.0165  C=-0.13,  N=-0.14,  O=-0.17,  Ne=-0.24,  Si=-0.05 (affects meteor. abd.)

19. New Solar Composition 2/4 Two main sources: Spectral lines from solar photosphere/corona Meteorites 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. 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) 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

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. Standard Solar Model 2005 Old and new metallicity (Z/X)  down from 0.0229 to 0.0165 (~30% decrease) Main effect: radiative opacity  goes down Consequence: smaller radiative gradient Stability criterion: location of convective boundaries is modified BS05(GS98)BS05(ASG05)Helioseism. R CZ 0.7130.7280.713±0.001

23. Standard Solar Model 2005 Old and new metallicity Towards the center: temperature (radiative) gradient smaller  initial helium must be lower to match present day Sun  SSM prediction for Y SURF too low BS05(GS98)BS05(ASG05)Helioseism. R CZ 0.7130.7280.713±0.001 Y SURF 0.2430.2290.2485 ±0.0035

24. Standard Solar Model 2005 Old and new metallicity BS05(GS98)BS05(ASG05)Helioseism. R CZ 0.7130.7280.713±0.001 Y SURF 0.2430.2290.2485 ±0.0035 <c><c> 0.0010.005--- 0.0120.044--- Sound speed and density profiles are degraded

25. Standard Solar Model 2005 Old and new metallicity Central temperature lower by 1.2%  changes in neutrino fluxes BS05(GS98)BS05(AGS05) pp5.99x10 10 6.06x10 10 pep1.42x10 8 1.45x10 8 hep7.93x10 3 8.25x10 3 7Be4.84x10 9 4.34x10 9 8B5.69x10 6 4.51x10 6 13N3.05x10 8 2.00x10 8 15O2.31x10 8 1.44x10 8 17F5.84x10 6 3.25x10 6 Cl(SNU)8.126.6 Ga(SNU)126.1118.9  SNO  8 B)=4.99±0.33x10 6 cm -2 s -1

26. Standard Solar Model Uncertainties 1 st 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 2 nd 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. Standard Solar Model Power law dependences Using 1 st approach, power-law dependences of fluxes are very good approximation (Bahcall & Ulrich 1988)  ij can be calculated from (at least) 2 SSMs computed with x j +  x j and x j -  x j In the more general case, if many inputs are varying

28. Standard Solar Model Power law dependences S 11 S 1,14 LL (Z/X)  pp+0.14-0.02+0.73-0.07 7 Be-0.970.0+3.40+0.69 8B 8B-2.59+0.01+6.76+1.28 13 N-2.530.85+5.16+1.01 15 O-2.931.00+5.94+1.27 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  8 B) 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  8 B) 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 2 nd 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. Standard Solar Model Monte Carlo Simulations Solar abundance dichotomy  two choices for central values and uncertainties “Conservative”: 1-  defined as difference between GS98 and AGS05 central values (this is very conservative) “Optimistic”: 1-  as given by AGS05 OptimisticConservative 0.05 0.22 0.04 0.05 0.24 0.17 0.14 0.13 0.03Fe 0.08Ar 0.04S 0.02Si 0.03Mg 0.06Ne 0.05O 0.06N 0.05C

32. Standard Solar Model Monte Carlo Simulations Some results for helioseismology: R CZ and Y SURF

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

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

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

36. Standard Solar Model Monte Carlo Simulations Some results on neutrino fluxes: other fluxes 13 N+ 15 O mean and most probable values from GS98 and AGS05 distributions differ by 3.5  OPT and 2.6  OPT respectively Will neutrino experiments be able to determine the metallicity in the solar interior? GS98-Conservative Lognormal distributions reflect adopted composition uncertainties

37. Standard Solar Model Monte Carlo Simulations Fluxes uncertainties

38. The end.