1. Binarity as the tool for determining physical properties and evolutionary aspects of A-stars Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey

2. Life, death and heritage of a star depend mostly on its mass The physical conditions in the central regions of stars are primarily determined by total mass of the overlying layers and its distribution. The physical conditions in the central regions of stars are primarily determined by total mass of the overlying layers and its distribution. These physical conditions give the luminosity. These physical conditions give the luminosity. Radius depends on radiation field + Radius depends on radiation field + matter-matter and matter-matter and matter-radiation interactions in the matter-radiation interactions in the outer regions. outer regions.

3. The secondary effects: The secondary effects: In general, the observables (L, T eff or R) of a model is a function of many parameters: In general, the observables (L, T eff or R) of a model is a function of many parameters: Q=Q (M, cc, w, t, H,...) Q=Q (M, cc, w, t, H,...) For the model computations we need to know mass, chemical composition and For the model computations we need to know mass, chemical composition and -the mixing-length parameter for the late -the mixing-length parameter for the late type stars type stars -rotational properties and parameters for -rotational properties and parameters for other processes supposed to occur such other processes supposed to occur such as the overshooting as the overshooting

4. Binaries as the tools for measurement of stellar masses Double-lined eclipsing binaries: Double-lined eclipsing binaries: -M, R and L of more than 100 stars -M, R and L of more than 100 stars -the most accurate data 1-2 % for -the most accurate data 1-2 % for stellar mass and radius (Andersen 1991, Harmenec stellar mass and radius (Andersen 1991, Harmenec 1988, Popper 1980) 1988, Popper 1980) -plenty of these systems have apsidal -plenty of these systems have apsidal motion (Claret and Gimenez 1993) motion (Claret and Gimenez 1993) Visual binaries: Visual binaries: -M, total V and (B-V) of the -M, total V and (B-V) of the systems. systems. -the lunar occultation for data of individual stars -the lunar occultation for data of individual stars

5. Models for the components of DLEB Models for the components of DLEB Claret & Gimenez (1993,...) Claret & Gimenez (1993,...) - overshooting and mass loss - overshooting and mass loss Pols et al. (1997) Pols et al. (1997) - effects of enhanced mixing and overshooting - effects of enhanced mixing and overshooting Young et al. (2001) Young et al. (2001) Lastennet & Valls-Gabaud (2002) Lastennet & Valls-Gabaud (2002) -3 different grids (Geneva, Padova and Granada). -3 different grids (Geneva, Padova and Granada). Yıldız (2003, 2004) Yıldız (2003, 2004) -rapidly rotating interior -rapidly rotating interior

6. The overshooting paradigm ? ------------------ M ov,R ov =? ------------------ M ov,R ov =? ^ | | α ov =0.2-0.6 H P | α ov =0.2-0.6 H P | | -------- O-------- M conv,R conv -------- O-------- M conv,R conv Easy to apply: Easy to apply: - α ov =0.2-0.6 H P - α ov =0.2-0.6 H P It makes the chemical composition homogeneous also in the overshooting region It makes the chemical composition homogeneous also in the overshooting region outside the convective core. outside the convective core.

7. Models of V380 Cyg with overshooting (Guinan et al. 2000 ) X=0.722? X=0.722? There are many There are many possibilities for possibilities for X-Z combinations. X-Z combinations. For PV Cas For PV Cas α ov =0.25 => α ov =0.25 => M ov = 1.48 M conv M ov = 1.48 M conv R ov = 1.16 R conv R ov = 1.16 R conv

8. The degeneracy in the HR diagram: * For single stars Simplifying assumption: w=H=0 Simplifying assumption: w=H=0 For a given mass: L (X, Z, t) & R (X, Z, t) For a given mass: L (X, Z, t) & R (X, Z, t) Consider the typical values for the numerical derivatives L and R (for  342): Consider the typical values for the numerical derivatives L and R (for  342): q dLog L/dlog q dLog R/dlog q q dLog L/dlog q dLog R/dlog q X -4 -0.6-... l x/ l z ~ 5, r x /r z ~ 4 X -4 -0.6-... l x/ l z ~ 5, r x /r z ~ 4 Z -0.8 -0.15-... Z -0.8 -0.15-... t 0.1 0.07 t 0.1 0.07 L (X 1, Z 1, t 1 ) = L (X 2, Z 2, t 2 ) L (X 1, Z 1, t 1 ) = L (X 2, Z 2, t 2 ) R (X 1, Z 1, t 1 ) = R (X 2, Z 2, t 2 ) R (X 1, Z 1, t 1 ) = R (X 2, Z 2, t 2 )

