Modeling sub-giant stars. Fernando Jorge Gutiérrez Pinheiro Centro de Astrofísica da Universidade do Porto ESO Visiting Scientist

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1 Modeling sub-giant stars Fernando Jorge Gutiérrez Pinheiro Centro de Astrofísica da Universidade do Porto ESO Visiting Scientist ESO (Santiago), 9th of April of 2008

2 In collaboration with: J. Fernandes (FCTUC, CFCUC)

3 Stellar structure & evolution - Why?

4 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 IC 433 Cariulo 2004, AA 421, 1121 Stellar structure & evolution - Why?

5 Sub-giant stars shell H burn. (Thomas, 1967, Z Ast., 67, 420) (Kippenhahn & Weigert, 1965, Z Ast., 61,241)

6 Sub-giant stars & age determination HRD + stellar evolutionay model => stellar age Note: sub-giant evol. is faster than MS evol. => better age indicator

7 Making stellar models Stellar Structure Equations Mass conserv. M = 4π R 2 ρ R Hydrostatic eq. P GM Ω2 = + M 4π R 4 6π R Energy conserv. L = ε M Nucl. Stellar Evol. Code: q t CESAM (Morel, 1997, A&AS, 124, 597) Energy transp. Chem. el. abundance T P T = M M P nchem. El : ln T ; = ln P χ i = Dif i + Nuci t Kippenhan & Weigert, 1991, Stellar Structure & Evolution ATON (Ventura et al.2007ap&ss.tmp..420v) CLES (Scuflare et al., 2007, ASS)...

8 Making stellar models CESAM's input physics & parameters E.o.S. Opacities OPAL OPAL Nucl. Reac. Atmosphere Mixture Diff usion Rotation Convection NACRE gray Grevesse & Noels (1993) MLT (Bohn-Vitense, 1958, Z. Ast. 46, 108) Overshooting d = α Hp dov = αov Hp Mass Age Yo Zo (or [Z/X]o) (Rogers et al., 1996, ApJ 456, 902) (Iglesias & Rogers 1994, ApJ, 464, Alexander & Ferguson, 1994, ApJ 437, 879) (Angulo et al., 1999, Nuc. Physics A 656, 3) ; (Hp= -dr/dlogp)

9 Making stellar models CESAM'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),...

10 Making stellar models CESAM's output : Pulsation Code: ADIPLS (Christensen-Dalsgaard, arxiv: ) MAD (Dupret, 2001, A&A, 366, 166)... 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),... Frequencies: ν i Frequency separations: ν, δν

11 Making stellar models CESAM's output : Pulsation Code: ADIPLS (Christensen-Dalsgaard, arxiv: ) MAD (Dupret, 2001, A&A, 366, 166)... 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),... Frequencies: ν i Frequency separations: ν, δν Testing stellar models: Compare model's M, L, Teff, Z... with observations

12 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

13 β Hydri's model degeneracy Fernandes & Monteiro, 2003, A&A, 399, 243 M Y α + Ov. model S0 S1 S2 Sc1 Sc2 Sd1 Sd2 S5 M/Mo 1,10 1,05 1,15 1,10 1,10 1,10 1,10 1,07 α 1,4 1,4 1,4 1,6 1,8 1,4 1,4 1,4 Y 0,27 0,30 0,23 0,27 0,27 0,27 0,27 0,27 Z Ov 0,00 0,15 Z 0,014 0,014 0,014 0,014 0,014 0,014 0,014 0,012 t (Myr)

14 β Hydri's model degeneracy Fernandes & Monteiro, 2003, A&A, 399, 243 M Y α + Ov. model S0 S1 S2 Sc1 Sc2 Sd1 Sd2 S5 M/Mo 1,10 1,05 1,15 1,10 1,10 1,10 1,10 1,07 α 1,4 1,4 1,4 1,6 1,8 1,4 1,4 1,4 Y 0,27 0,30 0,23 0,27 0,27 0,27 0,27 0,27 Ov 0,00 0,15 Z 0,014 0,014 0,014 0,014 0,014 0,014 0,014 0,012 t (Myr) Z Does it happens for other masses?

