220 likes | 251 Views
Understanding the impact of magneto-rotational instability in the solar core and Ap star envelopes through differential-rotation decay and numerical simulations. Investigating how MRI may influence internal rotation in the Sun and Ap stars.
E N D
Magneto-rotational instability in the solar core and Ap star envelopes Rainer ArltAstrophysikalisches Institut Potsdam and Günther Rüdiger, Rainer Hollerbach
Solar rotational evolution • Wind model by Stępień (1988)
The solar tachocline and the core • Thompson et al. 2003 from various sources
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
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?
Magneto-rotational instability • Angular velocity decreasing withaxis distance • Magnetic field or arbitrary geometry • Instability with growth rate of the order of
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
Upper limit for MRI Wavelength of most un-stable MRI mode exceeds object size in kG
Numerical simulations • Spherical spectral code (Hollerbach 2000)
Initial conditions • Vertical cut through radiativezone • Left:Magnetic field • Right:Angular velocity
Differential-rotationdecay – close-up Rm = 104Pm = 1Ra = 0
Resolution at high Reynolds number t = 4 rotations t = 8 rotations t = 1 rotation
Resolution at high Reynolds number t = 4 rotations t = 1 rotation t = 8 rotations
Differential-rotation decay • Steepness of rotation profile versus time • Initially • Rayleigh-stable
Effect of negative buoyancy Rm = 2·104Pm = 1Ra = -108
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.