A-type stars: evolution, rotation and binarity

Arlette Noels, Josefina MontalbanArlette Noels, Josefina MontalbanInstitut d’ Astrophysique et Géophysique Université de Liège, BelgiumInstitut d’ Astrophysique et Géophysique Université de Liège, Belgium

andand

Arlette Noels, Josefina MontalbanArlette Noels, Josefina MontalbanInstitut d’ Astrophysique et Géophysique Université de Liège, BelgiumInstitut d’ Astrophysique et Géophysique Université de Liège, Belgium

andand

Carla MaceroniCarla MaceroniINAF - Rome Astronomical Observatory, ItalyINAF - Rome Astronomical Observatory, Italy

Carla MaceroniCarla MaceroniINAF - Rome Astronomical Observatory, ItalyINAF - Rome Astronomical Observatory, Italy

THE A STAR PUZZLE - IAU Symposium 224 Poprad, Slovakia July 8, 2004THE A STAR PUZZLE - IAU Symposium 224 Poprad, Slovakia July 8, 2004THE A STAR PUZZLE - IAU Symposium 224 Poprad, Slovakia July 8, 2004THE A STAR PUZZLE - IAU Symposium 224 Poprad, Slovakia July 8, 2004

Mass ~ 1.5 – 3 M

Teff ~ 7000 – 11000 KB-V ~ 0.0 – 0.30L ~ 10 – 50 L

Fundamental Fundamental parametersparametersFundamental Fundamental parametersparameters

age = 3.12 108 yr

age = 8.107 yr

age = 3.108 yr

H burning phaseH burning phaseH burning phaseH burning phase

Convective coreConvective core Convective coreConvective core X profile

Convective core: Convective core: temperature profiletemperature profile


Convective coreConvective core Convective coreConvective core

Overshooting Overshooting Overshooting Overshooting

t = 4. 106

t = 2. 107

H = 3.0 108 yrH = 2.2 108 yr

H = 2.9 108 yr


Needed to fit CMD for open clusters and eclipsing binariesNeeded to fit CMD for open clusters and eclipsing binaries

Increases with mass (Andersen et al. 1990)Increases with mass (Andersen et al. 1990)


NoNo isothermal core isothermal coreNoNo isothermal core isothermal core



Isothermal coreIsothermal core


same size of He coresame size of He core same size of He coresame size of He core

Pre-main Pre-main sequencesequencePre-main Pre-main sequencesequence 1.5 – 4 M

Fully convectiveFully convective

Fully radiativeFully radiative

FormicolaFormicola et al. 2004et al. 2004

Pre-main Pre-main sequencesequencePre-main Pre-main sequencesequence

Palla & Stahler 1993Palla & Stahler 1993dM/dt = 10dM/dt = 10-5-5

Behrend & Maeder 2001,Behrend & Maeder 2001,dM/dt=1/3 (dM/dt)dM/dt=1/3 (dM/dt)discdisc

BirthlinesBirthlinesBirthlinesBirthlines

Pre-main Pre-main sequencesequencePre-main Pre-main sequencesequence

Effect of Effect of treatment of treatment of convection on convection on PMS evolutionary PMS evolutionary tracks location tracks location

Effect of Effect of treatment of treatment of convection on convection on PMS evolutionary PMS evolutionary tracks location tracks location

FST (Canuto et al. 1996).FST (Canuto et al. 1996).

MLT, MLT, =1.6=1.6MLT, MLT, =1.6=1.6

Convective Convective envelopeenvelopeConvective Convective envelopeenvelope

1.8 M

Convection in A-type star envelopes is superadiabaticConvection in A-type star envelopes is superadiabatic

> > > > > > > >

HI, HeIHI, HeIHI, HeIHI, HeI HeIIHeIIHeIIHeII

Thickness of the mixed layersThickness of the mixed layers Abundance anomaliesAbundance anomalies

Gravitational Gravitational settlingsettlingGravitational Gravitational settlingsettling

Microscopic Microscopic diffusiondiffusionMicroscopic Microscopic diffusiondiffusion

Radiative forcesadiative forces (Michaud et al. 1976, …) Turbulent transporturbulent transport (Schatzman 1969, Vauclair et al. 1978)

Radiative forcesadiative forces (Michaud et al. 1976, …) Turbulent transporturbulent transport (Schatzman 1969, Vauclair et al. 1978)

Enough but not too muchEnough but not too much Enough but not too muchEnough but not too much

Changes in the surface abundances (Richer et al. 2000)Changes in the surface abundances (Richer et al. 2000)

