Local
Helioseismology
Laurent Gizon (Stanford)
Outline
Some background
 Time-distance helioseismology:
 Solar-cycle variations of large-scale flows
 Near surface convection
 Sunspots: structure and dynamics

Why is helioseismology useful?
To test the standard model of stellar
structure
 To help understand solar magnetism

Global modes
of resonance
Millions of modes of oscillation
excited by near-surface turbulent
convection.
Acoustic modes with similar wave
speeds probe similar depths.
MDI-SOHO measures
Dopplergrams every minute
since 1996.
Figure: m-averaged medium-l
power spectrum (60-day run).
Mean rotation (GONG & MDI)
Global p-mode frequency shifts
Palle et al.

Frequencies of low-degree
acoustic modes of oscillation
increase with magnetic activity.

Woodard & Noyes (1985) first
notice changes in irradiance
oscillation data (ACRIM).

Confirmed by ground-based fulldisk velocity data (e.g. Bison).

Fractional change of 2x10-4
through the solar cycle.
Freq. shifts are localized in latitude
microHz
medium-l
GONG 1D RLS
Howe et al.
ApJ, 2002
Contours:
Kitt Peak
magnetic data
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Spatially resolved observations: Mt Wilson, GONG, MDI.
Libbrecht & Woodard (1989) showed that frequency shifts must be caused
by near-surface perturbations.
The physics of frequency shifts is not understood. We don’t know how to
separate magnetic from thermal/density perturbations.
Shifts likely to be caused by magnetic perturbations within 2 Mm of the
photosphere (Goldreich, Goode/Dziembowski) or above (Roberts).
Other suggestion: changes in turbulent velocities (Kuhn).
Local helioseismology
The goal is to make 3D images of flows, temperature and density inhomogeneities,
and magnetic field in the solar interior. Local helioseismology includes different
techniques that complement each other (see Gizon & Birch, Living Reviews, submitted).
Time-distance helioseismology (Duvall et al. 1993) is based on measurements of travel
times for wavepackets travelling between any two points on the solar surface.
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Flows along the path break the symmetry between
travel times for waves propagating in opposite
directions
Travel-time difference  flows
Measurements of travel times between all pairs of
points give access to the 3D vector flow field, in
principle.
Local helioseismology is potentially more powerful
than global-mode helioseismology:
 Longitudinal resolution (3D image)
 North-south flows
Time-distance diagram (Duvall)
Correlation between two surface locations versus distance and time-lag.
Near-surface “global” flows
Longitudinal averages from f-mode time-distance helioseismology
Rotation
Meridional circulation
Mean meridional circulation is
poleward in both hemispheres
(~20 m/s at 20 deg latitude)
Important ingredient in some
theories of the solar dynamo.
CONFIRMS
GLOBAL-MODE
HELIOSEISMOLOGY
Directly observed down to
0.8R, so far (Giles 1998).
NEW
INFORMATION
To study solar-cycle
variations: subtract time
average over many years…
Meridional circulation vs. depth
(Giles 2001)
Fractional radius r/R

Inversion of travel times with
mass-conservation constraint
through the whole convection
zone (Giles PhD thesis).

For r/R>0.8 the mean meridional
circulation is poleward in both
hemispheres and peaks around
25 deg latitude.

