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The Sun’s internal rotation. Michael Thompson University of Sheffield [email protected]. Global-mode seismology. Measure mode properties ω ; A, Γ ; line-shapes Eigenfunctions / spherical harmonics. Frequencies ω nlm (t) depend on conditions in solar - PowerPoint PPT Presentation
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Global-mode seismology
Measure mode properties ω; A, Γ; line-shapesEigenfunctions / spherical harmonics
Frequencies ωnlm(t) depend on conditions in solar interior determining wave propagation
ωnlm – degeneracy lifted by rotation and by structural asphericities and magnetic fields
Inversion provides maps such as of c and ρ and rotation and wave-speed asphericities
North-south averagesSnapshots at successive times: typically 2-month averages
Spherical harmonics
Data from space – in particular from three instruments on the SOHO sateliteSOI-MDIGOLFVIRGO
Data from ground-basednetworks, in particularGONG, BiSON, LOWL GONG network sites
Radial Stratification
Sound speed profile
Temperature
/12 Tc
(Sound speed is in units of hundreds of km/s)
Helioseismic determination of location of base of convection zone at 0.713 +/- 0.003 R (Christensen-Dalsgaard et al. 1991). No temporal or latitudinal variation in this location (Basu & Antia 2001).
Note that this measures the extent of the essentially adiabaticallystratified region. Sun’s transition smoother than in models.
Christensen-Dalsgaard (2004)
Sun minus model
New model(Z=0.015)
Old model(Z=0.020)
Old ‘standard’ Model S (Christensen-Dalsgaard et al. 1996)left little room for overshoot – near-perfect match to depth ofSun’s convection zone. But newly determined abundancesgive a model with 1-2% shallower convection zone. (See Basu & Antia 2004; Bahcall et al. 2004 submitted; C-D 2004)
Mean internal rotation
Rotation rate inferred from MDI data using two different analysis techniques
Radial cuts through inferred rotation profile of the solar interior (at latitudes indicated)
Dashed lines are at 25 degrees to polar axis – a better match to the isorotation contours than radial lines (or Taylor columns!)
Rotation rate in the deeper interior
(LOWL + BiSON data)Fast core strongly ruled out (unless very small). Possibly slightly slow core rotation. But inversionsconsistent with uniform rotation in deep interior.
The Tachocline
Artificial data Solar data
Charbonneau et al. (1999)
Kosovichev (1996) – fit to early data, characterizing the tachocline transition with the function
0.5{ 1 + erf [2 ( r - r0 ) / w ] }
Obtained width w = (0.09+/-0.05)R and central locationr0 = (0.692+/-0.005)R, i.e. just beneath base of convection zone.
More recent analyses have typically yielded substantially smaller width, e.g. Charbonneau et al. (1999):width w = (0.039+/-0.013)RPosition r0 = (0.693+/-0.002)R at equator.Prolate with location different by (0.024+/-0.004)R at 60 degrees.
Extent of prolateness confirmed by Basu & Antia (2001), whofurther found no temporal variation in the tachocline properties.
Near-surface shear layer
Near-surface rotation rate from inversion of f-mode splittings
Mean shear gradient as function of latitude
Logarithmic derivative
Logarithmic derivative
Gradient using only l<250 f modes
Conclusion: Rotational gradient negative (logarithmic derivative approx. -1) at low-/mid-latitudes. Vanishes just above 50 degrees latitude.Small or positive gradient in shallow layer at high latitude.
High-latitude jet (Schou et al. 1998)Evidence weak – could be real buttime-dependent.
Jet at 75 degreesapparent in RLSinversion of first144-days of MDI data.
