Fernando Jorge Gutiérrez Pinheiro - ESO
Transcript of Fernando Jorge Gutiérrez Pinheiro - ESO
Modeling sub-giant stars
Fernando Jorge Gutiérrez PinheiroCentro de Astrofísica da Universidade do Porto
ESO Visiting Scientist
ESO (Santiago), 9th of April of 2008
In collaboration with: J. Fernandes (FCTUC, CFCUC)
Stellar structure & evolution - Why?
Stellar structure & evolution - Why?
Planetary formation, evolution & origin of life ISM: Metal enrichment History and evol. of stellar clusters and galaxies Cosmology Get global properties of stars
e.g.: age determination of sub-giant stars
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Sub-giant stars
shell H burn.
(Kippenhahn & Weigert, 1965, Z Ast., 61,241)(Thomas, 1967, Z Ast., 67, 420)
Sub-giant stars & age determination
position @ HRD + stellar evolutionay model => stellar age
Note: sub-giant evol. is “faster” than MS evol. => better age indicator
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Stellar Structure Equations
Mass conserv.
Hydrostatic eq.
Energy conserv.
Energy transp.
Chem. el. abundance Kippenhan & Weigert, 1991, Stellar Structure & Evolution
Making stellar models
Stellar Evol. Code:
CESAM (Morel, 1997, A&AS, 124, 597)
ATON (Ventura et al.2007Ap&SS.tmp..420V)
CLES (Scuflare et al., 2007, ASS)
...
CESAM's input physics & parameters
E.o.S. OPAL (Rogers et al., 1996, ApJ 456, 902) Opacities OPAL (Iglesias & Rogers 1994, ApJ, 464, 943 +
Alexander & Ferguson, 1994, ApJ 437, 879) Nucl. Reac. NACRE (Angulo et al., 1999, Nuc. Physics A 656, 3) Atmosphere gray Mixture Grevesse & Noels (1993) Diffusion ------ Rotation ------ Convection MLT (Bohn-Vitense, 1958, Z. Ast. 46, 108)
d = α Hp ; (Hp= -dr/dlogP) Overshooting dov = αov Hp
Mass Age Yo Zo (or [Z/X]o)
Making stellar models
Making stellar modelsCESAM's output :
M, age, L, Teff ( or R or log(g) )Z ( or Z/X )+ A(Fe), A(C), A(N), A(O), A(Li), A(Be), ...
Making stellar modelsCESAM's output :
M, age, L, Teff ( or R or log(g) )Z ( or Z/X )+ A(Fe), A(C), A(N), A(O), A(Li), A(Be), ...
Pulsation Code:ADIPLS (Christensen-Dalsgaard, arXiv:0710.3106) MAD (Dupret, 2001, A&A, 366, 166) ...
Frequencies: ν i
Frequency separations: ∆ν, δν
Making stellar modelsCESAM's output :
M, age, L, Teff ( or R or log(g) )Z ( or Z/X )+ A(Fe), A(C), A(N), A(O), A(Li), A(Be), ...
Testing stellar models: Compare model's M, L, Teff, Z ... with observations
Pulsation Code:ADIPLS (Christensen-Dalsgaard, arXiv:0710.3106) MAD (Dupret, 2001, A&A, 366, 166) ...
Frequencies: ν i
Frequency separations: ∆ν, δν
Problems faced
Cold/dense stars (molecular opacities, non ideal effects on E.o.S.)
Nuclear reaction rates for advanced evolutionary stages
Convection, transport of chemical elements & angular momentum
Uncertainties in parameter determination for hot (earlier than A) & cool stars (later than K)
Chemical composition: Grevesse-Noels (1993) Vs. Asplund (2004)e.g.: Guzik, 2006, ESA-SP624, 17
Model degeneracies
β Hydri's model degeneracy
Fernandes & Monteiro, 2003, A&A, 399, 243
M – Y α + Ov. Z
model M/Mo Y α Ov Z t (Myr) R/Ro L/Lo Teff(K)S0 1,10 0,27 1,4 0,25 0,014 6820 1,899 3,540 5751S1 1,05 0,30 1,4 0,25 0,014 6414 1,878 3,529 5778S2 1,15 0,23 1,4 0,25 0,014 7125 1,883 3,477 5749Sc1 1,10 0,27 1,6 0,25 0,014Sc2 1,10 0,27 1,8 0,25 0,014 7038 1,908 3,595 5760Sd1 1,10 0,27 1,4 0,00 0,014 6553 1,878 3,520 5775Sd2 1,10 0,27 1,4 0,15 0,014S5 1,07 0,27 1,4 0,25 0,012 6926 1,830 3,443 5818
β Hydri's model degeneracy
Fernandes & Monteiro, 2003, A&A, 399, 243
M – Y α + Ov. Z
model M/Mo Y α Ov Z t (Myr) R/Ro L/Lo Teff(K)S0 1,10 0,27 1,4 0,25 0,014 6820 1,899 3,540 5751S1 1,05 0,30 1,4 0,25 0,014 6414 1,878 3,529 5778S2 1,15 0,23 1,4 0,25 0,014 7125 1,883 3,477 5749Sc1 1,10 0,27 1,6 0,25 0,014Sc2 1,10 0,27 1,8 0,25 0,014 7038 1,908 3,595 5760Sd1 1,10 0,27 1,4 0,00 0,014 6553 1,878 3,520 5775Sd2 1,10 0,27 1,4 0,15 0,014S5 1,07 0,27 1,4 0,25 0,012 6926 1,830 3,443 5818
Does it happens for other masses?