1.5M 1.7M2.5M

Changes in the internal structure

1. Mass of the convective envelope2. Fe convection zone around 200000 K

Changes in the internal structure

1. Mass of the convective envelope2. Fe convection zone around 200000 K

Rotation Rotation Rotation Rotation

A-type stars are rapid rotators: A-type stars are rapid rotators: vvrotrot up to 300 up to 300

km/s.km/s. Am and Ap: vAm and Ap: vrot rot < 120 km/s< 120 km/s

Normal A0-F0 stars : vNormal A0-F0 stars : vrot rot > 120 km/s (Abt & Morrel 1995)> 120 km/s (Abt & Morrel 1995)










Normal A0-F0 stars : vNormal A0-F0 stars : vrot rot > 120 km/s (Abt & Morrel 1995)> 120 km/s (Abt & Morrel 1995)Abt & Morrell 1995, Abt 1995:Abt & Morrell 1995, Abt 1995:Rotation alone can explain the occurrence of abnormal or Rotation alone can explain the occurrence of abnormal or normal normal main-sequence A stars because of our inability to main-sequence A stars because of our inability to distinguish marginal Am stars from normal ones in A2-F0 distinguish marginal Am stars from normal ones in A2-F0 and our inability to disentangle evolutionary effectsand our inability to disentangle evolutionary effects

Abt & Morrell 1995, Abt 1995:Abt & Morrell 1995, Abt 1995:Rotation alone can explain the occurrence of abnormal or Rotation alone can explain the occurrence of abnormal or normal normal main-sequence A stars because of our inability to main-sequence A stars because of our inability to distinguish marginal Am stars from normal ones in A2-F0 distinguish marginal Am stars from normal ones in A2-F0 and our inability to disentangle evolutionary effectsand our inability to disentangle evolutionary effects

BUTBUTBUTBUT

Debernardi & North 2001 V392 Carinae: vsini ~ 27 km/s no peculiarDebernardi & North 2001 V392 Carinae: vsini ~ 27 km/s no peculiarDebernardi & North 2001 V392 Carinae: vsini ~ 27 km/s no peculiarDebernardi & North 2001 V392 Carinae: vsini ~ 27 km/s no peculiar


New Catalogue by Royer et al. 2002New Catalogue by Royer et al. 2002:

M > 1.6MM > 1.6M or B-V < 0.25-0.3: or B-V < 0.25-0.3: Little or no stellar activityLittle or no stellar activity No evidence of significant angular momentum lossNo evidence of significant angular momentum loss There is no trend on rotation with age (vsin i ~ cte) There is no trend on rotation with age (vsin i ~ cte)

M < 1.6MM < 1.6M or B-V > 0.25-0.3: or B-V > 0.25-0.3: Stellar activity does not depend on age or rotationStellar activity does not depend on age or rotation Very slow angular momentum loss. Braking time ~ 10Very slow angular momentum loss. Braking time ~ 1099yryr.

M > 1.6MM > 1.6M or B-V < 0.25-0.3: or B-V < 0.25-0.3: Little or no stellar activityLittle or no stellar activity No evidence of significant angular momentum lossNo evidence of significant angular momentum loss There is no trend on rotation with age (vsin i ~ cte) There is no trend on rotation with age (vsin i ~ cte)

M < 1.6MM < 1.6M or B-V > 0.25-0.3: or B-V > 0.25-0.3: Stellar activity does not depend on age or rotationStellar activity does not depend on age or rotation Very slow angular momentum loss. Braking time ~ 10Very slow angular momentum loss. Braking time ~ 1099yryr.

Rotation on Rotation on MSMSRotation on Rotation on MSMS

Rotational velocity distribution Rotational velocity distribution must be imposed the pre-main sequence evolutionmust be imposed the pre-main sequence evolution

(Wolff & Simon 1997)

Rotation in PMSRotation in PMSRotation in PMSRotation in PMS

Importance of the Birthline locationImportance of the Birthline locationImportance of the Birthline locationImportance of the Birthline location

From vsini in 145 From vsini in 145 in Orion (1 Myr), Wolff et al. 2004in Orion (1 Myr), Wolff et al. 2004:

1.1. Braking of stars with M< 2 MBraking of stars with M< 2 M as they evolve down as they evolve down their convective tracks (disk interaction)their convective tracks (disk interaction)

2.2. Conservation of angular momentum as stars evolve Conservation of angular momentum as stars evolve long their radiative traks long their radiative traks

1.1. Braking of stars with M< 2 MBraking of stars with M< 2 M as they evolve down as they evolve down their convective tracks (disk interaction)their convective tracks (disk interaction)

2.2. Conservation of angular momentum as stars evolve Conservation of angular momentum as stars evolve long their radiative traks long their radiative traks

High accretion rate birthline High accretion rate birthline at larger R at larger RLow accretion rate birthline Low accretion rate birthline at radiatively low R at radiatively low R

Rotation: effect on stellar evolutionRotation: effect on stellar evolutionRotation: effect on stellar evolutionRotation: effect on stellar evolution

Surface effects:Surface effects: Photometric parameters Photometric parameters Anisotropic mass lossAnisotropic mass loss

Departure from sphericity: meridional circulationDeparture from sphericity: meridional circulation Differential rotation and instabilities Differential rotation and instabilities (e.g. Pinsonneault (e.g. Pinsonneault

1997)1997) Transport of angular momentum and chemicalsTransport of angular momentum and chemicals

Similar to overshooting in the HRDSimilar to overshooting in the HRDButBut

Different internal structure?Different internal structure?

