1. 1 B.Ricci* What have we learnt about the Sun from the measurement of 8B neutrino flux? Experimental results SSM predictions SSM uncertainties on  (8B) nuclear inputs astrophysical inputs Comparison between experiment and SSM upper bound on sterile neutrinos Information on SSM inputs from  (8B) exp Solar temperature and  (8B) exp Conclusions Vulcano 19-26 May 2002 * and G. Fiorentini, PLB 2002

2. 2 Experimental results Superkamiokande (ES):  (8B) SK  = 2.32  (1±  3.5%) 10 6 cm -2 s -1  e      SNO - CC:  (8B) SNO =1.75 (1  ±  8.0%) 10 6 cm -2 s -1  e  Combined*:  (8B) EXP  = 5.20 (1  ±18%) 10 6 cm -2 s -1 Note: agreement with recent SNO - NC:  (8B) NC  = 5.09 (1  ±12%) 10 6 cm -2 s -1 (assuming std. spectrum)  (8B) NC  = 6.42 (1  ±25%) 10 6 cm -2 s -1 (free spectrum): * see. Fogli, Lisi,Montanino, Villante PRD 1999; Fogli, Lisi, Montanino, Palazzo PRD 2001 flux of total active neutrinos produced in the Sun

3. 3 SSM predictions Different SSMs* give similar results ( ± 15%) BP2000:  (8B) SSM =5.05 (1  ±  18%) 10 6 cm -2 s -1 Where does the theoretical error comes from? * all models include diffusion and agree with helioseismic data

4. 4 8B neutrinos and SSM inputs 8B neutrino flux depends on several parameters: We change the parameters with respect the SSM value and  (8B) change according to:  (8B)=  (8B) SSM  i  (P i /P i )  i. Nuclear Parameters: S 11 : p+p ->d+e + + e S 33 :3He+3He ->4He+2p S 34 :3He+4He ->7Be+p S 17 :7Be+p -> 8B+  S e7 : 7Be+e -> 7Li+ e Astrophysical Parameters: L o : solar luminosity t o :solar age Z/X: metal content  :solar opacity D:diffusion

5. 5 Power laws and SSM uncertainties  values are in agreement with previous estimates (Bahcall 1989, Castellani et al. 1997)  only theoretical uncertainty on S 11  and D input errors arise from comparison among different theoretical calculations... helioseismology fix diffusion at 10% level, G. Fiorentini et al. A&A 1999  nucl. and astroph. give comparable contributions  (8B)=  (8B) SSM  i  (P i /P i )  i

6. 6 Comparison between EXP and SSM We have seen:  (8B) EXP =5.20 (1  ±  18%) 10 6 cm -2 s -1  (8B) SSM =5.05 (1  ±  18%) 10 6 cm -2 s -1 very good agreement between EXP and SSM similar errors affects both determinations we can derive an upper bound for sterile neutrinos:  (8B) sterile < 2.5 10 6 cm -2 s -1 (at 2  ) if sterile neutrinos exist,  (8B) EXP is a lower limit

7. 7  (8B) EXP and the solar parameters Neglecting sterile neutrinos, one can use  (8B) EXP as an independent way of estimating the accuracy of solar parameters. By using the power laws derived previously,  (8B) EXP can be used to determine each of the parameter listed in previous slides: For each parameters we have estimated the corresponding accuracy, taking into account the EXP error of 8B- and the uncertainty on all other parameters. P i =S 11, S 33,…,L o, t o......

8. 8 Information on nuclear and astrophysical inputs from  (8B) EXP All derived uncertainties are worse than those adopted in SSM. We remind however that: S 11 is not measured but it results from theoretical estimate (helioseismic constrain gives 2%, Degl’Innocenti et al. PLB 1998 ) for opacity the 2.5% error derives from comparison of different calculations Z/X corresponds to solar photosphere abundances, which might not be representative of the metal content of the solar interior (helioseismic analysis gives about 5%)

9. 9 The central solar temperature T c is not an independent variable *, for instance: if the p+p astrophysical S-factor rises, nuclear fusion gets easier and the fixed solar luminosity is obtained with a lower temperature; if Z/X increases, opacity increases and the radiative transfer of the solar energy requires higher temperature gradient, which in turn implies a higher Tc; a more luminous or an older Sun, have higher internal temperature In summary: T c depends on S 11, L o, t o, Z/X, , D * see e.g. Castellani et al. PR 1997 astro.nuc.

10. 10 8B neutrino flux and T c 8B neutrino flux depend both on temperature and on nuclear parameters:  is weakly dependent on which parameter is being varied to obtain a change of T c :  =20  (8B) /  (8B) SSM  c, /  c,SSM ± 10%

11. 11 8B neutrino flux measurement constrains central solar temperature By using the previous relationship and  (8B) EXP. one can text T c The agreement between theory and experiment on  (8B) implies that T c of the Sun agrees with the SSM prediction to within per cent level: Tc=15.7(1 ± 1%) 10 6 K where error gets comparable contribution from the measurement of 8B- and from nuclear physics. This result confirms the information provide by helioseismology: consistency with helioseismic data has been found only for solar models with T c within 1% of SSM predictions * T c =15.7(1 ± 1%) 10 6 K *BR et al. PLB 1997; Bahcall et al. PRL 1997, helioseismology:

12. 12 Conclusions By combining SNO-CC and SK data one can derive the total active neutrino flux produce by 8B decay in the Sun. We use this information to check the accuracy of several input parameters in solar model calculations. We have found that S 11 and opacity are constrained at less than 10%. The central temperature is determined at one percent level. We have also found an upper limit for sterile neutrino flux on Earth.