The data are consistent with a
3 m/s return flow at the base of
the convection zone.
 Hathaway obtains a similar
number from an analysis of
sunspot drifts.
Solar-cycle variation of large-scale flows
Plots of residuals of rotation and meridional circulation after subtraction of a
temporal average. About 50 Mm deep (Beck, Gizon & Duvall, 2002).
Latitude (deg)
Latitude (deg)
Zonal flow residuals (torsional oscillations)
red=prograde
blue= retrograde
Increased differential rotation shear at active
latitudes. First discovered by Howard & Labonte
(1980), agrees with global mode splittings.
May be caused by the back reaction of the
Lorentz force from a propagating dynamo wave
(Schuessler, 1981). [Other explanations exist.]
Meridional flow residuals
Residuals: red=equatorward, green=poleward
At 50 Mm depth, residual north-south flow
diverging from the mean latitude of activity
(agrees with Chou 2001, acoustic imaging).
The opposite is seen near the surface!
(Gizon 2003, Zhao 2003).
Year (19962002)
Residuals MC: longitudinal averages
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(e) surface inflow (5 m/s) TD/RD
(d) deeper outflow (5 m/s) TD
(a) zonal shear (+/- 5 m/s) TD/RD/Global
Near-surface flows around active regions
Local 50 m/s surface flows converging toward active regions (Gizon et al. 2001).
Excellent agreement with ring-diagram analysis (Hindman, Gizon et al. 2004).
 Local inflows responsible for temporal variations of surface meridional flow (Gizon 2004)
At depth of 10-15 Mm: an outflow is observed (Haber et al. 2003, Zhao et al. 2003)
Looks like a toroidal flow pattern around AR: surface outflow and deeper inflow.
Surface inflow consistent with a model by Spruit (2003).
Local flows around AR
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Sketch of near-surface flows from local helioseismology.
(a) Zonal shear. (m) meridional flow.
(b) 30-50 m/s large-scale inflow. (c) super-rotation.
Time-distance and ring analyses are consistent (Hindman et al. 2004).
Note that Spruit’s model predicts the inflow.
Convective flows
Supergranulation
F-mode time-distance
(Duvall & Gizon)
Spatial sampling = 3 Mm
Temporal sampling = 8 hr
Horizontal divergence:
white = divergent flows
black = convergent flows
Wavelike properties of supergranulation
The supergranulation pattern appears to propagate in the form of a modulated travelling
wave (Gizon, Duvall & Schou, 2003, Nature)
The direction of propagation is prograde at the equator, and slightly equatorward of the
prograde direction away from the equator. An analysis in Fourier space enables to
separate the background advective flows from the non-advective wave speed (65 m/s)
dt=24hr
Red: advective flow. Green: motion of magnetic features.
Dashed: Correlation tracking with 24 hr lag.
Supergranulation may be an example of travelling-wave
convection. No explanation yet. Although it is likely that
the influence of rotation (or rotational shear) on convection
is at the origin of this phenomenon (Busse 2003).
Advection of Supergranulation
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Flows introduce a Doppler
shift in the spectrum.
Shown are the longitudinal
averages of zonal and
meridional flows in the
supergranular layer.
Increased differential
rotation shear near AR
North-south residual flow
converging toward AR.
 consistent with nearsurface flows from local
helioseismology
Sunspot seismology?
Complex flow picture.
Not always meaningful…
Gizon et al. 2001
Zhao et al. 2003
Wave-speed anomalies
(Kosovichev 1999)
Far side imaging (Lindsey &Braun)
From MDI pipeline (almost real time)
 Predictive power
Flares produce sunquakes
(Kosovichev & Zharkova)
Linear forward and inverse problems
in local helioseismology
Linear sensitivity of travel time to small steady changes in the solar model:
In principle, have to consider all possible types ( ) of perturbations, including
flows, temperature, density, magnetic field, damping and excitation…
A general recipe for computing kernels must include a physical description of the
wave field generated by a stochastic source model and the details of the
measurement procedure (Gizon & Birch 2002). Linearization is achieved through
the Born or Rytov approximations (single-scattering). Done for sound-speed
perturbations (Birch et al. 2004). Need to do it for other types of perturbations
In short, we have a linear system t i  K ijm j  ni . The inverse problem is solving for m j .
Various technique s exist (e.g. Kosovichev 1996, Jensen 2001, Hughes 2003) . The answer
depends on the noise covariance matrix M ij  E[ni n j ], which can be estimated directly from
the data (Jensen et al. 2003) or calculated from a model (Gizon & Birch 2004).
Still some very hard problems to solve…
P-mode Born sensitivity kernel for
sound-speed perturbations (Birch 2004)
Toy problem : sound-speed only
(Couvidat et al. 2004)
Cut through 3D input
sound-speed perturbation
1)
2)
3)
4)
3D Inversion assuming
no correlation in data errors
3D Inversion taking account
of correlations in data errors
Known input sound speed perturbations
Compute travel times by convolution of (1) with 3D Born kernels.
Add noise to the data with the correct statistics (T=8 hrs).
3D multi-channel deconvolution
Conclusion
Complex flow patterns evolving with the solar
cycle in the near-surface shear layer.
Are these flows a secondary manifestation of
the solar dynamo, or do they play an
important role in the organization of solar
magnetic fields?