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can count as a major success story in solar physics. It adds condence in our
numerical methods and in our understanding of the physics of solar magnetic
activity.
There are many complications in local helioseismology that have not been
studied in detail, e.g. instrumental artifacts (point spread function, astigmatism,
plate scale), interpretation of the observable (e.g., ltergrams used to construct
Dopplergrams) in terms of physical conditions in the solar atmosphere, center-58 Gizon, Birch & Spruit
to-limb eects such as foreshortening, and light-of-sight projection of the solar
velocity. Other complications are related to the physics of wave propagation, e.g.
surface magnetic eects, scattering by time-varying heterogeneities (turbulence),
multiple scattering, and physical description of wave excitation and attenuation.
Understanding and, in some cases, correcting for these issues is needed to ap-
ply local helioseismology to challenging problems: deep meridional circulation
(Braun & Birch 2008), detecting subsurface emerging active regions, high lati-
tudes, statistical description of turbulent
ows (e.g. Reynolds stresses), etc. In
addition, inferring small amplitude perturbations in the solar interior may re-
quire may years of observations and/or appropriate spatial/temporal averaging
to optimize signal-to-noise ratio.
Finally, it is worth exploring the many connections between the results of local
helioseismology and global-mode helioseismology: for example, the contribution
of active regions to the temporal variations of low-degree mode frequencies, com-
parisons of rotation measurements (e.g., 1 :3-year tachocline oscillations), deep
sound speed anomalies (Zhao et al. 2009), and seismic radii (Gonz alez Hern andez,
Scherrer & Hill 2009; Kholikov & Hill 2008). In principle, local helioseismology
should help provide improve surface boundary conditions for global-mode inver-
sions.
SUMMARY POINTS
1. Local helioseismology shows that supergranules are characterized by
200 m s1horizontal out
ows and 20 m s1up
ows near the surface. Mag-
netic eld concentrations are observed at the boundaries of supergranules
and the inclined eld provides portals through which low-frequency waves
propagate into the chromosphere. The correlation between the horizontal
divergence of the
ow and the vertical component of vorticity has been
measured as a function of latitude: cyclonic convection is explained by the
eect of the Coriolis force. The pattern of supergranulation has (unex-
plained) wave-like properties.
2. The amplitudes, phases, and frequencies of the solar waves are strongly
aected by sunspots. Sunspots \absorb" a fraction of the ingoing waves
as they partially convert into downward propagating slow MHD waves.
Sunspots are surrounded by a horizontal out
ow (several hundred m s1)
in an annular region extending as far as twice the penumbral radius. This
moat
ow, which persists at least in the top 4 Mm, is consistent with di-
rect observations of the solar surface. Little is known about the subsurface
magnetic and thermal structure of sunspots. Forward modeling of the he-
lioseismic wave eld requires a surface eld of several kG. Multi-height ob-
servations of solar oscillations have been used to map the sunspot magnetic
canopy.Local Helioseismology 59
3. Local helioseismology has conrmed the latitudinal dierential rotation and
the increase of rotation with depth in the top 35 Mm of the convection
zone (near-surface shear layer). Flows in meridional planes have been mea-
sured by local helioseismology in the top 50 Mm. For latitudes less than
45, the longitudinal component of the
ow is poleward, with a maximum
amplitude of 15 m s1. It is not clear whether the meridional
ow can be
detected reliably deeper or at higher latitudes.
4. The solar-cycle variation of rotation has been conrmed: bands of faster
and slower rotation ( 10 m s1) migrate in latitude with magnetic activity.
In addition, local helioseismology has revealed that the longitudinal-average
of the meridional
ow also varies with the solar cycle ( 5 m s1), i.e. by
a signicant fraction of its mean value. Near the surface, the time residu-
als are consistent with a North-South in
ow around the mean latitude of
activity. At a depth of 50 Mm, the residuals are consistent with a small
out
ow.
5. On intermediate scales ( 20) weak horizontal in
ows ( 50 m s1) have
been detected around complexes of magnetic activity, near the surface. If
conrmed, these
ows may explain the time evolution of the longitudinal
average of the meridional
ow. At greater depths ( >10 Mm) the horizontal

