1 The pp-chain (and the CNO-cycle) after SNO and KamLAND Barbara Ricci, University of Ferrara and INFN Fourth International Conference on Physics Beyond the Standard Model “BEYOND THE DESERT ‘03” Castle Ringberg, Tegernsee, Germany 9-14 June 2003

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3 Outline Boron-neutrinos after SNO and KamLAND What can we learn from B-neutrinos? What have we learnt from Helioseismology? The Sun as a laboratory for fundamental physics Main messages: Neutrinos are now probes of the solar interior accurate determinations of S 17,S 34 and S 1,14 are particularly important now.

4 The new era of neutrino physics We have learnt a lot on neutrinos. Their survival/transmutation probabilities in matter are now understood. We have still a lot to learn for a precise description of the mass matrix (and other neutrino properties…) Now that we know the fate of neutrinos, we can learn a lot from neutrinosNow that we know the fate of neutrinos, we can learn a lot from neutrinos.

5 The measured boron flux The total active    ( e +  +   boron flux is now a measured quantity. By combining all observational data one has*:   = 5.05 (1 ± 0.06) 10 6 cm -2 s -1. The central value is in perfect agreement with the Bahcall 2000 SSM present   /   =6%Note the present 1  error is   /   =6% next few years   /    3%In the next few years one hope to reach   /    3% * Bahcall et al. astro-ph/ and astro-ph/ BP2000FRANECGARSOM   [10 6 s -1 cm -2 ]  level

6 s 33 s 34 s 17 s e7 s 11 Nuclear The Boron Flux, Nuclear Physics and Astrophysics  astro * Scaling laws derived from FRANEC models including diffusion. Coefficients closer to those of Bahcall are obtained if diffusion is neglected.   depends on nuclear physics and astrophysics inputs Scaling laws have been found numerically and are physically understood   =   (SSM) · s s s 17 1 s e7 -1 s · com 1.4 opa 2.6 dif 0.34 lum 7.2 These give flux variation with respect to the SSM calculation when the input X is changed by x = X/X (SSM). Can learn astrophysics if nuclear physics is known well enough.

7 Uncertainties budget Nuclear physics uncertainties, particularly on S 17 and S 34, dominate over the present observational accuracy   /   =6% (1 . The foreseeable accuracy   /   =3% could illuminate about solar physics if a significant improvement on S 17 and S 34 is obtained. For fully exploiting the physics potential of a   measurement with 3% accuracy one has to determine S 17 and S 34 at the level of 3% or better Lum ***Dif Opa Com S Se S17** S *S33   /    S/S(1  Source *LUNA result **Adelberger Compilation: see below ***by helioseismic const. [gf et al.A&A 342 (1999) 492] See similar table in JNB, astro- ph/

8 Progress on S 17 S 17 (0) [eV b] Ref. Adel.-Review RMP 70,1265 (1998) Nacre-Review 21 ± 2 NP 656A, 3 (1999) Hammache et al 18.8 ± 1.7 PRL 86, 3985 (2001) Strieder et al 18.4 ± 1.6 NPA 696, 219 (2001) Hass et al 20.3 ± 1.2 PLB 462, 237 (1999). Junghans et al.* 22.3 ± 0.7 PRL 88, (2002) Baby et al ± 0.7 PRL. 90, (2003) Results of direct capture expts**. Adelberger and NACRE use a conservative uncertainty (  9%), Recently high accuracy determinations of S 17 have appeared. Average from 5 recent determinations yields: S 17 (0)= 21.1 ± 0.4 S 17 (0)= 21.1 ± 0.4 (1  ) In principle an accuracy of 2% has been reached, however    dof=2 indicating some tension among different data. S17(0)[eV b] Data published **See also Davids & Typel (2003): 19 ± 0.5 eVb :

9 Remark on S 34 S 17 (0) S 34 (0)If really S 17 (0) has a 2% accuracy, the 9% error of S 34 (0) is the main source of uncertainty for extracting physics from Boron flux Lum ***Dif Opa Com S Se S S *S33   /    S/S (1  Source LUNA results on S 34 will be extremely important.LUNA results on S 34 will be extremely important.

