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Standard Solar Models II Aldo Serenelli Institute for Advanced Study, Princeton. SUSSP61: Neutrino Physics - St. Andrews, Scotland – 8 th to 23 rd , August, 2006. is only function of T. Homework. Ratio 238 U/ 235 U known and constant (in space, not in time) in solar system material - PowerPoint PPT Presentation
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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
Updates since 2001 2/3
• 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
Updates since 2001 3/3
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
Standard Solar Model (2005)Neutrino production
HeCpN
eNO
OpN
NpC
eCN
NpC
41215
1515
1514
1413
1313
1312
e
e
CN-cycle
C+N (+O) = Const.
Standard Solar Model (2005)Neutrino production
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 !!!
New Solar Composition 3/4
• 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
New Solar Composition 4/4
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
Standard Solar Model 2005Old and new metallicity
Towards the center: temperature (radiative) gradient smaller initial helium must be lower to match present day Sun SSM prediction for YSURF too low
BS05(GS98) BS05(ASG05) Helioseism.
RCZ 0.713 0.728 0.713±0.001
YSURF 0.243 0.229 0.2485 ±0.0035
Standard Solar Model 2005Old and new metallicity
BS05(GS98) BS05(ASG05) Helioseism.
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
Standard Solar Model 2005Old and new metallicity
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)
Standard Solar Model Monte Carlo Simulations
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
Standard Solar Model Monte Carlo Simulations
Some results for helioseismology: RCZ and YSURF
Standard Solar Model Monte Carlo Simulations
Some results for helioseismology: sound speed and density profiles
AGS05 - Optimistic
GS98 - Conservative
Standard Solar Model Monte Carlo Simulations
Some results on neutrino fluxes: 8B) and 7Be)
Standard Solar Model Monte Carlo Simulations
Some results on neutrino fluxes: pp) and pep)
Standard Solar Model Monte Carlo Simulations
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
Standard Solar Model Monte Carlo Simulations
Fluxes uncertainties
The end.