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Standard Solar Model Calculation of Neutrino Fluxes Aldo Serenelli Institute for Advanced Study NOW 2006 Conca Specchiulla 11-Sept-2006

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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