Transcript Diapositiva 1

Arlette Noels, Josefina Montalban
Institut d’ Astrophysique et Géophysique Université de Liège, Belgium
and
Carla Maceroni
INAF - Rome Astronomical Observatory, Italy
THE A STAR PUZZLE - IAU Symposium 224 Poprad, Slovakia July 8, 2004
Fundamental parameters
Mass
Teff
B-V
L
~
~
~
~
1.5 – 3 M
7000 – 11000 K
0.0 – 0.30
10 – 50 L
H burning phase
age = 3.108 yr
age = 8.107 yr
age = 3.12 108 yr
Convective core
X profile
Convective core:
temperature profile
Convective core
Overshooting
2.210
108 8yr
yr
tHtH==3.0
Dt = 4. 106
tH = 2.9 108 yr
Dt = 2. 107
Overshooting
Needed to fit CMD for open clusters and eclipsing binaries
Increases with mass (Andersen et al. 1990)
Overshooting
No isothermal core
Convective core:
temperature profile
Isothermal core
Overshooting
same size of He core
Pre-main sequence
1.5 – 4 M
Fully convective
Fully radiative
Formicola et al. 2004
Pre-main sequence
Birthlines
Behrend & Maeder 2001,
dM/dt=1/3 (dM/dt)disc
Palla & Stahler 1993
dM/dt = 10-5
Pre-main sequence
FST (Canuto et al. 1996).
Effect of treatment
of
convection
on
PMS
evolutionary
tracks location
MLT, a=1.6
Convective envelope
Convection in A-type star envelopes is superadiabatic
HeII
HI, HeI
1.8 M
 >  >
Thickness of the mixed layers
Abundance anomalies
Gravitational settling
Microscopic diffusion
 Radiative forces (Michaud et al. 1976, …)
 Turbulent transport (Schatzman 1969, Vauclair et al. 1978)
Enough but not too much
Changes in the surface abundances (Richer et al. 2000)
Changes in the internal structure
1. Mass of the convective envelope
2. Fe convection zone around 200000 K
1.5M
1.7M
2.5M
Rotation
 A-type stars are rapid rotators: vrot up to 300 km/s.
 Am and Ap: vrot < 120 km/s
 Normal A0-F0 stars : vrot > 120 km/s (Abt & Morrel 1995)
Rotation
 A-type stars are rapid rotators: vrot up to 300 km/s.
 Am and Ap: vrot < 120 km/s
 Normal A0-F0 stars : vrot > 120 km/s (Abt & Morrel 1995)
Abt & Morrell 1995, Abt 1995:
Rotation alone can explain the occurrence of abnormal or normal
main-sequence A stars because of our inability to distinguish
marginal Am stars from normal ones in A2-F0 and our inability to
disentangle evolutionary effects
BUT
Debernardi & North 2001 V392 Carinae: vsini ~ 27 km/s no peculiar
Rotation
New Catalogue by Royer et al. 2002:
Rotation on MS
 M > 1.6M or B-V < 0.25-0.3:
 Little or no stellar activity
 No evidence of significant angular momentum loss
 There is no trend on rotation with age (vsin i ~ cte)
 M < 1.6M or B-V > 0.25-0.3:
 Stellar activity does not depend on age or rotation
 Very slow angular momentum loss. Braking time ~ 109yr.
Rotational velocity distribution
must be imposed the pre-main sequence evolution
(Wolff & Simon 1997)
Rotation in PMS
From vsini in 145  in Orion (1 Myr), Wolff et al. 2004:
1. Braking of stars with M< 2 M as they evolve down their
convective tracks (disk interaction)
2. Conservation of angular momentum as stars evolve long their
radiative traks
Importance of the Birthline location
High accretion rate birthline  at larger R
Low accretion rate birthline  at radiatively low R
Rotation: effect on stellar evolution
 Surface effects:
 Photometric parameters
 Anisotropic mass loss
 Departure from sphericity: meridional circulation
 Differential rotation and instabilities (e.g. Pinsonneault 1997)
 Transport of angular momentum and chemicals
Similar to overshooting in the HRD
But
