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

7

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)

10

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)

11

Cycle Cycle dependencedependence

of of (r,(r,))

12

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

14

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

15

Simulations of near-surface shearSimulations of near-surface shear

4x4x1 aspect ratio512x512x256

0o lat

15o latnegative uyuz stress negative shear

16

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

18

Prograde propagating patternsPrograde propagating patterns),( tyU y

dzdx 9.0 ,2

dgtu y //254at and

Slope: 0.064 (=pattern speed)

19

No relation to interior speedNo relation to interior speed

Prograde pattern speed versus interior speed

20

Not so clear from snapshotsNot so clear from snapshots

Entropyat z=0.9d

21

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

22

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!