10 Sensitivity to the central temperature Boron neutrinos are mainly determined by the central temperature, almost independently in the way we vary it. (The same holds for pp and Be neutrinos) Bahcall and Ulmer. ‘96  i /  i SSM B Be pp Tc/Tc SSM Castellani et al. ‘97

11 The central solar temperature The various inputs to   can be grouped according to their effect on the solar temperature. All nuclear inputs (but S 11 ) only determine pp-chain branches without changing solar structure. The effect of the others can be reabsorbed into a variation of the “central” solar temperature:   =   (SSM) [Tc /Tc (SSM) ] 20.. S S S 17 S e7 -1 Source dlnT/dlnS  dln  B /dlnS   S S S1701 Se70 S Com Opa Dif Lum (  20)Boron neutrinos are excellent solar thermometers due to their high (  20) power dependence.

12 Present and future for measuring T with B-neutrinos   /   =6%  S nuc / S nuc = 12% (cons.)At present,   /   =6% and  S nuc / S nuc = 12% (cons.) translate into  Tc/Tc= 0.7 % the main error being due to S 17 and S 34.  S nuc /S nuc =0If nuclear physics were perfect (  S nuc /S nuc =0) already now we could have:  Tc/Tc= 0.3 %   /   =3%When   /   =3% one can hope to reach (for  S nuc /S nuc =0) :  Tc/Tc= 0.15 % 1  level

13 Helioseismic observables From the measurements of p-modes one derives: a)sound speed squared: u=P/  (1  ) accuracy  0.1 – 1%, depending on the solar region  u/u 1  3  See e.g. Dziembowski et al. Astr.Phys. 7 (1997) 77 b) properties of the convective envelope R b /R o = 0.711(1± 0.14%) (1  ) Y ph =0.249 (1±1.4%) u

14 SSM and helioseismology Standard solar models are generally in agreement with data to the “(1  ) ” level: e.g. BP2000 Some possible disagreement just below the convective envelope (a feature common to almost every model and data set) Y BP2000 =0.244Y= 0.249±0.003 R bBP2000 =0.714 R b =0.711 ± BP2000=Bahcall et al. ApJ 555 (2001) 990

15 Helioseismology constrains solar models and solar temperature (1) Helioseismology constrains solar models and solar temperature (1) Temperature of the solar interior cannot be determined directly from helioseismology: chemical composition is needed: (u=P/  T/  ) But we can obtain the range of allowed values of Tc by using th following approach: build solar models by varying the solar inputs which mainly affect Tc (S 11, chemical composition, opacity…) select those models consistent with helioseismic data(sound speed profile, properties of the convective envelope)

16 S 11 is constrained at 2% level (1  ) The metal content is constrained at the 5% level (1  ) S 11 Z/X Examples: Examples: Actually one has to consider: 1) all parameters which affect Tc in the proper way (compensation effects) 2) not only sound speed, but above all the properties of the convective envelope.…..

17 Helioseismology constrained solar models and solar temperature (2) Helioseismology constrained solar models and solar temperature (2) BR et al. PLB 407 (1997) 155 Temperature of the solar interior cannot be determined directly from helioseismology So - if we build solar models by varying the solar inputs which mainly affect Tc -and select those models consistent with helioseismic data(sound speed profile, properties of the convective envelope) We find: Helioseismic constraint:  Tc/Tc= 0.5 % 1  level

18 Comparison between the two approaches Helioseismic constrained solar models give:  Tc/Tc= 0.5 % Boron neutrinos observation translate into  Tc/Tc= 0.7 % (main error being due to S 17 and S 34 ) For the innermost part of the sun, neutrinos are now almost as accurate as helioseismology (They can become more accurate than helioseismology in the near future) 1  level

19 The Sun as a laboratory for astrophysics and fundamental physics An accurate measurement of the solar temperature near the center can be relevant for many purposes –It provides a new challenge to SSM calculations –It allows a determination of the metal content in the solar interior, which has important consequences on the history of the solar system (and on exo-solar systems) One can find constraints (surprises, or discoveries) on: –Axion emission from the Sun –The physics of extra dimensions (through Kaluza-Klein emission) –Dark matter (if trapped in the Sun it could change the solar temperature very near the center) – … BP-2000FRANECGAR-SOM T6T

