prograde patterns in rotating convection and implications for the dynamo axel brandenburg (nordita,...
DESCRIPTION
3 Departure from Taylor-ProudmanTRANSCRIPT
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
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Internal angular velocityInternal angular velocityfrom helioseismologyfrom helioseismology
spoke-like at equ.d/dr>0 at bottom
? d/dr<0 at top
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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)
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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)
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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!
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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!