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Binarity as the tool for determining physical properties and evolutionary aspects of A-stars

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. Life, death and heritage of a star depend mostly on its mass.

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Binarity as the tool for determining physical properties and evolutionary aspects of A-stars

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  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. • These physical conditions give the luminosity. • Radius depends on radiation field + matter-matter and matter-radiation interactions in the outer regions.

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

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

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

  6. The overshooting paradigm? ------------------ Mov,Rov=? ^ | | αov=0.2-0.6 HP | | -------- O-------- Mconv,Rconv • Easy to apply: - αov=0.2-0.6 HP • It makes the chemical composition homogeneous also in the overshooting region outside the convective core.

  7. Models of V380 Cyg with overshooting (Guinan et al.2000) • X=0.722? There are many possibilities for X-Z combinations. • For PV Cas αov=0.25 => Mov= 1.48 Mconv Rov= 1.16 Rconv

  8. The degeneracy in the HR diagram: * For single stars • Simplifying assumption: w=H=0 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): q dLog L/dlog q dLog R/dlog q X -4 -0.6-... lx/lz ~ 5, rx/rz ~ 4 Z -0.8 -0.15-... t 0.1 0.07 L(X1,Z1,t1) =L(X2,Z2,t2) R(X1,Z1,t1)=R(X2,Z2,t2)

  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. • So, the degeneracy is not removed. • Therefore, very special binaries should be selected to study: - dissimilar components (one early & one late type star) - apsidal motion with short period - binaries which are members of the same cluster.

  10. The selected binaries: • EK Cep: M1=2.02 M2=1.12 (The secondary is a PMS) • PV Cas: M1=2.82 M2=2.76 (short apsidal motion period; 91 years) • θ ² Tau and  342 (members of the Hyades cluster) θ ² Tau : M1=2.42 M2=2.11  342 : M1=1.36 M2=1.25 in units of Msun. (Andersen 1991,Torres et al. 1997a, 1997b)

  11. Rotation of the early- type stars • They rotate rapidly as a result of contraction. - angular momentum transportation is not a sudden process. • Their inner regions should rotate much faster than their surface regions. -the inner regions contract much more 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.

  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. * 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 (Veq(A)~23km/s)

  14. EK Cep (RA/RB) 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.

  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. *How fast? It depends on the chemical composition and the mass of the synchronized outer mass.

  16. EK Cep * Assumption: LA(obs)= LA(Min) & LB(obs)= LB(Max) X=0.614, Z=0.04 ==> (core) = 65 X (surface) & half of the total (outer) mass 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).

  17. The apsidal Motion • The second stellar harmonic • As a measure of mass distribution in the outer regions. • Any effect which decreases the density of outer regions will increase k2 and also the radius.

  18. PV Cas * Fundamental properties of the system (Barembaum & Etzel, 1995) * U= 91 yıl. * Ap like variation in its light curve. * Vequ =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 (S2) t=100 My => X=0.66, Z=0.043 (S3) t=200 My => 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 (Claret & Gimenez 1989;1991). 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 (Ms) ___________ L(c,Ms) and R(c,Ms)

  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 * For the metal rich cc t= 10 My

  24. Binaries of Hyades •  342: V=6.46 * θ ² Tau (de Bruijne et al. 2001) A B MV0.47±0.04 1.57±0.04 B-V 0.17±0.01 0.16±0.01 veq 110km/s 125-235 km/s * Z of Hyades? Z>Zsun! For a given Z, X is found from the models of  342: V(models  342)= V(obs.  342) age (t) is found from models of θ² Tau A MV(models θ ² Tau A)=MV(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 andage 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) X=0.718, t=721 My (from θ ² Tau A) b) Z=0.033: 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 same age!

  26. Results • Binarity is one of the essential tools for determination of structure and evolution of stars. • 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. • Does overshooting solve any problem?? • Is the chemical peculiarity associated with internal rotation? (Arlt et al. 2003)

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