Binarity as the tool for Binarity as the tool for determining physical determining physical

properties and evolutionary properties and evolutionary aspects of aspects of

A-starsA-stars

Mutlu YıldızMutlu Yıldız

Ege University, Dept. of Astronomy and Space Sciences, TurkeyEge University, Dept. of Astronomy and Space Sciences, Turkey

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

The physical conditions The physical conditions in the central regions of in the central regions of stars are primarily stars are primarily determined by total determined by total mass of the overlying mass of the overlying layers and its layers and its distribution.distribution.

These physical These physical conditions give the conditions give the luminosity.luminosity.

Radius depends on Radius depends on radiation field + radiation field +

matter-matter and matter-matter and matter-radiation matter-radiation

interactions in the interactions in the outer regions.outer regions.

The secondary effects:The secondary effects:

In general, the observableIn general, the observabless (L, T (L, Teffeff or R) of a or R) of a model is a function of many parameters:model is a function of many parameters:

Q=QQ=Q (M,(M, cc,cc, w,w, t,t, H,H, ...)...)

For the model computations we need to know For the model computations we need to know mass, chemical composition and mass, chemical composition and

-the mixing-length parameter for the late -the mixing-length parameter for the late type starstype 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 overshootingas the overshooting

Binaries as the tools for Binaries as the tools for measurement of stellar measurement of stellar massesmasses 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, stellar mass and radius (Andersen 1991,

Harmenec 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 -the lunar occultation for data of individual

starsstars

Models for the Models for the components of DLEB 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 -3 different grids (Geneva, Padova and

Granada).Granada).

Yıldız (2003, 2004)Yıldız (2003, 2004) -rapidly rotating interior-rapidly rotating interior

The overshooting The overshooting

paradigmparadigm??

------------------ M------------------ Movov,R,Rovov=? =?

^̂ || | | ααovov=0.2-0.6 =0.2-0.6

HHPP

||

|| -------- O-------- M-------- O-------- Mconvconv,R,Rconvconv

Easy to apply:Easy to apply: - - ααovov=0.2-0.6 H=0.2-0.6 HPP

It makes the It makes the

chemical composition chemical composition homogeneous also in homogeneous also in the overshooting the overshooting regionregion

outside the outside the convective core.convective core.

Models of V380 Cyg with Models of V380 Cyg with overshooting (Guinan et overshooting (Guinan et al.al.20002000))

X=0.722?X=0.722?

There are manyThere are many

possibilities for possibilities for

X-Z X-Z combinations.combinations.

For PV Cas For PV Cas ααovov=0.25 => =0.25 =>

MMovov= 1.48 M= 1.48 Mconvconv

RRovov= 1.16 R= 1.16 Rconvconv

The degeneracy in The degeneracy in the HR diagram: the HR diagram:

* For single stars * For single stars Simplifying assumption: w=H=0Simplifying assumption: w=H=0 For a given mass: LFor a given mass: L (X,(X, Z,Z, t) & Rt) & R (X,(X, Z,Z, t) t) Consider the typical values for the numerical Consider the typical values for the numerical

derivatives L and R (for derivatives L and R (for 342): 342): q dLog L/dlog q dLog R/dlog qq dLog L/dlog q dLog R/dlog q X -4 -0.6-... lX -4 -0.6-... lx/x/llzz ~ 5, ~ 5,

rrxx/r/rzz ~ 4 ~ 4 Z -0.8 -0.15-...Z -0.8 -0.15-... t 0.1 0.07t 0.1 0.07

LL (X(X11,, ZZ11,, tt11) =) = LL (X(X22,, ZZ22,, tt22)) RR (X(X11,, ZZ11,, tt11)) == RR (X(X22,, ZZ22,, tt22))

The degeneracy in The degeneracy in the HR diagram: the HR diagram:

* For binaries * For binaries

we have 4 equations (2x2), but, if the derivatives we have 4 equations (2x2), but, if the derivatives for the components are similar these 4 equations for the components are similar these 4 equations are not then independent. are not then independent.

So, the degeneracy is not removed. So, the degeneracy is not removed. Therefore, very special binaries should be selected Therefore, very special binaries should be selected

to to study:study: - dissimilar components (one early & one late type - dissimilar components (one early & one late type

star)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.

