Transcript BIL3: YILDIZ

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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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.
The secondary effects:
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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
Binaries as the tools for
measurement of stellar masses
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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
Models for the
components of DLEB
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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
The overshooting paradigm?
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Easy to apply:
- αov=0.2-0.6 HP
It makes the chemical
composition
homogeneous also in
the overshooting region
outside the convective
core.
------------------ Mov,Rov=?
^
|
| αov=0.2-0.6 HP
|
|
-------- O-------- Mconv,Rconv
Models of V380 Cyg with
overshooting (Guinan et al.2000)
X=0.722?
There are many
possibilities for
X-Z combinations.
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For PV Cas
αov=0.25 =>
Mov= 1.48 Mconv
Rov= 1.16 Rconv
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
X
Z
t
dLog L/dlog q
-4
-0.8
0.1
dLog R/dlog q
-0.6-...
-0.15-...
0.07
L (X1, Z1, t1) = L (X2, Z2, t2)
R (X1, Z1, t1) = R (X2, Z2, t2)
lx/lz ~ 5, rx/rz ~ 4
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.
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The selected binaries:
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EK Cep: M1=2.02 M2=1.12 (The secondary is a PMS)
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PV Cas: M1=2.82
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θ ² Tau and  342
M2=2.76 (short apsidal motion
period; 91 years)
θ ² Tau : M1=2.42
(members of the Hyades
cluster)
M2=2.11
 342 : M1=1.36 M2=1.25
in units of Msun.
(Andersen
1991,Torres et al. 1997a, 1997b)
Rotation of the early - type
stars
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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.
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.
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)
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.
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.
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).
The apsidal Motion
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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.
PV Cas
* Fundamental
properties of the
system (Barembaum
& Etzel, 1995)
* U= 91 yıl.
* Ap like variation in its
light curve.
* Vequ =65 km/s
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
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.
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)
Rotation rate throughout the DR
models of PV Cas A: solar cc.
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
Binaries of Hyades
•
 342:
V=6.46
* θ ² Tau (de Bruijne et al. 2001)
A
B
MV 0.47±0.04
1.57±0.04
B-V 0.17±0.01
veq 110km/s
*
0.16±0.01
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)
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)
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!
Results
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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)