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 velocity from helioseismology spoke-like at equ. d  /dr>0 at bottom ? d  /dr<0 at top

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

4 Near-surface shear d  /dr >> (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)  =  AZ  =(180/  ) (1.5x10 7 ) (2  ) =360 x 0.15 = 54 degrees!

6 In the days before helioseismology Angular velocity (at 4 o 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 d  /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 –d  /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)

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

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

10 Arguments against and in favor? 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.) 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 in favor against Tachocline dynamosDistributed/near-surface dynamo Brandenburg (2005, ApJ 625, 539)

11 Cycle dependence of  (r,  )

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

Convection with rotation Inv. Rossby Nr. 2  d/u rms =4 (at bottom, <1 near top)

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

15 Simulations of near-surface shear 4x4x1 aspect ratio 512x512x256 0 o lat 15 o lat negative u y u z stress  negative shear

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

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

18 Prograde propagating patterns Slope: (=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!