Standard Solar Model Calculation of Neutrino Fluxes
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Transcript of Standard Solar Model Calculation of Neutrino Fluxes
Standard Solar Model Calculation of Neutrino Fluxes
Aldo SerenelliInstitute for Advanced Study
NOW 2006 Conca Specchiulla 11-Sept-2006
John N. Bahcall (1934-2005)
Standard Solar Model: What is done…
What is done… • Initial 1M=1.9891033g, homogeneous composition• Evolve it during t=4.57 109yrs • Match present Sun: L=3.842 1033erg s-1
R=6.96 1010cm
(Z/X)= 0.0229/0.0165 (note differing values!!)
Free parameters… • Convection prescription: 1 parameter (MLT)
• Initial solar composition: X+Y+Z=1 2 free parameters, e.g. X, Z
Basic assumptions: spherical symmetry no rotation no magnetic fields
Standard Solar Model: predictions
• 8 Neutrino fluxes: total flux and internal distribution. Only 8B directly measured so far (negligible contribution to solar energetics)• Nuclear and gravothermal (negligible) energy contributions to solar luminosity “luminosity constraint”
• Chemical elements internal distributions electron and neutron density profiles
• Sound speed profile c(r)
• Density profile (r)
• Depth of the convective envelope RCZ
• Surface helium abundance YS
For helioseismology…
SSM - BS05(OP,GS98)Bahcall, Serenelli & Basu (2005)
• Most updated input physics including• Grevesse & Sauval (1998; GS98) solar composition: (Z/X),today= 0.0229
---0.012<>
---0.001<c>
0.2485 ±0.00350.243YSURF
0.713±0.0010.713RCZ
Helios.BS05
0.74040.34610.7087X
SurfaceCenter
Present day values
Initial
0.01700.02020.0188Z
0.24260.63370.2725Y
SSM - BS05(OP,GS98)
5.84x106 (1±0.52)17F
2.31x108 (1+0.33-0.29)15O
3.05x108 (1+0.31-0.28)13N
5.69x106 (1±0.16)8B
4.84x109 (1±0.10) 7Be
7.93x103 (1±0.16) hep
1.42x108 (1±0.02) pep
5.99x1010(1±0.01) pp
BS05(OP,GS98)
Neutrino fluxes on Earth (cm-2 s-1)
SNO8B)=4.94x106 (1±0.08) cm-2 s-1
Neutrino production profiles together with electron and neutron density profiles needed for oscillation studies: e.g. 8B s affected by MSW effect, pp and 7Be s only by vacuum oscillations
SSM – New Solar Composition
Results from the “Asplund group” summarized in Asplund, Grevesse & Sauval (2005; AGS05): improved modeling of solar atmosphere large reduction in volatile elements: C, N, O, Ne, Ar
0.05
0.22
0.04
0.05
0.05
0.24
0.17
0.14
0.13
Reduction [dex]
0.03
0.08
0.04
0.02
0.03
0.06
0.05
0.06
0.05
Quoted uncert.[dex]
Fe
Ar
S
Si
Mg
Ne
O
N
C
Element
(Z/X),today= 0.0165 (old 0.0229)Main effect: lower radiative opacity
• Shallower convective envelope and low surface helium
• Sound speed and density profiles in disagreement with Helioseismology
• Flatter T-gradient in core (somewhat lower central T)
SSM – BS05(OP,AGS): Helioseismology
Sound speed and density profiles are degraded, particularly outer half
0.2485 ±0.0040.2290.243YSURF
---0.0440.012<>
---0.0050.001<c>
0.713±0.0010.7280.713RCZ
ASG05 Helioseism.GS98
SSM – BS05(OP,AGS): Neutrino fluxes
• Central temperature lower by ~ 1%
• Lower CNO abundances directly affect CNO fluxes
3.25x1065.84x10617F
1.44x1082.31x10815O