Different internal structure?
Rotation: effect on stellar evolution
 Maeder & Zahn (1998), Zahn (1992)
Transport by meridional circulation
and highly anisotropic turbulence
in a rotating and non magnetic star.
2.2 M
1.8 M
1.5 M
1.4 M
1.35M
Palacios et al. 2003
Time spent on MS increases by
 20% in lower mass stars
 10% in higher mass models
Rotation: effect on stellar evolution
Maeder (2003): balance between
Maeder 2003
No rotation
horizontal turbulence and excess of
energy in the differential rotation
Dh
Maeder 2003
>> Dh
Maeder & Zahn
Maeder & Zahn 1998
“New prescription of Dh
keeps the size of the core”
(Maeder 2003)
Rotation: effect on stellar evolution
β-viscosity prescription to determine Dh
Horizontal turbulent diffusivity: Dh
Mathis & Zahn 2004
Mathis et al. 2004
Vertical effective diffusivity: Deff
Rotation: effect on stellar evolution
 Differential rotation in radiative layers
(Tayler instability)  Magnetic field (Spruit 1999, 2002).
 Magneto-rotational instability (Balbus & Hawley 1991) could
transport J to the surface (Arlt et al. 2003).
Timescale ~ life time for A type stars 
Effect on J of Ap stars
Interaction rotation-convection
 Convective envelope:
 Reduce the size of the overshooting layer at the
bottom of the convective envelope
(Chan 1996, Julien et al. 1996)
 Convective core (Browning et al. 2004):
 Differential rotation
 Overshooting
Rotation: open questions
 Overshooting and/or rotatonal mixing in the
internal regions?
 Mixing close to the surface:
 Li, Be in A-type stars and in the Sun
 Am surface abundances (D ~ wD(He)0(r/ro)n)
 Transport of angular momentum in the radiative
regions internal rotation in A-type stars:
 solid or differential rotation?
 role of magnetic instabilities
Puzzle pieces (general trends)
A
Am
Ap
(Sr-Cr,Si)
close binary
frequency
norm
Very
high
Low
Norm
rotation
Fast
Slow
Slow
Slow
magnetic
fields
no
no
Binarity
yes, strong
slowing-down of rotation
magnetic Ap’s: strong magnetic fields
Ap (HgMn)
no
Am phenomenon
binarity
A-type star binarity/non-binarity
 Typically (~ not far from always) Am’s are (close) binaries
 Rarely Ap’s are binaries, and anyway with an orbital P≥2.5d
Questions on binarity:
is binarity a necessary and sufficient condition to be an Am
Perhaps
is binarity - through syncronization and circularization
mechanisms - just an efficient brake of stellar rotation or
does it affect the stellar structure in other ways?
..no definite answer…
?
...l king for the answers
The synchronization (and circularization) theories are
usually compared withthe Observed (orbital) Period
Distributions (OPD), the rotational data and the
eccentricity - P plots.
Three sorts of problems:
Limits of the available theories or in their application
Small and non homogeneous available samples with
sufficiently accurate elements
Selection effects on the OPD
Synchronization & circularization theories:
I. Zahn’s tidal mechanisms
Ω
a
ω
a
Two necessary ingredients:
 tidal bulges
 dissipation mechanism
non-alignement
torque
R
In late-type stars it is the turbulent dissipation in the outer
convection zone that retards the equilibrium tide,
In early type stars the dissipation mechanism is radiative
damping, which acts on the dynamical tide (forced gravity waves
are emitted from a lagging convective core and damped in the
outer layers).
Zahn tidal theory: timescales
Late-type stars:
1
t sync
1 dw
k 2 2 MR 2  R 

