SUSSP61: Neutrino Physics - St. Andrews, Scotland – 8 th to 23 rd, August, 2006 Standard Solar Models II Aldo Serenelli Institute for Advanced Study, Princeton.

SUSSP61: Neutrino Physics - St. Andrews, Scotland – 8th to 23rd, August, 2006

Standard Solar Models IIAldo Serenelli

Institute for Advanced Study, Princeton

Homework• Dating the Solar System

• Ratio 238U/235U known and constant (in space, not in time) in solar system material

• Primordial isotopic composition of lead (Pb) known from meteoritic samples with very low abundances of U or Th

• Measure the ratio 206Pb/204Pb and 207Pb/204Pb in your sample, and, taking into account that 204Pb does not change, write

1

1

235

238

235204204

207

204

207*207

238204204

206

204

206*206

TPRIM

PRIM

TPRIM

PRIM

eUPbPb

Pb

Pb

PbPb

eUPbPb

Pb

Pb

PbPb

1

1235

238

235

238

*207

*206

T

T

e

e

U

U

Pb

Pb

is only function of T

Updates since 2001 1/3

Microscopic physics

• Relativistic corrections to electrons missing Updated EoS (OPAL 2001)

• Independent calculations of opacities: Opacity Project

• 10% increase in 7Be + p cross section (Junghans et al. 2003)

HeHeBe

eBeB

BpBe

448

88

87

eppIII1%

change in 8B) flux


• Minor change (1%) in pp and also in hep cross sections (Park et al. 2003)

Microscopic physics

• Factor of 2 reduction in the 14N+p cross section (experimental result from LUNA collaboration)

HeCpN

eNO

OpN

NpC

eCN

NpC

41215

1515

1514

1413

1313

1312

e

e

CN-cycle

CN cycle slowed down by similar amount 13N) and 15O) ~ of previous theoretical value


Solar composition

• Large change in solar composition: mostly reduction in C, N, O, Ne. Results presented in many papers by the “Asplund group”. Summarized in Asplund, Grevesse & Sauval (2005)

Standard Solar Model (2005)

BS05 (updated microphysics, Grevesse & Sauval 1998 composition)

(Bahcall, Serenelli & Basu 2005)

Quantities to match

R=6.9598 1010cm

0.1%

Solar radius

(Z/X)= 0.0229Solar metals/hydrogen ratio

L=3.842 1033erg s-1

0.4%

Solar luminosity

Initial Present day values

Center Surface

X 0.7087 0.3461 0.7404

Y 0.2725 0.6337 0.2426

Z 0.0188 0.0202 0.0170

Standard Solar Model (2005)

BS05 Helios. BP00

RCZ 0.713 0.713±0.001 0.714

YSURF 0.2485 ±0.0035 0.244

<c> 0.001 --- 0.001

<> 0.012 --- 0.005

Difference in the sense: Sun - model

Standard Solar Model (2005)Sound speed

p-modes are acoustic modes sound speed c is the key to i

dr

dT

dr

dTTkN

dr

dcTkNc AvAv

21

321

/2

1

Radiat. transport Convect. transport change in temp. gradient

Change in slope

dc/dr < 0 gradient important: information about composition

Standard Solar Model (2005)Internal structure

Standard Solar Model (2005)Neutrino production

2pHeHeHe

HepH

Hpp

ppI433

32

2ee

24)/(

)(r

RRd

FluxdFN

Distribution of neutrino fluxes


HeCpN

eNO

OpN

NpC

eCN

NpC

41215

1515

1514

1413

1313

1312

e

e

CN-cycle

C+N (+O) = Const.


BS05 BP00

pp 5.99x1010 5.95x1010

pep 1.42x108 1.40x108

hep 7.93x103 9.3x103

7Be 4.84x109 4.77x109

8B 5.69x106 5.05x106

13N 3.05x108 5.48x108

15O 2.31x108 4.80x108

17F 5.84x106 5.63x106

Cl(SNU) 8.12 7.6

Ga(SNU) 126.1 128

Neutrino fluxes on Earth (cm-2 s-1)

No neutrino oscillation

SNO8B)=4.99±0.33x106 cm-2 s-1

Standard Solar Model (2005)Comparison with experiments

Standard Solar Model (2005)Solar neutrino spectra

Standard Solar Model (2005)Electron and neutron density

)(2)( rnGrV eFFor matter effects the “neutrino potential” is

Standard Solar Model (2005)Solar neutrinos and matter effects

)(2)( xnGxV eF

Fogli, et al. 2006 (hep-ph/0506083)

Solar neutrinos heavily affected by matter effects, but…

Standard Solar Model (2005)Solar neutrinos and matter effects

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

New Solar composition 1/4Troubles in paradise?

• Large change in solar composition: mostly reduction in C, N, O, Ne. Results presented in many papers by the “Asplund group”. Summarized in Asplund, Grevesse & Sauval (2005)

Authors (Z/X) Main changes (dex)

Grevesse 1984 0.0277

Anders & Grevess 1989 0.0267 C=-0.1,

Grevesse & Noels 1993 0.0245

Grevesse & Sauval 1998 0.0229 C=-0.04, N=-0.07, O=-0.1

Asplund, Grevesse & Sauval 2005

0.0165 C=-0.13, N=-0.14,

O=-0.17, Ne=-0.24, Si=-0.05 (affects meteor. abd.)

New Solar Composition 2/4

Two main sources:

• Spectral lines from solar photosphere/corona• Meteorites

• Volatile elements (do not aggregate easily into solid bodies): e.g. C, N, O, Ne, Ar only in solar spectrum• Refractory elements, e.g. Mg, Si, S, Fe, Ni both in solar spectrum and meteorites: meteoritic measurements more robust

Abundances from spectral lines: a lot of modeling required !!!