The selected binaries: The selected binaries:

EK Cep: MEK Cep: M11=2.02 M=2.02 M22=1.12 =1.12 (The secondary is a PMS)(The secondary is a PMS)

PV Cas: MPV Cas: M11=2.82 M=2.82 M22=2.76 =2.76 (short apsidal motion (short apsidal motion

period; 91 period; 91 years)years)

θ ² Tau and θ ² Tau and 342 342 (members of the Hyades (members of the Hyades

cluster)cluster) θ ² Tau : Mθ ² Tau : M11=2.42 M=2.42 M22=2.11 =2.11

342 : M342 : M11=1.36 M=1.36 M22=1.25 =1.25 in units of Min units of Msun. sun.

((Andersen 1991,Torres et al. 1997a, 1997b)Andersen 1991,Torres et al. 1997a, 1997b)

Rotation of the earlyRotation of the early - - type starstype 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 Their inner regions should rotate much faster

than their surface regions. 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 In binary systems, as time goes on, their

rotation period becomes the same as the rotation period becomes the same as the orbital period due to tidal interaction.orbital period due to tidal interaction.

Zahn’s theory of Zahn’s theory of synchronization synchronization (Zahn 1977; Goldreich and Nicholson (Zahn 1977; Goldreich and Nicholson 1989)1989)

* Due to tidal * Due to tidal interaction, gravity interaction, gravity waves are excited at waves are excited at the surface of the surface of convective core.convective core.

* They carry negative * They carry negative angular momentumangular momentum

and propagate in and propagate in the radiative the radiative regions.regions.

* Tidal despinning to * Tidal despinning to synchronous rotation synchronous rotation proceeds from proceeds from outside to inside.outside to inside.

EK Cep ‘s LA/LB (Yıldız EK Cep ‘s LA/LB (Yıldız 2003)2003)

* The observed * The observed ratio of the ratio of the luminosities is luminosities is less than the less than the minimum value minimum value computed from computed from the models.the models.

• The components The components are rotating are rotating (pseudo-) (pseudo-) synchronously synchronously

(V(Veqeq(A)~23km/s)(A)~23km/s)

EK Cep (RA/RB)EK Cep (RA/RB)

This is the case This is the case also for the ratio also for the ratio of the radii. of the radii.

But, mixing-But, mixing-length parameter length parameter for the secondary for the secondary star may have star may have some effect on some effect on this result.this result.

Solution for EK Cep Solution for EK Cep (Yıldız 2003) (Yıldız 2003)

*The system should be very young.*The system should be very young.

*Metal rich composition: Z ~ 0.04*Metal rich composition: Z ~ 0.04 EK Cep A is a ZAMS star and its EK Cep A is a ZAMS star and its

central regions rotate very rapidly.central regions rotate very rapidly.

*How fast? *How fast? It depends on the chemical It depends on the chemical

composition and the mass of the composition and the mass of the synchronized outer mass.synchronized outer mass.

EK Cep EK Cep

* Assumption:* Assumption: LLAA(obs)= L(obs)= LAA(Min) & L(Min) & LBB(obs)= L(obs)= LBB(Max) (Max)

X=0.614, Z=0.04 ==> X=0.614, Z=0.04 ==> (core) = 65 X (core) = 65 X (surface)(surface)

& & half of the total half of the total

(outer) mass(outer) mass is synchronizedis synchronized

* The observed apsidal motion period is in * The observed apsidal motion period is in agreement with AMP found from the models with agreement with AMP found from the models with metal rich composition, metal rich composition,

but, AMP is not very sensitive to the models of but, AMP is not very sensitive to the models of the primary star (U=4400 years).the primary star (U=4400 years).

The apsidal MotionThe apsidal Motion

The second stellar harmonicThe second stellar harmonic

As a measure of mass distribution in the outer As a measure of mass distribution in the outer regions.regions.

Any effect which decreases the density of outer Any effect which decreases the density of outer regions will increase regions will increase kk22 and also the radius. and also the radius.

PV CasPV Cas

* * FundamentalFundamental

properties of theproperties of the

system system (Barembaum(Barembaum

& Etzel, 1995)& Etzel, 1995)

* U= 91 yıl.* U= 91 yıl.

