prograde patterns in rotating convection and implications for the dynamo axel brandenburg (nordita,...

Prograde patterns in rotating Prograde patterns in rotating convection and convection and

implications for the dynamoimplications for the dynamoAxel BrandenburgAxel Brandenburg (Nordita, Copenhagen (Nordita, Copenhagen Stockholm) Stockholm)

• Taylor-Proudman problem• Near-surface shear layer• Relation to any interior depth?• Prograde pattern speed

• Pattern speed of supergranulation

2

Internal angular velocityInternal angular velocityfrom helioseismologyfrom helioseismology

spoke-like at equ.d/dr>0 at bottom

? d/dr<0 at top

3

Departure from Taylor-ProudmanDeparture from Taylor-Proudman 02 uΩ

02 uΩ 02 STuΩ

SThp 1

STz

ˆ2

02

z

012

S

rT

rz

<0 <0+

-

Brandenburg et al. (1992, A&A 265, 328)

warmerpole

first pointed out by Durney & Roxburgh

sTF jiji (conv)

4

Near-surface shearNear-surface shear

• d/dr < 0 when <ur2> >> <u

2> (Kippenhahn 1963)

• Expected when radial plumes important

Kitchatinov & Rüdiger (2005, AN 326, 379)

5

Application to the sun: spots rooted at Application to the sun: spots rooted at r/Rr/R=0.95=0.95

Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998)

nHz 473/360024360

/7.14

dsd

o

o

=AZ=(180/) (1.5x107) (210-8)

=360 x 0.15 = 54 degrees!

6

In the days before In the days before helioseismologyhelioseismology

• 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 d/dr<0: equatorward migr

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The path toward the The path toward the overshoot dynamo scenarioovershoot 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?Is magnetic buoyancy a problem?

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

Magnetic buoyancy for strong tubesMagnetic buoyancy for strong tubes

Brandenburg et al. (2001)

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Arguments against and in favor?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 dynamos Distributed/near-surface dynamo

Brandenburg (2005, ApJ 625, 539)

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Cycle Cycle dependencedependence

of of (r,(r,))

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Simulations of near-surface shearSimulations of near-surface shear

• Unstable layer in 0<z<1• 0o latitude• 4x4x1 aspect ratio• 512x512x256

Prograde pattern speed, but rather slow(Green & Kosovichev 2006)

Convection with rotationConvection with rotation

Inv. Rossby Nr. 2d/urms=4(at bottom, <1 near top) 7102Ra

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Vertical velocity profiles Vertical velocity profiles

ip uH /2Ro 1

Ro-1 about 5 at bottom…less than 1 at the top

Mean flow

Exactly at equatormean flow monotonous

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Simulations of near-surface shearSimulations of near-surface shear

4x4x1 aspect ratio512x512x256

0o lat

15o latnegative uyuz stress negative shear

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Explained by Reynolds stressExplained by Reynolds stress

negative uyuz stress negative shear

0

zU

uu ytzy

Vanishingtotal stress(…,+b.c.)

5.0/ zU y

30t

find:

good fit parameter:

Horizontal flow patternHorizontal flow pattern

Stongly retrograde motionsPlunge into prograde shock

yx

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Prograde propagating patternsPrograde propagating patterns),( tyU y

dzdx 9.0 ,2

dgtu y //254at and

Slope: 0.064 (=pattern speed)

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No relation to interior speedNo relation to interior speed

Prograde pattern speed versus interior speed

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Not so clear from snapshotsNot so clear from snapshots

Entropyat z=0.9d

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Relation to earlier workRelation 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

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ConclusionsConclusions• 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!