Magnetorotational instability in the solar core and Ap star envelopes

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Magneto-rotational instability in the solar core
and Ap star envelopes

• Rainer ArltAstrophysikalisches Institut Potsdam
• and Günther Rüdiger, Rainer Hollerbach

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Solar rotational evolution

• Wind model by Stepien (1988)

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The solar tachocline and the core

• Thompson et al. 2003 from various sources

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Stellar radiative envelopes

• Star of spectral type A and B
• Small convective core
• Extensive radiative zone
• 10 of these starshave magnetic fields
• These 10 are slowrotators

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Differential-rotation decay

• Rotation of solar core is slow and uniform
• Rotation period has increased by factor of 10
  during life
• Viscosity too small to reduce rotation
  homogeneously throughout the Sun
• Magnetic Ap stars rotate much slower than
  normal A stars
• Did MRI reduce the internal rotation of Sun and
  Ap stars?

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Magneto-rotational instability

• Angular velocity decreasing withaxis distance
• Magnetic field or arbitrary geometry
• Instability with growth rate of the order of ?

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Lower limit for MRI
k 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 MRI
Wavelength of most un-stable MRI mode exceeds
object size
in kG
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Numerical simulations

• Spherical spectral code (Hollerbach 2000)

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Initial conditions

• Vertical cut through radiativezone
• LeftMagnetic field
• RightAngular velocity

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Differential-rotationdecay close-up
Rm 104Pm 1Ra 0
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Differential-rotationdecay close-up
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Resolution at high Reynolds number
t 4 rotations
t 8 rotations
t 1 rotation
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Resolution at high Reynolds number
t 4 rotations
t 1 rotation
t 8 rotations
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Differential-rotation decay

• Steepness of rotation profile versus time
• Initially
• Rayleigh-stable

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Differential-rotation decay timeversus Reynolds
number
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Effect of negative buoyancy
Rm 2104Pm 1Ra -108
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Effect of negative buoyancy
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Differential-rotation decay

• Extrapolation to stellar parameters
• Decay time of 10-100 million years
• Short compared with the age of the Sun (5 billion
  years) ? MRI may have provided the enormous
  angular-momentum transport for slow-down
• Considerable fraction of Ap star ages (life-time
  lt 109 yr) ? MRI may still beoperating in them.

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The End