Angular momentum transport and mixing in rotating stars
Post on 03-Feb-2016
37 Views
Preview:
DESCRIPTION
Transcript
Angular momentum transport and mixing in rotating stars
Jean-Paul Jean-Paul Zahn
Observatoire de ParisObservatoire de Paris
Second Corot-Brazil Workshop Ubatuba, 2-6 November 2005Second Corot-Brazil Workshop Ubatuba, 2-6 November 2005
Why bother about rotation in stars?Why bother about rotation in stars?
• Rotation is the main cause of mixing in stellar radiation zones
• It plays a major role in the generation and decay of magnetic field
• Rotation intervenes in the mass loss
hence its impact on stellar and galactic evolution
In convection zones
- Very efficient mixing, due to turbulence
- Angular momentum transport due to the turbulent stresses differential rotation
Red GiantSun
Massive parallel simulations - no simple prescription (yet)
Brun & Toomre 2002 Brun et al. 2005
Mixing processes in radiation zones
- Rotational mixing of type I
Matter and angular momentum are transported by the same processes :meridional circulation and turbulence
- Rotational mixing of type II
Mixing is caused by circulation and turbulence,but another process (magnetic field, waves) intervenes
in the transport of angular momentum
Main cause : (differential) rotation
Mixing processes in radiation zones: rotational mixing of type I
• Meridional circulation
Classical picture: circulation is due to thermal imbalance caused by perturbing force (centrifugal, etc.)
Eddington (1925), Vogt (1925), Sweet (1950), etc
Eddington-Sweet time
Revised picture: after a transient phase of about tES,
circulation is driven by the loss (or gain) of angular momentum Busse (1981), JPZ (1992), Maeder & Z (1998)
No AM loss: no need to transport AM weak circulation
AM loss by wind: need to transport AM to surface strong circulation
Turbulence caused by differential rotation
By vertical shear r(baroclinic instability)
turbulence if
from which one deduces the turbulent diffusivity (if = cst)
K thermal diffusion; viscosity; N buoyancy frequency
- if maximum of vorticity: linear instability
- if no maximum of vorticity: finite amplitude instability
Townsend 1959Dudis 1974; JPZ 1974Lignières et al. 1999
reduced by radiative diffusion- stabilizing effect of stratification
Richardson criterion
Turbulence caused by differential rotation
By horizontal shear ( (barotropic instability)
Chaboyer & Z 1992
Assumptions:
- instability acts to suppress its cause, i.e. (
2 important properties: - erodes stabilising effect of stratification
- turbulent transport is anisotropic (due to stratification): Dh Dv
Main weakness: no firm prescription for Dh Maeder 2003 Mathis, Palacios & Z 2004
Talon & Z 1997
- changes advection of chemicals into vertical diffusion
Rotational mixing of type I - the observational test
The same processes (circulation and turbulence) are responsible for the mixing of chemical elements
and for the transport of angular momentum
Zahn (1992), Maeder & Zahn (1998)
For late-type stars, predicts
- fast rotating core helioseismology
Quite successful with early-type stars Talon et al. 1997; Maeder & Meynet 2000; Talon & Charbonnel 1999
Rotation profiles in the Sun
GONG
predicted by standard rotational mixing
Talon (1997), Matias & Zahn (1998)
tachocline
observed throughacoustic sounding
Rotational mixing of type I - the observational test
The same processes (circulation and turbulence) are responsible for the mixing of chemical elements
and for the transport of angular momentumZahn (1992), Maeder & Zahn (1998)
· For late-type stars, predicts - fast rotating core helioseismology
- strong destruction of Be in Sun(may be explained by tachocline mixing)
- mixing correlated with loss of angular momentum Li in tidally locked binaries little dispersion in the Spite plateau
Quite successful with early-type stars Talon et al. 1997; Maeder & Meynet 2000; Talon & Charbonnel 1999
Another, more powerful process is responsible for the transport of angular momentum
Rotational mixing of type II
Circulation and turbulence are responsible for the mixing of chemical elements
Another process operates for the transport of angular momentum;has indirect impact on mixing, by shaping the rotation profile
· Magnetic field ?
· Internal gravity waves ?
Role of a fosssil magnetic field
Does it prevent the spread of tachocline?Does it enforce uniform rotation?
convection zone
tachoclinevoid of magnetic field
magnetopause
Gough & McIntyre 1998
Role of a fossil magnetic field
Does it prevent the spread of tachocline?Does it enforce uniform rotation?