9. The degeneracy in the HR diagram: * For binaries we have 4 equations (2x2), but, if the derivatives for the components are similar these 4 equations are not then independent. we have 4 equations (2x2), but, if the derivatives for the components are similar these 4 equations are not then independent. So, the degeneracy is not removed. So, the degeneracy is not removed. Therefore, very special binaries should be selected to Therefore, very special binaries should be selected to study: study: - dissimilar components (one early & one late type star) - dissimilar components (one early & one late type star) - apsidal motion with short period - apsidal motion with short period - binaries which are members of the same cluster. - binaries which are members of the same cluster.

10. The selected binaries: EK Cep: M 1 =2.02 M 2 =1.12 (The secondary is a PMS) EK Cep: M 1 =2.02 M 2 =1.12 (The secondary is a PMS) PV Cas: M 1 =2.82 M 2 =2.76 (short apsidal motion PV Cas: M 1 =2.82 M 2 =2.76 (short apsidal motion period; 91 years) period; 91 years) θ ² Tau and  342 (members of the Hyades θ ² Tau and  342 (members of the Hyades cluster) cluster) θ ² Tau : M 1 =2.42 M 2 =2.11 θ ² Tau : M 1 =2.42 M 2 =2.11  342 : M 1 =1.36 M 2 =1.25  342 : M 1 =1.36 M 2 =1.25 in units of M sun. in units of M sun. ( Andersen 1991,Torres et al. 1997a, 1997b) ( Andersen 1991,Torres et al. 1997a, 1997b)

11. Rotation of the early - type stars They rotate rapidly as a result of contraction. They rotate rapidly as a result of contraction. - angular momentum transportation is not - angular momentum transportation is not a sudden process. a sudden process. Their inner regions should rotate much faster than their surface regions. Their inner regions should rotate much faster than their surface regions. -the inner regions contract much more -the inner regions contract much more than the surface regions. than the surface regions. In binary systems, as time goes on, their rotation period becomes the same as the orbital period due to tidal interaction. In binary systems, as time goes on, their rotation period becomes the same as the orbital period due to tidal interaction.

12. Zahn’s theory of synchronization (Zahn 1977; Goldreich and Nicholson 1989) * Due to tidal interaction, gravity waves are excited at the surface of convective core. * They carry negative angular momentum and propagate in the radiative regions. and propagate in the radiative regions. * Tidal despinning to synchronous rotation proceeds from outside to inside.

13. EK Cep ‘s LA/LB (Yıldız 2003) * The observed ratio of the luminosities is less than the minimum value computed from the models. The components are rotating (pseudo-) synchronously The components are rotating (pseudo-) synchronously (V eq (A)~23km/s) (V eq (A)~23km/s)

14. EK Cep (RA/RB) EK Cep (RA/RB) This is the case also for the ratio of the radii. This is the case also for the ratio of the radii. But, mixing-length parameter for the secondary star may have some effect on this result. But, mixing-length parameter for the secondary star may have some effect on this result.

15. Solution for EK Cep (Yıldız 2003) *The system should be very young. *Metal rich composition: Z ~ 0.04 EK Cep A is a ZAMS star and its central regions rotate very rapidly. EK Cep A is a ZAMS star and its central regions rotate very rapidly. *How fast? It depends on the chemical composition and the mass of the synchronized outer mass. It depends on the chemical composition and the mass of the synchronized outer mass.

16. EK Cep * Assumption: L A (obs)= L A (Min) & L B (obs)= L B (Max) L A (obs)= L A (Min) & L B (obs)= L B (Max) X=0.614, Z=0.04 ==>  (core) = 65 X  (surface) X=0.614, Z=0.04 ==>  (core) = 65 X  (surface) & half of the total (outer) mass half of the total (outer) mass is synchronized is synchronized * The observed apsidal motion period is in agreement with AMP found from the models with metal rich composition, but, AMP is not very sensitive to the models of the primary star (U=4400 years). but, AMP is not very sensitive to the models of the primary star (U=4400 years).