• Improvements in the modeling: 3D model atmospheres, MHD equations solved, NLTE effects accounted for in most cases• Improvements in the data: better selection of spectral lines. Previous sets had blended lines (e.g. oxygen line blended with nickel line)

What is good…

• Much improved modeling

• Different lines of same element give same abundance (e.g. CO and CH lines)

• Sun has now similar composition to solar neighborhood


What is not so good …

Agreement between helioseismology and SSM very much degraded

Was previous agreement a coincidence?

Standard Solar Model 2005Old and new metallicity

(Z/X) down from 0.0229 to 0.0165 (~30% decrease)

Main effect: radiative opacity goes down

Consequence: smaller radiative gradient 416

3

mT

PL

acGm

rad

radad

Stability criterion:

location of convective boundaries is modified

BS05(GS98) BS05(ASG05) Helioseism.

RCZ 0.713 0.728 0.713±0.001


Towards the center: temperature (radiative) gradient smaller initial helium must be lower to match present day Sun SSM prediction for YSURF too low


RCZ 0.713 0.728 0.713±0.001

YSURF 0.243 0.229 0.2485 ±0.0035



RCZ 0.713 0.728 0.713±0.001

YSURF 0.243 0.229 0.2485 ±0.0035

<c> 0.001 0.005 ---

<> 0.012 0.044 ---

Sound speed and density profiles are degraded


Central temperature lower by 1.2% changes in neutrino fluxes

BS05(GS98) BS05(AGS05)

pp 5.99x1010 6.06x1010

pep 1.42x108 1.45x108

hep 7.93x103 8.25x103

7Be 4.84x109 4.34x109

8B 5.69x106 4.51x106

13N 3.05x108 2.00x108

15O 2.31x108 1.44x108

17F 5.84x106 3.25x106

Cl(SNU) 8.12 6.6

Ga(SNU) 126.1 118.9

SNO8B)=4.99±0.33x106 cm-2 s-1

Standard Solar Model Uncertainties

• 1st approach: compute SSM varying one input at the time compute dependences of desired quantity on each input (composition, nuclear cross sections, etc.). Draw back: estimation of total uncertainty is a bit fuzzy

• 2nd approach: do a Monte Carlo simulation using a (large) bunch of SSMs where all inputs are varied randomly and simultaneously better overall estimates of uncertainties. However input uncertainties are “hard wired”. Individual contributions to total uncertainties are hidden

Standard Solar Model Power law dependences

Using 1st approach, power-law dependences of fluxes are very good approximation (Bahcall & Ulrich 1988)

11ln

ln0

000

ijij

j

jii

j

j

i

iij

j

i

x

x

x

x

xd

d

ij can be calculated from (at least) 2 SSMs computed with xj+xj and xj-xj

In the more general case, if many inputs are varying

j j

j

i

i

ij

x

x

00

Standard Solar Model Power law dependences

S11 S1,14 L (Z/X)

pp +0.14 -0.02 +0.73 -0.07

7Be -0.97 0.0 +3.40 +0.69

8B -2.59 +0.01 +6.76 +1.28

13N -2.53 0.85 +5.16 +1.01

15O -2.93 1.00 +5.94 +1.27

Power laws: some instructive examples

Standard Solar Model Power-law dependences

• One word of warning for very interested people: flux dependences on metallicity (details in Bahcall & Serenelli 2005)

• Better treat elements individually than (Z/X) uncertainty estimations for fluxes can get smaller, specially for 8B)

• Uncertainty in Z/X dominated by C, N, O, Ne; but fluxes depend more strongly on Si, S, Fe (these have small uncertainties as abundances are determined in meteorites) smaller uncertainties in the fluxes

• Total uncertainty for 8B) goes from 23% (using total uncertainty of Z/X) to 13% using individual element uncertainties and power-law dependences

Standard Solar Model Monte Carlo Simulations

2nd approach: compute a large numbers of SSM by varying individual inputs independently and simultaneously. Originally done by Bahcall & Ulrich (1988)

An update: 10000 SSMs (in 2 groups of 5000) using 21 variable input parameters: 7 cross sections, age, luminosity, diffusion velocity, 9 individual elements, EoS and opacities.Details can be found in Bahcall, Serenelli & Basu (2006)


Solar abundance dichotomy two choices for central values and uncertainties• “Conservative”: 1- defined as difference between GS98 and AGS05 central values (this is very conservative)

• “Optimistic”: 1- as given by AGS05

OptimisticConservative

0.05

0.22

0.04

0.05

0.05

0.24

0.17

0.14

0.13

0.03Fe

0.08Ar

0.04S

0.02Si

0.03Mg

0.06Ne

0.05O

0.06N

0.05C


Some results for helioseismology: RCZ and YSURF


Some results for helioseismology: sound speed and density profiles

AGS05 - Optimistic

GS98 - Conservative


Some results on neutrino fluxes: 8B) and 7Be)


Some results on neutrino fluxes: pp) and pep)


Some results on neutrino fluxes: other fluxes

• 13N+15O mean and most probable values from GS98 and AGS05 distributions differ by 3.5OPT and 2.6OPT respectively

• Will neutrino experiments be able to determine the metallicity in the solar interior?

GS98-Conservative• Lognormal distributions reflect adopted composition uncertainties


Fluxes uncertainties

The end.

SUSSP61: Neutrino Physics - St. Andrews, Scotland – 8 th to 23 rd, August, 2006 Standard Solar Models II Aldo Serenelli Institute for Advanced Study, Princeton.

Documents

model slide

standard solar models

solar neutrino spectra

composition slide

solar system ratio

solar metalshydrogen

solar composition large

princeton slide