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

Magneto-rotational instability in the solar core and Ap star envelopes. Rainer Arlt Astrophysikalisches Institut Potsdam and Günther Rüdiger, Rainer Hollerbach. Solar rotational evolution. Wind model by St ępień (1988). The solar tachocline and the core.

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

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  1. Magneto-rotational instability in the solar core and Ap star envelopes Rainer ArltAstrophysikalisches Institut Potsdam and Günther Rüdiger, Rainer Hollerbach

  2. Solar rotational evolution • Wind model by Stępień (1988)

  3. The solar tachocline and the core • Thompson et al. 2003 from various sources

  4. 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

  5. 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?

  6. Magneto-rotational instability • Angular velocity decreasing withaxis distance • Magnetic field or arbitrary geometry • Instability with growth rate of the order of 

  7. 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

  8. Upper limit for MRI Wavelength of most un-stable MRI mode exceeds object size in kG

  9. Numerical simulations • Spherical spectral code (Hollerbach 2000)

  10. Initial conditions • Vertical cut through radiativezone • Left:Magnetic field • Right:Angular velocity

  11. Differential-rotationdecay – close-up Rm = 104Pm = 1Ra = 0

  12. Differential-rotationdecay – close-up

  13. Resolution at high Reynolds number t = 4 rotations t = 8 rotations t = 1 rotation

  14. Resolution at high Reynolds number t = 4 rotations t = 1 rotation t = 8 rotations

  15. Differential-rotation decay • Steepness of rotation profile versus time • Initially • Rayleigh-stable

  16. Differential-rotation decay timeversus Reynolds number

  17. Effect of negative buoyancy Rm = 2·104Pm = 1Ra = -108

  18. Effect of negative buoyancy

  19. 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 < 109 yr)  MRI may still beoperating in them.

  20. The End

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