Maeder & Zahn (1998), Zahn (1992) Maeder & Zahn (1998), Zahn (1992)


Palacios et al. 2003

2.2 M2.2 M

1.8 M1.8 M

1.5 M1.5 M

1.4 M1.4 M

1.35M1.35M

Time spent on MS increases by 20% in lower mass stars 10% in higher mass models

Transport by meridional circulationTransport by meridional circulationand highly anisotropic turbulence and highly anisotropic turbulence in a rotating and non magnetic star.in a rotating and non magnetic star.

Transport by meridional circulationTransport by meridional circulationand highly anisotropic turbulence and highly anisotropic turbulence in a rotating and non magnetic star.in a rotating and non magnetic star.

““New prescription of DhNew prescription of Dhkeeps the size of the keeps the size of the core”core” (Maeder 2003)

Maeder & Zahn 1998Maeder & Zahn 1998Maeder & Zahn 1998Maeder & Zahn 1998

Maeder 2003Maeder 2003Maeder 2003Maeder 2003 No rotationNo rotationNo rotationNo rotation


Dh Dh Maeder 2003Maeder 2003 >> Dh >> Dh Maeder & ZahnMaeder & Zahn Dh Dh Maeder 2003Maeder 2003 >> Dh >> Dh Maeder & ZahnMaeder & Zahn

Maeder (2003): Maeder (2003): balance balance between horizontal turbulence between horizontal turbulence and excess of energy in the and excess of energy in the differential rotation differential rotation

Maeder (2003): Maeder (2003): balance balance between horizontal turbulence between horizontal turbulence and excess of energy in the and excess of energy in the differential rotation differential rotation

Horizontal turbulent Horizontal turbulent diffusivity: Dhdiffusivity: DhHorizontal turbulent Horizontal turbulent diffusivity: Dhdiffusivity: Dh

Vertical effective diffusivity: DeffVertical effective diffusivity: DeffVertical effective diffusivity: DeffVertical effective diffusivity: Deff


Mathis & Zahn 2004Mathis et al. 2004

ββ-viscosity prescription to determine Dh-viscosity prescription to determine Dhββ-viscosity prescription to determine Dh-viscosity prescription to determine Dh

Differential rotation in radiative layers Differential rotation in radiative layers (Tayler instability)(Tayler instability) Magnetic field Magnetic field (Spruit 1999, 2002).(Spruit 1999, 2002).

Magneto-rotational instability Magneto-rotational instability (Balbus & Hawley 1991)(Balbus & Hawley 1991) could could transport J to the surface transport J to the surface (Arlt et al. 2003).(Arlt et al. 2003). Timescale ~ life time for A type stars Timescale ~ life time for A type stars Effect on J of Ap starsEffect on J of Ap stars


Interaction rotation-convectionInteraction rotation-convectionInteraction rotation-convectionInteraction rotation-convection

Convective envelope:Convective envelope:

Reduce the size of the overshooting layer at the Reduce the size of the overshooting layer at the bottom of the convective envelope bottom of the convective envelope (Chan 1996, Julien et al. 1996)(Chan 1996, Julien et al. 1996)

Convective core Convective core ((Browning et al. 2004):Browning et al. 2004):

Differential rotationDifferential rotation Overshooting Overshooting

Rotation: open Rotation: open questionsquestionsRotation: open Rotation: open questionsquestions

Overshooting and/or rotatonal mixing in theOvershooting and/or rotatonal mixing in the

internal regions?internal regions? Mixing close to the surface:Mixing close to the surface:

Li, Be in A-type stars and in the SunLi, Be in A-type stars and in the Sun Am surface abundances (D ~ Am surface abundances (D ~

D(He)D(He)00((//oo))nn))

Transport of angular momentum in the Transport of angular momentum in the

radiative radiative

regions internal rotation in A-type stars: regions internal rotation in A-type stars: solid or differential rotation?solid or differential rotation? role of magnetic instabilities role of magnetic instabilities

Puzzle pieces (general trends)Puzzle pieces (general trends)

A Am Ap

(Sr-Cr,Si) Ap (HgMn)

close close binary binary

frequencyfrequency normnorm

VeryVery

highhighLowLow NormNorm

rotationrotation FastFast SlowSlow SlowSlow SlowSlow

magneticmagnetic

fieldsfields nono nono yes, strongyes, strong nono

Binarity slowing-down of rotation Am phenomenon

magnetic Ap’s: strong magnetic fields 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 ?

is binarity - through syncronization and circularization mechanisms - just an efficient brake of stellar rotation or does it affect the stellar structure in other ways?