Mean Angular Velocity in 3-D ModelsMean Angular Velocity in 3-D Models
REASONABLEREASONABLECONTACT WITHCONTACT WITHHELIOSEISMICHELIOSEISMICDEDUCTIONSDEDUCTIONS
Case ABCase ABBrun & ToomreBrun & Toomre
Courtesy J. Toomre
Angular Momentum BalanceAngular Momentum Balance
REYNOLDS STRESSESREYNOLDS STRESSES (R) transport angular momentum TOWARD equator, unlike (R) transport angular momentum TOWARD equator, unlike MERIDIONAL CIRCULATIONMERIDIONAL CIRCULATION (MC) SLOW POLES from weak MC at high latitudes (MC) SLOW POLES from weak MC at high latitudes
RR
MCMC
RR
MCMCVV
VV
totaltotal totaltotalMERIDIONALMERIDIONALCIRCULATIONCIRCULATION
Poleward flowPoleward flowat equatorat equator
Courtesy J. Toomre
Temporal variations of the Sun’s internal rotation
1986 2000
Torsional oscillations (Howard & LaBonte 1980)
Evolution of surface velocity field (upper panel) and surface magnetic field (lower panel)
Ulrich 2001
Torsional oscillations of whole convection zone
Differencing rotation inversions relative to solar minimum (1996) at successive 72-day epochs reveals the torsional oscillations at low and high latitudes through much of theconvection zone.
It is also revealing to stack fewer results, so the evolution of the whole convection zone can be seen. Here we difference rotation inversions relative to solar minimum at successive 1-year epochs.
Variation of rotation at fixed depth (3 different inversions)
GONGRLS
MDIRLS
MDIOLA
0.99 R 0.95 R 0.90 R 0.84 R
0.99 R
0.95 R
0.90 R
0.84 R
Equator 30o 60o 75o
Systematic variations – consistent between analyses
Howeet al.(2004)
Variation of rotation at fixed depth (3 different inversions)
30o 45o15oEquator
GONG
MDI
MDI
0.8 R
0.9 R
Flows inferred with ring-diagram analysis (10 Mm deep)
Haber et al.
1999
1997
Longitudinal averages of flows from ring-diagram analysis
Zonal flowsat 1 Mm and 7 Mm depth(note torsional oscillation)
Meridional flowsMostly poleward but with transientcounter-cell in N hemisphere
Comparison of near-surface torsional oscillation flow from global analysis (contours) and ring analysis(coloured shading) – symmetrized.
SSW and Active Complex 9393
7 Mm7 Mm
16 Mm16 Mm
Flows near and beneath active region Apr 2001
Phase of variations in the CZ
(A) Amplitude and ( B) phase of 11-year harmonic fit
(C) 22-yr extrapolation as function of latitude; with residuals also shown
(D) 22-yr extrapolation as function of depth; with residuals also shown
Comparison of phase of variations with isorotation contours(nb different colour scheme)
Constant-phase surfaces tend to align with contours of constant rotation.
Summary: Variability in the convection zone
Komm et al. 2003
Angular momentum variations
Aug 2002May 1996
Evolving of zonal flows
Vorontsov et al. 2002
Torsional oscillations – what is relation to magnetic field?
Whole convection zone involvedStrong evolution at high latitude
Physical understanding of the phase propagation of perturbations through the convection zone?
Role of polar open field-lines?
Variability in and near the tachocline
Rotation residuals show a quasi-periodic 1.3-yr variation at low latitudes (Howe et al. 2000).
Boberg et al. 2002
Solar mean magnetic field
1975 2000
Wavelet analysis of the Sun’s mean photospheric magnetic field: prominent periods are the rotation period and its 2nd harmonic, and the 1.3/1.4-yr period
0 11 22
Toroidal magnetic field strength Angular velocity variationsTime (yrs)
Lat
itud
e
Equator
Time (yrs)
0 11 22 D
ep
th
Surface
CZ base
The evolution of the angular velocity and the magnetic field arecoupled.
Results of Covas et al. (2000, 2001) model (spatio-temporal fragmentation):
Summary: variability in and near tachocline
Howe et al. 2000
1996 2002
Variations in Ω ( r , θ ; t )1.3-yr variations in inferred rotation rate at low latitudes above and beneath tachocline
Signature of dynamo field evolution?Radiative interior also involved in solar cycle?
Link between tachocline and 1.3/1.4-yr variations in • solar wind, • aurorae,• solar mean magnetic field ?
Some questions
• What further constraints on tachocline / c.z. base would be useful?
• Is comparison of variability in c.z. between Sun and numerical models worthwhile?
• What determines the phase propagation of variations in the c.z.?
• What is the nature of the torsional oscillation? What causes the high-latitude variability?