17. The apsidal Motion The second stellar harmonic The second stellar harmonic As a measure of mass distribution in the outer regions. As a measure of mass distribution in the outer regions. Any effect which decreases the density of outer regions will increase k 2 and also the radius. Any effect which decreases the density of outer regions will increase k 2 and also the radius.

18. PV Cas * Fundamental properties of the properties of the system (Barembaum system (Barembaum & Etzel, 1995) & Etzel, 1995) * U= 91 yıl. * Ap like variation in its light curve. light curve. * V equ =65 km/s

19. PV Cas: for fitting luminosity and radius of model to the observations (S1) t= 10 My => X=0.62, Z=0.063 X=0.62, Z=0.063 (S2) t=100 My => X=0.66, Z=0.043 X=0.66, Z=0.043 (S3) t=200 My => X=0.754, Z=0.026 X=0.754, Z=0.026

20. PV Cas: overshooting could solve the problem? * In principle, no. * Because, near the ZAMS overshooting (homogeneous cc) has no effect. In the later course, it increases apsidal advance rate (homogeneous cc) has no effect. In the later course, it increases apsidal advance rate (Claret & Gimenez 1989;1991). (Claret & Gimenez 1989;1991). So, the situation worsens. So, the situation worsens.

21. Differentially rotating models for the components of PV Cas A: solar cc. DR as determined by contraction + Synchronized outer mass (M s ) ___________ ___________ L(  c, M s ) and R(  c, M s ) L(  c, M s ) and R(  c, M s )

22. Rotation rate throughout the DR models of PV Cas A: solar cc.

23. AAR for DR models of PV Cas: solar cc and metal rich cc (Z=0.04) * For the solar cc t= 140 My t= 140 My * For the metal rich cc rich cc t= 10 My t= 10 My

24. Binaries of Hyades  342: V=6.46  342: V=6.46 * θ ² Tau (de Bruijne et al. 2001) A B A B M V 0.47±0.04 1.57±0.04 M V 0.47±0.04 1.57±0.04 B-V 0.17±0.01 0.16±0.01 B-V 0.17±0.01 0.16±0.01 v eq 110km/s 125-235 km/s v eq 110km/s 125-235 km/s * Z of Hyades? Z>Zsun! For a given Z, X is found from the models of  342: For a given Z, X is found from the models of  342: V (models  342)= V (obs.  342) V (models  342)= V (obs.  342) age (t) is found from models of θ² Tau A age (t) is found from models of θ² Tau A M V (models θ ² Tau A)=M V (obs. θ ² Tau A) M V (models θ ² Tau A)=M V (obs. θ ² Tau A) (B-V) (models θ ² Tau A)= (B-V) (obs. θ ² Tau A) (B-V) (models θ ² Tau A)= (B-V) (obs. θ ² Tau A)

25. Evolutionary phase of  ² Tau A and age of Hyades (Poster GP7) Internal rotation of θ ² Tau A: 1)DR as determined by contraction a) Z=0.024: V (models  342)= V(  342) V (models  342)= V(  342) X=0.718, X=0.718, t=721 My (from θ ² Tau A) t=721 My (from θ ² Tau A) b) Z=0.033: X=0.676, t=671 My X=0.676, t=671 My 2) Solid body rotation? * Model of θ ² Tau B? t=450 My θ ² Tau A and B do not give the θ ² Tau A and B do not give the same age! same age!

26. Results Binarity is one of the essential tools for determination of structure and evolution of stars. Binarity is one of the essential tools for determination of structure and evolution of stars. Binaries in clusters are peerless. Binaries in clusters are peerless. Differentially rotating models is in better agreement with the observations than the NR models or models rotating like a solid body. Differentially rotating models is in better agreement with the observations than the NR models or models rotating like a solid body. Does overshooting solve any problem?? Does overshooting solve any problem?? Is the chemical peculiarity associated with internal rotation? (Arlt et al. 2003) Is the chemical peculiarity associated with internal rotation? (Arlt et al. 2003)