A-type star binarity/non-binarityA-type star binarity/non-binarity

Perhaps

..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

applicationSmall and non homogeneous available samples

with sufficiently accurate elementsSelection effects on the OPD

In late-type stars it is the turbulent dissipationturbulent dissipation in the outer convection zone that retards the equilibrium tide,

Synchronization & circularization Synchronization & circularization theories: theories:

I. Zahn’s tidal mechanismsI. Zahn’s tidal mechanisms

Synchronization & circularization Synchronization & circularization theories: theories:

I. Zahn’s tidal mechanismsI. Zahn’s tidal mechanisms

In early type stars the dissipation mechanism is radiative radiative dampingdamping, which acts on the dynamical tide (forced gravity waves are emitted from a lagging convective core and damped in the outer layers).

Two necessary ingredients:

tidal bulges

dissipation mechanism

non-alignement torque

a

R

Ω

ω

,611

6222

a

R

I

MRq

t

k

dt

d

t fsync

,151 2

17

22

652

21

3

a

RE

I

MRqq

R

GM

tsync

,12

211 221

22

6112

21

3

a

RE

I

MRqq

R

GM

tcirc

8

2 1 2

21eln 1

a

Rqq

t

k

dt

d

t fcirc

Zahn tidal theory: timescales

E2 is a constant strongly dependent on the size of the convective dependent on the size of the convective corecore

time friction typical the and constant apsidal 2 the is , ndf tkmmq 221

related to the density profilerelated to the density profile inside the star

In early type stars the timescales increase more rapidly In early type stars the timescales increase more rapidly with a (or P) and the forces have a shorter rangewith a (or P) and the forces have a shorter range

Late-type stars:

Early –type stars:

,a

R

R

MLq)q ( cost

tγ

sync

N8

3381

83

4

9

2

1101

II. Tassoul’s hydrodynamical theoryII. 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.

Timescales:

8498

1

811

4

9

22)1(10

1

a

R

R

MLβq cost'

tγ

circ

N

,logr

vN

where is the eddy and the radiative viscosity of the outer layers (N=0 for radiative envelopes).

rv

with

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 Tassoul’s mechanism has a longer range and a much higher efficiency for early-type starsefficiency 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 & quasi-synchronized 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.

log (t/tcri) log (t/tcri)

e e

Application to A and early type stars(Matthews & Mathieu 1992, Claret et al. 1995, 1997)

Zahn Tassoul, = 1.6

t: binary age, tcrit : time for circularization.

Circ.Non-circ.

From Claret et al. 1995, 1997

Application to A and early type stars, II(Matthews & Mathieu 1992, Claret et al. 1995, 1997)

Tassoul, = 1.6Tassoul, = 0

log (t/tcri) log (t/tcri)

e e

Spin – orbit synchronization:Am

orbsyn P

Riviv 6.50)90(sin

(Am sample from Budaj 96 (Segewiss 93) + Updated v sin i from Royer et al. 2002)

Expected syncronization P: R/a≈0.25 ( North & Zahn 02)

M=2.0 R=3.0 q=0.2

R=2.1 q=1.0

ω=ΩIn a synchronized binary:

d 21

23

125.0

1159.0 1

qmR

Psyn

Spin – orbit synchronization Am (Am sample from Budaj 96 (Segewiss 93) + Updated v sin i from Royer et al. 2002)


M=2.0 R=3.0 q=0.2

R=2.1 q=1.0

ω=Ω

v sin i before updating

Empty region

P-dependent tidal mixing

Spin – orbit synchronization Am (Am sample from Budaj 96 (Segewiss 93). Updated v sin i from Royer et al. 2002)


M=2.0 R=3.0 q=0.2

R=2.1 q=1.0

ω=Ω

Selection effects on SB’sSelection effects on SB’s

days 31

22

3316

1max)1()1(

sin1063.9)(

23

Kqe

iqmKP

minimum observable radial velocity amplitude, K1≠ instr. limit

maximum observable orbital Period:

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.

m1=2.0

Missed SB1

A-type stars: evolution, rotation and binarity

Documents

starin early type stars

type stars warnings

shorter rangelatetype

zahn tassoul

zahn tidal theory

available theories

updated v sin i

north zahn