* Ap like variation in * Ap like variation in its its

light curve.light curve.

* V* Vequ equ =65 km/s=65 km/s

PV Cas: for fitting luminosity and PV Cas: for fitting luminosity and radius of model to the radius of model to the observationsobservations

(S1) (S1) t= 10 My => t= 10 My =>

X=0.62, X=0.62, Z=0.063Z=0.063

(S2)(S2) t=100 My => t=100 My =>

X=0.66, X=0.66, Z=0.043Z=0.043

(S3)(S3) t=200 My => t=200 My =>

X=0.754, X=0.754, Z=0.026Z=0.026

PV PV Cas: overshooting Cas: overshooting could solve the could solve the problemproblem??* In principle, no.* In principle, no.

* Because, near the ZAMS overshooting* Because, near the ZAMS overshooting (homogeneous cc) has no effect. In the (homogeneous cc) has no effect. In the

later course, it increases apsidal later course, it increases apsidal advance rateadvance rate

(Claret & Gimenez 1989;1991). (Claret & Gimenez 1989;1991).

So, the situation worsens.So, the situation worsens.

Differentially rotating models for Differentially rotating models for the the components of PV Cas A: solar cc.components of PV Cas A: solar cc.

DR as determined DR as determined

by contraction by contraction

++

Synchronized outer Synchronized outer mass (Mmass (Mss))

______________________

L(L(c,c,MMss) and ) and R(R(c,c,MMss) )

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

AAR for DR models of PV Cas: AAR for DR models of PV Cas: solar cc and metal rich cc solar cc and metal rich cc (Z=0.04)(Z=0.04)

* For the solar * For the solar cc cc

t= 140 Myt= 140 My

* For the metal * For the metal

rich cc rich cc

t= 10 My t= 10 My

Binaries of HyadesBinaries of Hyades

342: V=6.46342: V=6.46

* θ ² Tau (de Bruijne et al. 2001)* θ ² Tau (de Bruijne et al. 2001)

A BA B

MMVV 0.47±0.04 1.57±0.04 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

vveqeq 110km/s 125-235 km/s 110km/s 125-235 km/s

* Z of Hyades? Z>Zsun!* Z of Hyades? Z>Zsun!

For a given Z, X is found from the models of For a given Z, X is found from the models of 342: 342:

VV (models (models 342)= V 342)= V (obs. (obs. 342) 342)

age (t) is found from models of θ² Tau A age (t) is found from models of θ² Tau A

MMVV (models θ ² Tau A)=M(models θ ² Tau A)=MVV (obs. θ ² Tau A)(obs. θ ² Tau A)

(B-V) (models θ ² Tau A)= (B-V) (obs. θ ² (B-V) (models θ ² Tau A)= (B-V) (obs. θ ² Tau A)Tau A)

Evolutionary phase of Evolutionary phase of ² Tau A ² Tau A andandage of Hyades (Poster GP7)age of Hyades (Poster GP7)

Internal rotation of θ ² Tau A:Internal rotation of θ ² Tau A:

1)DR as determined by 1)DR as determined by contractioncontraction

a) Z=0.024: a) Z=0.024:

VV (models (models 342)= V( 342)= V( 342) 342)

X=0.718, X=0.718,

t=721 My (from t=721 My (from θ ² Tau Aθ ² Tau A))

b) Z=0.033: b) Z=0.033:

X=0.676, t=671 MyX=0.676, t=671 My

2) Solid body rotation?2) Solid body rotation?

* Model of θ ² Tau B? t=450 My * Model of θ ² Tau B? t=450 My

θ ² Tau A and B do not give θ ² Tau A and B do not give the the

same age! same age!

ResultsResults

Binarity is one of the essential tools for Binarity is one of the essential tools for determination of structure and evolution of determination of structure and evolution of stars.stars.

Binaries in clusters are peerless.Binaries in clusters are peerless. Differentially rotating models is in better Differentially rotating models is in better

agreement with the observations than the NR agreement with the observations than the NR models or models rotating like a solid body.models or models rotating like a solid body.

Does overshooting solve any problem??Does overshooting solve any problem?? Is the chemical peculiarity associated with Is the chemical peculiarity associated with

internal rotation? (Arlt et al. 2003) internal rotation? (Arlt et al. 2003)