M – Y degeneracy
Z = 0.02α = 1.6Ov = 0.0
M – Y degeneracy
Z = 0.02α = 1.6Ov = 0.0
α degeneracy
Y = 0.28Z = 0.02Ov = 0.0
α degeneracy
Y = 0.28Z = 0.02Ov = 0.0
α degeneracy
Y = 0.28Z = 0.02Ov = 0.0
Core overshooting degeneracy
Y = 0.28Z = 0.02α = 1.6
M - Z degeneracy
Y = 0.28α = 1.6Ov = 0.0
M - Z degeneracy
Y = 0.28α = 1.6Ov = 0.0
M - Z degeneracy
Y = 0.28α = 1.6Ov = 0.0
∴ Several combinations of the parameters can reproduce the position of a sub-giant star @ HRD
e.g.: log(Teff) = 3.75 log(L/L) = 0.61
M/Mo Y α Ov. Z t (Myr) log(T) log(L)1,100 0,28 1,9 0,25 0,01 5787 3,754 0,6131,200 0,28 1,3 0,00 0,02 5620 3,755 0,6061,200 0,28 1,3 0,25 0,02 5674 3,755 0,6111,200 0,28 1,6 0,00 0,02 5850 3,754 0,6211,200 0,28 1,6 0,25 0,02 5769 3,754 0,6121,200 0,28 1,9 0,00 0,02 6003 3,756 0,6091,200 0,28 1,9 0,25 0,02 5817 3,756 0,5991,300 0,28 1,3 0,25 0,02 4090 3,755 0,6031,300 0,28 1,3 0,00 0,03 4897 3,755 0,6091,185 0,29 1,6 0,25 0,02 5660 3,753 0,6131,215 0,27 1,6 0,25 0,02 5855 3,753 0,609
How to select the right set of parameters?
∴ Several combinations of the parameters can reproduce the position of a sub-giant star @ HRD
e.g.: log(Teff) = 3.75 log(L/L) = 0.61
M/Mo Y α Ov. Z t (Myr) log(T) log(L)1,100 0,28 1,9 0,25 0,01 5787 3,754 0,6131,200 0,28 1,3 0,00 0,02 5620 3,755 0,6061,200 0,28 1,3 0,25 0,02 5674 3,755 0,6111,200 0,28 1,6 0,00 0,02 5850 3,754 0,6211,200 0,28 1,6 0,25 0,02 5769 3,754 0,6121,200 0,28 1,9 0,00 0,02 6003 3,756 0,6091,200 0,28 1,9 0,25 0,02 5817 3,756 0,5991,300 0,28 1,3 0,25 0,02 4090 3,755 0,6031,300 0,28 1,3 0,00 0,03 4897 3,755 0,6091,185 0,29 1,6 0,25 0,02 5660 3,753 0,6131,215 0,27 1,6 0,25 0,02 5855 3,753 0,609
Can we probe interiors?
Can we probe interiors?
Seismology
Ultrasounds
Do stars oscillate?
Do stars oscillate?Oscillations are seen as: Spectral line variations Luminosity variations
http://www.konkoly.hu/staff/kollath/gallery.html
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Do stars oscillate?Which ones?
Low mass sub-giant stars
© J. Christensen-Dalsgaard
Do Stars Oscillate?
Driving mechanisms: κ mechanism convection (stochastic excitation)
Type of pulsations p modes – restoring force: pressure g modes – restoring force: gravity
(depend on location and frequency)
Which ones? Why?