15 M Y degeneracy Z = 0.02 α = 1.6 Ov = 0.0

16 M Y degeneracy Z = 0.02 α = 1.6 Ov = 0.0

17 α degeneracy Y = 0.28 Z = 0.02 Ov = 0.0

18 α degeneracy Y = 0.28 Z = 0.02 Ov = 0.0

19 α degeneracy Y = 0.28 Z = 0.02 Ov = 0.0

20 Core overshooting degeneracy Y = 0.28 Z = 0.02 α = 1.6

21 M - Z degeneracy Y = 0.28 α = 1.6 Ov = 0.0

22 M - Z degeneracy Y = 0.28 α = 1.6 Ov = 0.0

23 M - Z degeneracy Y = 0.28 α = 1.6 Ov = 0.0

24 Several combinations of the parameters can reproduce the position of a sub-giant HRD e.g.: log(teff) = 3.75 log(l/l ) = 0.61 M/Mo 1,100 1,200 1,200 1,200 1,200 1,200 1,200 1,300 1,300 1,185 1,215 Y 0,29 0,27 α 1,9 1,3 1,3 1,6 1,6 1,9 1,9 1,3 1,3 1,6 1,6 Ov. 0,00 0,00 0,00 0,00 Z 0,01 0,03 t (Myr) log(t) 3,754 3,755 3,755 3,754 3,754 3,756 3,756 3,755 3,755 3,753 3,753 log(l) 0,613 0,606 0,611 0,621 0,612 0,609 0,599 0,603 0,609 0,613 0,609

25 Several combinations of the parameters can reproduce the position of a sub-giant HRD e.g.: log(teff) = 3.75 log(l/l ) = 0.61 M/Mo 1,100 1,200 1,200 1,200 1,200 1,200 1,200 1,300 1,300 1,185 1,215 Y 0,29 0,27 α 1,9 1,3 1,3 1,6 1,6 1,9 1,9 1,3 1,3 1,6 1,6 Ov. 0,00 0,00 0,00 0,00 Z 0,01 0,03 t (Myr) log(t) 3,754 3,755 3,755 3,754 3,754 3,756 3,756 3,755 3,755 3,753 3,753 log(l) 0,613 0,606 0,611 0,621 0,612 0,609 0,599 0,603 0,609 0,613 0,609 How to select the right set of parameters?

26 Can we probe interiors?

27 Can we probe interiors? Seismology Ultrasounds

28 Do stars oscillate?

29 Do stars oscillate? Oscillations are seen as: Spectral line variations Luminosity variations kollath/gallery.html Ripepi et al., 2003 A&A, 408, 1047 De Pauw et al., 1993 A&A, 280, 493 V351 Ori

30 Do stars oscillate? Which ones? Low mass sub-giant stars J. Christensen-Dalsgaard

31 Do Stars Oscillate? Which ones? Why? 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) Low mass sub-giant stars J. Christensen-Dalsgaard

32 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

33 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

34 General properties of pulsations n radial degree ( overtone ) n=0 n=1 n=2

35 General properties of pulsations n radial degree ( overtone ) n=0 n=1 n=2 Oscillation described by: l;m;n

36 General properties of pulsations n radial degree ( overtone ) n=0 n=1 n=2 Oscillation described by: l;x m;n not important for non-rotating stars

37 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)

38 Asymptotic regime For p modes with n >> l : GONG νn,l = ν ( n + l /2 + α ) + εn,l (Tassoul, 1980, ApJSS, 43,469)

39 Asymptotic regime For p modes with n >> l : Large frequency separation 1 ν n, l = ν n + 1, l ν n, l ν = R r 2 0 Cs GONG νn,l = ν ( n + l /2 + α ) + εn,l (Tassoul, 1980, ApJSS, 43,469) M / R3

40 Asymptotic regime For p modes with n >> l : Large frequency separation 1 ν n, l = ν n + 1, l ν n, l ν = R r 2 0 Cs GONG νn,l = ν ( n + l /2 + α ) + εn,l δν M / R3 Small frequency separation n,l =ν n 1,l + 2 ν n,l ν ν ri = ν n,l ν n,l (Tassoul, 1980, ApJSS, 43,469) R Cs r 0 r r

41 Asteroseismic test of stellar models M/Mo 1,100 1,200 1,200 1,200 1,200 1,200 1,200 1,300 1,300 1,185 1,215 Y 0,29 0,27 α 1,9 1,3 1,3 1,6 1,6 1,9 1,9 1,3 1,3 1,6 1,6 Ov. 0,00 0,00 0,00 0,00 Z 0,01 0,03 ν µηz 50,34 53,44 52,86 51,98 52,85 53,81 54,82 55,39 55,10 52,06 53,10 ν/ρ^.5 r_i 146,31 19,49 145,82 1,11 145,55 2,45 146,66 3,79 146,28 4,94 146,15 7,52 146,10 9,37 144,41 2,37 144,47 0,36 146,34 5,52 146,26 4,57 t (Myr) log(t) 3,754 3,755 3,755 3,754 3,754 3,756 3,756 3,755 3,755 3,753 3,753 log(l) 0,613 0,606 0,611 0,621 0,612 0,609 0,599 0,603 0,609 0,613 0,609 R/Ro 2,10 2,08 2,09 2,12 2,09 2,07 2,04 2,07 2,08 2,11 2,10 log(g) 3,83 3,88 3,88 3,86 3,87 3,89 3,90 3,92 3,92 3,86 3,88 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

42 Which region of the HRD should be analysed? Beware of avoided crossings!!! Suran et al. (2001, A&A, 372, 233) Overlap between MS and SubG *s!

43 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)

44 Thanks for your attention!!!

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