Prograde patterns in rotating convection and implications for the dynamo

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/drgt0 at bottom ? dW/drlt0
at top
3
Departure from Taylor-Proudman
first pointed out by Durney Roxburgh

lt0
lt0
warmer pole
-
Brandenburg et al. (1992, AA 265, 328)
4
Near-surface shear

• dW/dr lt 0 when ltur2gt gtgt ltuf2gt (Kippenhahn
  1963)
• Expected when radial plumes important

Kitchatinov Rüdiger (2005, AN 326, 379)
5
Application to the sun spots rooted at r/R0.95
Benevolenskaya, Hoeksema, Kosovichev, Scherrer
(1999)
Pulkkinen Tuominen (1998)
DftAZDW(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/drlt0 equatorward migr

7
The path toward the overshoot dynamo scenario

• Since 1980 dynamo at bottom of CZ
• Flux tubes 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
Arguments against and in favor?
Tachocline dynamos
Distributed/near-surface dynamo

• 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.)

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 (Hales 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 0ltzlt1
• 0o latitude
• 4x4x1 aspect ratio
• 512x512x256

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Convection with rotation
Inv. Rossby Nr. 2Wd/urms4 (at bottom, lt1 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
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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 z0.9d
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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
  (lt20m/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 doesnt explain time-distance
  measurements or sunspot proper motion

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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!