Low mass sub-giant stars
© J. Christensen-Dalsgaard
General properties of pulsations
Described by spherical harmonics:l - degree m - azimuthal order
l=0, m=0 l=1, m=0 l=1, m=1
l=2, m=0 l=2, m=1 l=1, m=2
l=3, m=0 l=3, m=2 l=3, m=3
General properties of pulsations
Described by spherical harmonics:l - degree m - azimuthal order
(oscillations with different degrees probe different layers)
l=0, m=0 l=1, m=0 l=1, m=1
l=2, m=0 l=2, m=1 l=1, m=2
l=3, m=0 l=3, m=2 l=3, m=3
General properties of pulsations
n – radial degree ( overtone )
n=0 n=1 n=2
General properties of pulsations
n – radial degree ( overtone )
n=0 n=1 n=2
Oscillation described by:l ; m ; n
General properties of pulsations
n – radial degree ( overtone )
n=0 n=1 n=2
Oscillation described by:l ; m ; nX
not important for non-rotating stars
Solar-type oscillations
displayed by solar-type (e.g. Sun) and sub-giants (e.g. β Hyd) p-modes stochastically driven by outer convective layers amplitude: ∆L/L ~5 ppm & vosc ~ 20 cm/s high overtone: nMax. Ampl. ~ 22
α Cen A (Bouchy, Carrier, 2002, A&A, 390, 205)
Asymptotic regime
For p modes with n >> l :
νn,l = ∆ν ( n + l /2 + α ) + εn,l
(Tassoul, 1980, ApJSS, 43,469)
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Asymptotic regime
For p modes with n >> l :
νn,l = ∆ν ( n + l /2 + α ) + εn,l
Large frequency separation
(Tassoul, 1980, ApJSS, 43,469)
© G
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Asymptotic regime
For p modes with n >> l :
νn,l = ∆ν ( n + l /2 + α ) + εn,l
Large frequency separation
Small frequency separation
(Tassoul, 1980, ApJSS, 43,469)
rr
rCsr
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lni
lnlnlnln
∂∂
∂×∆=×∆∝−= ∫+−0,,
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ννννδ ν
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Asteroseismic test of stellar models
M/Mo Y α Ov. Z r_i t (Myr) log(T) log(L) R/Ro log(g)1,100 0,28 1,9 0,25 0,01 50,34 146,31 19,49 5787 3,754 0,613 2,10 3,831,200 0,28 1,3 0,00 0,02 53,44 145,82 1,11 5620 3,755 0,606 2,08 3,881,200 0,28 1,3 0,25 0,02 52,86 145,55 2,45 5674 3,755 0,611 2,09 3,881,200 0,28 1,6 0,00 0,02 51,98 146,66 3,79 5850 3,754 0,621 2,12 3,861,200 0,28 1,6 0,25 0,02 52,85 146,28 4,94 5769 3,754 0,612 2,09 3,871,200 0,28 1,9 0,00 0,02 53,81 146,15 7,52 6003 3,756 0,609 2,07 3,891,200 0,28 1,9 0,25 0,02 54,82 146,10 9,37 5817 3,756 0,599 2,04 3,901,300 0,28 1,3 0,25 0,02 55,39 144,41 2,37 4090 3,755 0,603 2,07 3,921,300 0,28 1,3 0,00 0,03 55,10 144,47 0,36 4897 3,755 0,609 2,08 3,921,185 0,29 1,6 0,25 0,02 52,06 146,34 5,52 5660 3,753 0,613 2,11 3,861,215 0,27 1,6 0,25 0,02 53,10 146,26 4,57 5855 3,753 0,609 2,10 3,88
∆ν µΗz ∆ν/ρ .5
small differences in ∆ν/ρ^.5 =>=> ∆ν is a good indicator of ρ
error bars: assume a 2% uncertainty in ∆ν and a 5% uncertainty in ri
Which region of the HRD should be analysed?
Beware of avoided crossings!!!
Overlap between MS and SubG *s!
Suran et al. (2001, A&A, 372, 233)
Conclusions
Sub-giant stars can be used as age indicators
In the range of parameters analyzed: 0.9M<M<1.3M; 0.28<Y<0.29; 0.01<Z<0.01; 1.3<α<1.9 & 0.0 <Ov.<0.25 we find several model degeneracies
In theory, asteroseismology could break this degeneracy
As stars move along the sub-giant branch=> start presenting avoided crossings (non-radial frequencies are shifted)
Thanks for your attention!!!