Transcript Helioseismology and nuclear reactions in the sun

Vulcano 19-26 May 2002
B.Ricci*
What have we learnt about the Sun from
the measurement of 8B neutrino flux?







Experimental results
SSM predictions
SSM uncertainties on F(8B)
 nuclear inputs
 astrophysical inputs
Comparison between experiment and SSM
 upper bound on sterile neutrinos
Information on SSM inputs from F(8B)exp
Solar temperature and F(8B)exp
Conclusions
* and G. Fiorentini, PLB 2002
1
Experimental results



Superkamiokande (ES):
F(8B)SK = 2.32 (1± 3.5%) 106 cm-2 s-1 (ne,nm,nt)
SNO - CC:
F(8B)SNO=1.75 (1 ± 8.0%) 106 cm-2 s-1 (ne)
Combined*:
F(8B)EXP = 5.20 (1 ±18%) 106 cm-2 s-1
flux of total active neutrinos produced in the Sun
Note: agreement with recent SNO - NC:
F(8B)NC = 5.09 (1 ±12%) 106 cm-2 s-1 (assuming std. spectrum)
F(8B)NC = 6.42 (1 ±25%) 106 cm-2 s-1 (free spectrum):
* see. Fogli, Lisi,Montanino, Villante PRD 1999; Fogli, Lisi, Montanino, Palazzo PRD 2001
2
SSM predictions



Different SSMs* give similar results (± 15%)
BP2000
FRANEC97 JCD96 GARSOM97
Tc [106 K]
15.569
15.69
15.67
15.7
F(8B)
[106cm-2s-1]
5.05
5.16
5.87
5.30
BP2000: F(8B)SSM=5.05 (1 ± 18%) 106 cm-2 s-1
Where does the theoretical error comes
from?
* all models include diffusion and agree with helioseismic data
3
8B neutrinos and SSM inputs

8B neutrino flux depends on several parameters:
Nuclear Parameters:
•S11: p+p ->d+e++ne
•S33: 3He+3He ->4He+2p
•S34: 3He+4He ->7Be+p
•S17: 7Be+p -> 8B+g
•Se7: 7Be+e -> 7Li+ ne

Astrophysical Parameters:
•Lo : solar luminosity
•to: solar age
•Z/X: metal content
• k : solar opacity
• D: diffusion
We change the parameters with respect the SSM
value and F(8B) change according to:
F(8B)= F(8B)SSM Pi (Pi/Pi)ai .
4
F(8B)= F(8B)SSM Pi (Pi/Pi)ai
Power laws and SSM uncertainties
Nuclear
Astrophysical
Pi
a
S11 S33
-2.7 -0.43 0.84 -1
1
Input error [%]
1.7
6.1
9.4
2
Contributed
4.6
error to F(B) [%]
2.6
7.9
2
F(B)/F(B)
S34 Se7 S17
Lo
to
Z/X
k
D
1.4
1.4
2.6
0.34
9
0.4
0.4
6.1
2.5
15
9
2.9
0.56 8.5
6.5
5
7.2
13.3 %
-a values are in agreement with previous estimates
(Bahcall 1989, Castellani et al. 1997)
- only theoretical uncertainty on S11
- k and D input errors arise from comparison among
different theoretical calculations
... helioseismology fix diffusion at 10% level, G. Fiorentini et al. A&A 1999
12.2%
Conclusion:
F(8B)
 18%
F(8B) TOT
- nucl. and astroph. give comparable contributions
5
Comparison between EXP and SSM

We have seen:
F(8B)EXP=5.20 (1 ± 18%) 106 cm-2 s-1
F(8B)SSM=5.05 (1 ± 18%) 106 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:

F(8B)sterile< 2.5 106 cm-2 s-1
(at 2s)
if sterile neutrinos exist, F(8B)EXP is a lower limit
6
F(8B)EXP and the solar parameters


Neglecting sterile neutrinos, one can use F(8B)EXP as an
independent way of estimating the accuracy of solar parameters.
By using the power laws derived previously, F(8B)EXP can be used to
determine each of the parameter listed in previous slides:
1/α i
 F(8B) EXP 

Pi  
 F(8B) SSM 

 Pi
P i  j 
 Pi,SSM




-α i /α j
Pi=S11, S33,…,Lo, to...
For each parameters we have estimated the corresponding accuracy,
taking into account the EXP error of 8B-n and the uncertainty on all
other parameters.
Δ Pi
Pi
F (8B )
1

αi
2
 Pi 
 F(8B) 



 i  j α i
 F(8B)  EXP
 Pi 
2
...
7
Information on nuclear and
astrophysical inputs from F(8B)EXP
Nuclear
Pi
Input error [%]
S11 S33
1.7
uncertainty derived 9
from F(8B)EXP [%]


Astrophysical
S34 Se7 S17
6.1
9.4
2
9
58
28
25
23
Lo
to
Z/X k
0.4
6.1
2.5
3.5
18
18
9.3
0.4
D
15
75
All derived uncertainties are worse than those adopted in SSM.
We remind however that:
•S11is not measured but it results from theoretical estimate
(helioseismic constrain gives 2% , Degl’Innocenti et al. PLB 1998 )
•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%)
•for opacity the 2.5% error derives from comparison of
different calculations
8
The central solar temperature

Tc 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:
Tc depends on S11, Lo, to, Z/X, k, D
* see e.g. Castellani et al. PR 1997
nuc.
astro.
9
8B neutrino flux and Tc
8B neutrino flux depend both on temperature and on
nuclear parameters:
 Tc
F(8B)  F(8B) SSM 
 TSSM




β
 Snuc

S
 nuc,SSM
b is weakly dependent on
which parameter is being
varied to obtain a change
of Tc :
b=20




-α i /α j
-0.43
Snuc  S0.84
33 S34 S17 /Se7
F(8B) /F(8B)SSM

± 10%
Tc, /Tc,SSM
10
8B neutrino flux measurement
constrains central solar temperature


β
By using the previous relationship
 Tc   Snuc
 
F(8B)  F(8B) SSM 

and F(8B)EXP. one can text Tc
 TSSM   Snuc,SSM




-α i /α j
The agreement between theory and experiment on F(8B) implies
that Tc of the Sun agrees with the SSM prediction to within per cen
level:
Tc=15.7(1 ± 1%) 1066 K
Tc=15.7(1
where error gets comparable contribution from the measurement
of 8B-n and from nuclear physics.

helioseismology:
This result confirms the information provide by helioseismology:
consistency with helioseismic data has been found only for solar
models with Tc within 1% of SSM predictions*
*BR et al. PLB 1997; Bahcall et al. PRL 1997,
11
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 S11 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.
12