2.00x1083.05x10813N
4.51x1065.69x1068B
4.34x1094.84x109 7Be
8.25x1037.93x103 hep
1.45x1081.42x108 pep
6.06x10105.99x1010 pp
AGS05GS98
SNO8B)=4.94x106 cm-2 s-1
↑ 1%
↑ 2%
↑ 4%
↓ 10%
↓ 20%
↓ 33%
↓ 38%
↓ 44%
SSM – Uncertainties
Composition uncertainties: two approaches to define 1-
0.05
0.22
0.04
0.05
0.05
0.24
0.17
0.14
0.13
(Very) Conservative1-Change [dex]
0.03
0.08
0.04
0.02
0.03
0.06
0.05
0.06
0.05
Optimistic1-Quoted uncert.[dex]
Fe
Ar
S
Si
Mg
Ne
O
N
C
Element
Two approaches to compute SSM uncertainties: Monte Carlo simulations (Bahcall, Serenelli & Basu 2006) and Power-Law dependences (improved treatment of composition in Bahcall & Serenelli 2005)
SSM – Uncertainties: MC
Monte Carlo simulations: 2 sets with 5000 SSMs each, 9 individual elements, 7 nuclear rates, age, luminosity, diffusion, rad. opac. & EOS
GS98 - Conservative
AGS05 - Optimistic
Helioseismology mostly affected by uncertainties in composition
SSM – Uncertainties: MC
Some cross section uncertainties: S11 (0.6%) - S33 (6.0%) - S34 (9.4%) S17 (3.8%) - S1,14 (8.4%)
3.25x1065.84x10617F
1.44x1082.31x10815O
2.00x1083.05x10813N
4.51x1065.69x1068B
4.34x1094.84x109 7Be
8.25x1037.93x103 hep
1.45x1081.42x108 pep
6.06x10105.99x1010 pp
AGS05GS98
Will neutrino experiments discriminate between GS98 & AGS05 compositions?
SSM – Uncertainties: MC Bahcall, Serenelli, Basu (2006)
Using “improved” (LUNA) optimisitc uncertainties SSM predictions (GS98 and AGS05) for 7Be and 13N-15O differ by approx. 1.2 and 1.9 It will be a difficult task!!
LUNA S34 ~5.5%
~8-9%
Difficult to reduce: composition dominates
Conclusions
• SSM with “high” (old; GS98) metallicity in excellent agreement with helioseismology and neutrino experiments
• New solar abundance determinations (AGS05) result in disagreement between SSM and helioseismology. Additional works with different approaches (Basu & Antia 2006, Basu et al. 2006, Pinsonneault & Delhaye 2006) also rule out new composition (but measurements are there!!!)
• Neutrino flux(es) agreement still excellent (SNO measurement right in the middle of both SSM predictions)
• Is the SSM paradigm not good enough for helioseismology? Need for independent group doing solar abundances at similar level of sophistication
• Will future neutrino experiments shed light on the solar core composition?
SSM – Production profiles of neutrino fluxes
Solar model gives the internal structure: T(r), (r), Xi(r), ne(r), nn(r) compute local neutrino production per unit mass, e.g. for pp neutrinos
1-1-22 sg 2
1)( vXNpp AV
and the production per unit radius
1)(
;)()( 2
RRdRRd
FluxdpprC
RRd
Fluxd pppp
pp
SSM – Neutrino potential
Combining with the electron (or neutron) density profile
Construct the “neutrino potential” for matter effects:
)(2)( xnGxV eF
Fogli, et al. 2006 (hep-ph/0506083)
SSM – Neutrino oscillations
Fogli, et al. 2006 (hep-ph/0506083)
12222
12
212
12
1212
2sin/)(2cos
/)(2cosˆ2cos
2cos)(ˆ2cos2
1
2
1
mxA
mxA
xPee
Survival probability Pee depends on A(x)=2EV(x) and matter
effect are important if A(x) m
Vacuum oscillations for pp and 7Be
Matter effects for 8B