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

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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)

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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)

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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!!!