Garaud 2002
Stationary solutions
intermediate field case (13000 G)
At high latitudepoloidal field threads through CZenforces diff. rotation(Ferraro’s law)
Role of a fossil magnetic field
Does it prevent the spread of tachocline? No
Brun & Zahn 2005
Time-dependent solutions: result strongly depends on initial field
Initial field connects with CZ
Does it enforce uniform rotation? No
Role of a fossil magnetic field
Does it prevent the spread of tachocline? No
Initial field does not connect with CZ
Does it enforce uniform rotation? No
Role of a fossil magnetic field
Brun & Zahn 2005
QuickTime™ et undécompresseur Cinepak
sont requis pour visionner cette image.
No field
Initially (too) deeply buriedpoloidal field
Time-dependentsolutions:result strongly depends on initial field
QuickTime™ et undécompresseur Cinepak
sont requis pour visionner cette image.
Role of a fossil magnetic field
Brun & Zahn 2005
QuickTime™ et undécompresseur Cinepak
sont requis pour visionner cette image.
No field
Initially (too) deeply buriedpoloidal field
Time-dependentsolutions:result strongly depends on initial field
QuickTime™ et undécompresseur Cinepak
sont requis pour visionner cette image.
Role of a fossil magnetic field
Does it prevent the spread of tachocline? No
Initial field is deeply buried in RZ
Does it enforce uniform rotation? No
Role of a fossil magnetic field
Polytrope n=32 Msol
Braithwaite & Nordlund 2005
Probably not important in solar-type stars
But in A-type stars?
Initial random field relaxes in
a mixed poloidal/toroidalconfiguration
which then diffusestoward the surface
Properties of internal gravity waves
• Propagate in stratified media
• restoring force buoyancy
• Excited by turbulence (e.g. in or close to convective zones)
• Conserve momentum (or angular momentum) – if they are not damped
transport AM to place where they are dissipated
buoyancy (Brunt-Väisälä) frequency oscillation frequency of a displaced element in a stratified region
Excitation of internal waves
2D simulations ofpenetrative convectionKiraga et al. 2003
Analytical treatmentGoldreich, Murray & Kumar 1994used by Talon & Charbonnel 2003
Momentum transport by waves
• In stars, IGW are damped by thermal diffusion
local frequency is Doppler shifted if there is differential rotation
thermal diffusion
flux at the base of the CZ
frequency in frame rotating with CZ
Waves transfer momentum from the region where they are excited to the region where they are dissipated
Momentum transport by waves
- if prograde (m>0) and retrograde (m<0) waves are equally excited and if there is no differential rotation
no net momentum deposition
· high l waves are damped very close to the CZ
- if there is differential rotation, +m and -m waves deposit their momentum at different locations
waves increase the local differential rotation
Below the convection zone high-degree waves
Talon & Charbonnel 2005
Below the convection zone high-degree waves
Talon & Charbonnel 2005
Shear Layer Oscillation(SLO)
Momentum transport by waves
• if prograde (m>0) and retrograde (m<0) waves are equally excited and there is no differential rotation
no net momentum deposition
• if there is differential rotation, +m and -m waves deposit their momentum at different locations
waves increase the local differential rotation
- high l waves are damped very close to the CZ
- low l, low frequency waves are damped in deep interior
Interiorlow-degree, low-frequency waves
Talon & Charbonnel 2005
Angular momentumextracted by solar wind
Interiorlow-degree, low-frequency waves
Talon & Charbonnel 2005
Angular momentumextracted by solar wind
Effect of SLOfiltered out
Effect of IGW on 1.2 Msol star
Rotation profile Li profile at 0.7 Gyr
Talon & Charbonnel 2005
type I
type Iwith IGW
0.7
0.5
0.2
Vi = 50 km/s Hyades
with all other hydrodynamical transport mechanisms included
Effect of IGW in the Sun
Charbonnel & Talon 2005
Rotation profileinitial velocity 50 km/s
Rotational mixing type I(without IGW)
Rot. mixing type II(with IGW)
All transport mechanisms included,except magnetic field
0.2, 0.5, 0.7, 1.0, 1.5, 3.0, 4.6 Gyr
microscopic diffusion
distribution of chemical elements
meridional circulation turbulent transport
magnetic field
rotation
convection
internal gravity waves
penetration, overshoot
standard model
rotational mixing type I
rotational mixing type II
Rotational mixing in radiation zones
(in tachocline)
Weakest points of present models
- Parametrisation of shear turbulence due to differential rotation
- Power spectrum for IGW emitted at base of convection zone
- Particle transport by IGW ?
- Role of magnetic field ?
- Convective penetration into radiation zones
CoRoT will put most valuable constraints
top related