20 Be neutrinos In the long run (KamLAND +Borexino+LENS…) one can expect to measure  Be with an accuracy  Be /  Be  5%  Be is insensitive to S 17, however the uncertainty on S 34 will become important.  Be is less sensitive to the solar structure/temperature (  Be  T 10 ). An accuracy   e /   e  5% will provide at best  T/T  5% Source  S/S  (1    e /   e S S S = Se70.02= Spp0.02 Com Opa Dif Lum Remark however that Be and B bring information on (slightly) different regions of the Sun

21 CNO neutrinos, LUNA and the solar interior LUNAThe principal error source is S 1,14. The new measurement by LUNA is obviously welcome. Source  S/S (1  )   /    O /  O S S S Se Spp S1, Com Opa Dif Lum Solar model predictions for CNO neutrino fluxes are not precise because the CNO fusion reactions are not as well studied as the pp reactions. Also, the Coulomb barrier is higher for the CNO reactions, implying a greater sensitivity to details of the solar model.

22Summary Solar neutrinosSolar neutrinos are becoming an important tool for studying the solar interior and fundamental physics helioseismologyAt present they give information about solar temperature as accurate as helioseismology does Better determinations of S 17, S 34 and S 1,14 are needed for fully exploiting the physics potential of solar neutrinos. All this could bring us towards fundamental questions:All this could bring us towards fundamental questions: –Is the Sun fully powered by nuclear reactions? –Is the Sun emitting something else, beyond photons and neutrinos?

23 Appendix

24 pp-chain 99,77% p + p  d+ e + + e E  0,42 MeV 0,23% p + e - + p  d + e E = 1,44 MeV 3 He + 3 He   + 2p S(0)=(5,4  0,4) MeVb 3 He + p   + e + + e E  18 MeV ~2  % 84,7% 13,8% 0,02%13,78% 3 He + 4 He  7 Be +  S(0)=(0,52  0,02) KeV b 7 Be + e -  7 Li +  + e E  0,86 MeV 7 Be + p  8 B +  d + p  3 He +  7 Li + p   +  pp I pp III pp II hep hep 8 B  8 Be*+ e + + e 2  E  14,06 MeV S(0)=(4,00  0,068)  KeV b

25 Observations On Earth: network of telescopes at different longitudines: - Global Oscillation Network Group (GONG) -Birmingham Solar Oscillations Network (BiSON). From satellite: since 1995: SoHo (Solar and Heliospheric Observatory) GONG D=1.5 10^6 km

26 Solar rotation Solar surface does not rotate uniformely: T=24 days (30 days) at equator (poles). Helioseismology (after 6 years of data taking) shows that below the convective region the sun rotates in a uniform way Note: E rot =1/2 m  rot R 2  0.02 eV E rot << KT giorni days

27 Magnetic field From the observation of sunspots number a 11 year solar cycle has been determined (Sunspots= very intense magnetic lines of force (3kG) break through the Sun's surface) the different rotation between convection and radiative regions could generate a dynamo mechanism: B< 30 kG near the bottom of the convective zone. ( e.g. N ghiem, Garcia, Turck-Chièze, Jimenez-Reyes, 2003) B< 30 MG in the radiative zone Anyhow also a 10 6 G field give an energy contribution << KT Radiative zone: B  B Tachocline B  B External zone, flux tube, B =4000G

28 Calculate frequencies  i as a function of u  i  i (u j ) j=radial coordinate Assume Standard Solar Model as linear deviation around the true sun:  i  i, sun + A ij (u j -u j,sun ) Minimize the difference between the measured  i and the calculated  i In this way determine  u j  =u j  -u j, sun Inversion method

29 Does the Sun Shine by pp or CNO Fusion Reactions? Solar neutrino experiments set an upper limit (3  ) of 7.8% (7.3% including the recent KamLAND measurements) to the fraction of energy that the Sun produces via the CNO fusion cycle, This is an order of magnitude improvement upon the previous limit. New experiments are required to detect CNO neutrinos corresponding to the 1.5% of the solar luminosity that the standard solar model predicts is generated by the CNO cycle. Bahcall, Garcia & Pena-Garay PRL 2003