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Prograde patterns in rotating convection and implications for the dynamo

Prograde patterns in rotating convection and implications for the dynamo. Axel Brandenburg (Nordita, Copenhagen  Stockholm ). Taylor-Proudman problem Near-surface shear layer Relation to any interior depth? Prograde pattern speed Pattern speed of supergranulation.

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Prograde patterns in rotating convection and implications for the dynamo

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  1. Prograde patterns in rotating convection and implications for the dynamo Axel Brandenburg (Nordita, Copenhagen  Stockholm) • Taylor-Proudman problem • Near-surface shear layer • Relation to any interior depth? • Prograde pattern speed • Pattern speed of supergranulation

  2. Internal angular velocityfrom helioseismology spoke-like at equ. dW/dr>0 at bottom ? dW/dr<0 at top

  3. Departure from Taylor-Proudman first pointed out by Durney & Roxburgh + <0 <0 warmer pole - Brandenburg et al. (1992, A&A 265, 328)

  4. Near-surface shear • dW/dr < 0 when <ur2> >> <uf2> (Kippenhahn 1963) • Expected when radial plumes important Kitchatinov & Rüdiger (2005, AN 326, 379)

  5. Application to the sun: spots rooted at r/R=0.95 Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998) • Df=tAZDW=(180/p) (1.5x107) (2p 10-8) • =360 x 0.15 = 54 degrees!

  6. In the days before helioseismology • Angular velocity (at 4o latitude): • very young spots: 473 nHz • oldest spots: 462 nHz • Surface plasma: 452 nHz • Conclusion back then: • Sun spins faster in deaper convection zone • Solar dynamo works with dW/dr<0: equatorward migr

  7. The path toward the overshoot dynamo scenario • Since 1980: dynamo at bottom of CZ • Flux tube’s buoyancy neutralized • Slow motions, long time scales • Since 1984: diff rot spoke-like • dW/dr strongest at bottom of CZ • Since 1991: field must be 100 kG • To get the tilt angle right Spiegel & Weiss (1980) Golub, Rosner, Vaiana, & Weiss (1981)

  8. Is magnetic buoyancy a problem? Stratified dynamo simulation in 1990 Expected strong buoyancy losses, but no: downward pumping Tobias et al. (2001)

  9. Magnetic buoyancy for strong tubes Brandenburg et al. (2001)

  10. Flux storage Distortions weak Problems solved with meridional circulation Size of active regions Neg surface shear: equatorward migr. Max radial shear in low latitudes Youngest sunspots: 473 nHz Correct phase relation Strong pumping (Thomas et al.) Arguments against and in favor? Tachocline dynamos Distributed/near-surface dynamo in favor against • 100 kG hard to explain • Tube integrity • Single circulation cell • Too many flux belts* • Max shear at poles* • Phase relation* • 1.3 yr instead of 11 yr at bot • Rapid buoyant loss* • Strong distortions* (Hale’s polarity) • Long term stability of active regions* • No anisotropy of supergranulation Brandenburg (2005, ApJ 625, 539)

  11. Cycle dependenceof W(r,q)

  12. Simulations of near-surface shear Prograde pattern speed, but rather slow (Green & Kosovichev 2006) • Unstable layer in 0<z<1 • 0o latitude • 4x4x1 aspect ratio • 512x512x256

  13. Convection with rotation Inv. Rossby Nr. 2Wd/urms=4 (at bottom, <1 near top)

  14. Vertical velocity profiles Mean flow Ro-1 about 5 at bottom …less than 1 at the top Exactly at equator mean flow monotonous

  15. Simulations of near-surface shear 0o lat 15o lat negative uyuz stress  negative shear 4x4x1 aspect ratio 512x512x256

  16. Explained by Reynolds stress Vanishing total stress (…,+b.c.) negative uyuz stress  negative shear find: good fit parameter:

  17. Horizontal flow pattern y x Stongly retrograde motions Plunge into prograde shock

  18. Prograde propagating patterns Slope: 0.064 (=pattern speed)

  19. No relation to interior speed Prograde pattern speed versus interior speed

  20. Not so clear from snapshots Entropy at z=0.9d

  21. Relation to earlier work • Prograde patterns seen in Doppler measurements of supergranulation • Busse (2004) found prograde patterns from rotating convection with l-hexagons • Green & Kosovichev (2005) found prograde patterns (<20m/s) from radial shear • Toomre et al. reported 3% prograde speed in ASH • Hathaway et al. (2006) explained Doppler measurements as projection effect • But this doesn’t explain time-distance measurements or sunspot proper motion

  22. Conclusions • to avoid Taylor-Proudman  need warm pole • Radial deceleration near surface • Dominance of plumes • Magnetic (and other) tracers • Relation to certain depth? • Negative shear reproduced by simulations • Explained by Reynolds stresses • But strong prograde pattern speed • No relation to any depth!

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