Magneto-rotational instability in the solar core and Ap star envelopes
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Transcript of Magneto-rotational instability in the solar core and Ap star envelopes
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Magneto-rotational Magneto-rotational instability in the instability in the solar core and Ap solar core and Ap
star envelopesstar envelopes
Rainer ArltRainer ArltAstrophysikalisches Institut PotsdamAstrophysikalisches Institut Potsdam
and Günther Rüdiger, Rainer and Günther Rüdiger, Rainer HollerbachHollerbach
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Solar rotational evolutionSolar rotational evolution
Wind model by StWind model by Stępień (1988)ępień (1988)
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The solar tachocline and the The solar tachocline and the corecore Thompson et al. 2003 from various Thompson et al. 2003 from various
sourcessources
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Stellar radiative envelopesStellar radiative envelopes
Star of spectral type A and Star of spectral type A and BB
Small convective coreSmall convective core Extensive radiative zoneExtensive radiative zone 10% of these stars10% of these stars
have magnetic fieldshave magnetic fields These 10% are slowThese 10% are slow
rotatorsrotators
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Differential-rotation decayDifferential-rotation decay Rotation of solar core is Rotation of solar core is
slow and uniformslow and uniform Rotation period has increased by Rotation period has increased by
factor of 10 during lifefactor of 10 during life Viscosity too small to reduce rotation Viscosity too small to reduce rotation
homogeneously throughout the Sunhomogeneously throughout the Sun Magnetic Ap stars rotate much Magnetic Ap stars rotate much
slower than „normal“ A starsslower than „normal“ A stars Did Did MRIMRI reduce the internal rotation reduce the internal rotation
of Sun and Ap stars?of Sun and Ap stars?
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Magneto-rotational Magneto-rotational instabilityinstability
Angular velocity decreasing withAngular velocity decreasing withaxis distanceaxis distance
Magnetic field or arbitrary Magnetic field or arbitrary geometrygeometry
Instability with growth rate of the Instability with growth rate of the order of order of
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Lower limit for MRILower limit for MRIk of most un-stable mode depends on B
Diffusive decay rate increases with k
MRI sup-pressed below certain B
in Gauss
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Upper limit for MRIUpper limit for MRI
Wavelength of most un-stable MRI mode exceeds object size
in kG
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Numerical simulationsNumerical simulations Spherical spectral code (Hollerbach 2000)Spherical spectral code (Hollerbach 2000)
0 and ,0 Bu
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Initial conditionsInitial conditions
Vertical cut Vertical cut through radiativethrough radiativezonezone
Left:Left:Magnetic fieldMagnetic field
Right:Right:Angular velocityAngular velocity
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Diff
ere
nti
al-
rota
tion
Diff
ere
nti
al-
rota
tion
deca
y
deca
y –
clo
se-u
p–
clo
se-u
p
Rm = 104
Pm = 1Ra = 0
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Diff
ere
nti
al-
rota
tion
Diff
ere
nti
al-
rota
tion
deca
y
deca
y –
clo
se-u
p–
clo
se-u
p
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Resolution at high Reynolds Resolution at high Reynolds numbernumber
t = 1 rotation
t = 4 rotations
t = 8 rotations
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Resolution at high Reynolds Resolution at high Reynolds numbernumber
t = 1 rotationt = 8 rotations
t = 4 rotations
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Differential-rotation decayDifferential-rotation decay
Steepness of rotation profile versus Steepness of rotation profile versus timetime
InitiallyInitially
Rayleigh-stableRayleigh-stable
qs 2
0
)2(1
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Differential-rotation decay Differential-rotation decay timetimeversus Reynolds numberversus Reynolds number
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Effect of negative Effect of negative buoyancybuoyancy
Rm = 2·104
Pm = 1Ra = -108
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Effect of negative Effect of negative buoyancybuoyancy
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Differential-rotation decayDifferential-rotation decay Extrapolation to stellar parametersExtrapolation to stellar parameters Decay time of 10-100 million yearsDecay time of 10-100 million years Short compared with the age of the Short compared with the age of the
Sun (5 billion years) Sun (5 billion years) MRI may have MRI may have provided the enormous angular-provided the enormous angular-momentum transport for slow-downmomentum transport for slow-down
Considerable fraction of Ap star ages Considerable fraction of Ap star ages (life-time < 10(life-time < 1099 yr) yr) MRI may still MRI may still bebeoperating in them.operating in them.
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The EndThe End