6 q
  ,
  w dt
tf
I a
6
1
tcirc
dln e 21 k 2
R


q 1  q   
dt
2 tf
a
8
q  m1 m2 , k2 is the 2nd apsidal constant and t f the typical friction time
related to the density profile inside the star
Early –type stars:
1
t sync
1
17
MR
 GM 
R
 5  3  q 2 1  q  6
E2  
I
 R 
a
2
5
2
2
,
1
tcirc
1
2
11 MR
21  GM  2 2
R
6

E2 
 3  q 1  q 
2  R 
I
a
E2 is a constant strongly dependent on the size of the convective core
In early type stars the timescales increase more rapidly with a
(or P) and the forces have a shorter range
21
2
,
II. Tassoul’s hydrodynamical theory
Transient strong meridional currents, produced by
the tidal action, transfer angular momentum between
the stellar interior and the Ekman layer close to the
surface. If ω>Ω the star spins down.
v
,
r
where  v is the eddy and  r
the radiative viscosity of the
outer layers (N=0 for radiative
envelopes).
Timescales:
1
t sync
1
t circ
 cost  10
with
N
 cost'  10
4 γ
N
 ML
q ( 1  q) 8  9
 R
4 γ
2
3
1
  R 8
   ,
 a
 ML
(1  q ) β  9
 R
2
11
8
2
33
8
1
  R
  
 a
8
49
8
N  log
γ takes somehow into account
the fact that the eqs are
solved for ~circular and
~synchronized motions.
Tassoul’s mechanism has a longer range and a much higher
efficiency for early-type stars
Warnings!
! the use of timescales cannot replace the integration
!
!
of the evolutionary equations, which require as well
the introduction of stellar evolutionary models (see
Claret et al. 1995, Claret et Cunha 1997)
Both theories are for quasi-circular & quasisynchronized orbits. Tassoul introduces an arbitrary
factor (~10-40) in the timescales.
The strong dependence of the processes on R/a
requires systems with very accurate element
determination.
Application to A and early type stars
(Matthews & Mathieu 1992, Claret et al. 1995, 1997)
Zahn
Non-circ.
e
Tassoul,  = 1.6
Circ.
e
log (t/tcri)
t: binary age, tcrit : time for circularization.
log (t/tcri)
From Claret et al. 1995, 1997
Application to A and early type stars, II
(Matthews & Mathieu 1992, Claret et al. 1995, 1997)
Tassoul,  = 0
e
Tassoul,  = 1.6
e
log (t/tcri)
log (t/tcri)
Spin – orbit synchronization:Am
(Am sample from Budaj 96 (Segewiss 93) + Updated v sin i from Royer et al. 2002)
In a synchronized
binary:
v sin i  vsyn (i  90)  50.6
ω=Ω
R
Porb
M=2.0
R=3.0
q=0.2
R=2.1
q=1.0
Expected syncronization P: R/a≈0.25 ( North & Zahn 02)
3
2
 R 
1
Psyn  0.1159  
 m1 1  q  2 d
 0.25 
Spin – orbit synchronization Am
(Am sample from Budaj 96 (Segewiss 93) + Updated v sin i from Royer et al. 2002)
ω=Ω
v sin i before
updating
Empty region
M=2.0
R=3.0
q=0.2
R=2.1
q=1.0
P-dependent tidal mixing
Expected syncronization P: R/a≈0.25 ( North & Zahn 02)
Spin – orbit synchronization Am
(Am sample from Budaj 96 (Segewiss 93). Updated v sin i from Royer et al. 2002)
ω=Ω
M=2.0
R=3.0
q=0.2
R=2.1
q=1.0
Expected syncronization P: R/a≈0.25 ( North & Zahn 02)
Selection effects on SB’s
minimum observable radial
velocity amplitude, K1≠ instr.
limit
maximum observable orbital
Period:
m1=2.0
Missed
SB1
P=P(m1,q,e) [ sin i =1.0]
if K1 =10 Km/s
detailed modeling of SB8
selection effects (Hogeveen
1992) suggests for A-type
stars:
K1≈ 25 Km/s
SB1 q distribution is peaked
around q≈0.2.
Pmax ( K1 )  9.63  10
6
m1q 3 sin3 i
(1  e ) (1  q )
2
3
2
2
K13
days