ows appear to switch sign and diverge from centers of magnetic activity
(50 m s1). In addition, the surface in
ows are associated with cyclonic
vorticity.
6. Farside helioseismology works. Large active regions can be detected on
the invisible hemisphere of the Sun, thus providing advanced warning of
energetic particle events, days before they occur on the front side.
FUTURE ISSUES
1. The most pressing issue in local helioseismology is how to interpret mag-
netic eects, which requires new methods of analysis. This is illustrated by
the fact that the standard methods of analysis yield con
icting inferences
regarding sunspot structure and dynamics (see e.g. Figure 16 ). The way
forward is to develop methods that incorporate appropriate physical mod-
els of the interaction of waves with strong magnetic elds near the surface.
Surface magnetic eects must be accounted for before we can detect and
study the magnetic eld below the photosphere.
2. Instrumental artifacts often dominate realization noise and hamper the
study of weak perturbations in the Sun. Ever-improving instrumenta-

can count as a major success story in solar physics. It adds condence in our

numerical methods and in our understanding of the physics of solar magnetic

activity.

There are many complications in local helioseismology that have not been

studied in detail, e.g. instrumental artifacts (point spread function, astigmatism,

plate scale), interpretation of the observable (e.g., ltergrams used to construct

Dopplergrams) in terms of physical conditions in the solar atmosphere, center-58 Gizon, Birch & Spruit

to-limb eects such as foreshortening, and light-of-sight projection of the solar

velocity. Other complications are related to the physics of wave propagation, e.g.

surface magnetic eects, scattering by time-varying heterogeneities (turbulence),

multiple scattering, and physical description of wave excitation and attenuation.

Understanding and, in some cases, correcting for these issues is needed to ap-

ply local helioseismology to challenging problems: deep meridional circulation

(Braun & Birch 2008), detecting subsurface emerging active regions, high lati-

tudes, statistical description of turbulent

ows (e.g. Reynolds stresses), etc. In

addition, inferring small amplitude perturbations in the solar interior may re-

quire may years of observations and/or appropriate spatial/temporal averaging

to optimize signal-to-noise ratio.

Finally, it is worth exploring the many connections between the results of local

helioseismology and global-mode helioseismology: for example, the contribution

of active regions to the temporal variations of low-degree mode frequencies, com-

parisons of rotation measurements (e.g., 1 :3-year tachocline oscillations), deep

sound speed anomalies (Zhao et al. 2009), and seismic radii (Gonz alez Hern andez,

Scherrer & Hill 2009; Kholikov & Hill 2008). In principle, local helioseismology

should help provide improve surface boundary conditions for global-mode inver-

sions.

SUMMARY POINTS

1. Local helioseismology shows that supergranules are characterized by

200 m s1horizontal out

ows and 20 m s1up

ows near the surface. Mag-

netic eld concentrations are observed at the boundaries of supergranules

and the inclined eld provides portals through which low-frequency waves

propagate into the chromosphere. The correlation between the horizontal

divergence of the

ow and the vertical component of vorticity has been

measured as a function of latitude: cyclonic convection is explained by the

eect of the Coriolis force. The pattern of supergranulation has (unex-

plained) wave-like properties.

2. The amplitudes, phases, and frequencies of the solar waves are strongly

aected by sunspots. Sunspots \absorb" a fraction of the ingoing waves

as they partially convert into downward propagating slow MHD waves.

Sunspots are surrounded by a horizontal out

ow (several hundred m s1)

in an annular region extending as far as twice the penumbral radius. This

moat

ow, which persists at least in the top 4 Mm, is consistent with di-

rect observations of the solar surface. Little is known about the subsurface

magnetic and thermal structure of sunspots. Forward modeling of the he-

lioseismic wave eld requires a surface eld of several kG. Multi-height ob-

servations of solar oscillations have been used to map the sunspot magnetic

canopy.Local Helioseismology 59

3. Local helioseismology has conrmed the latitudinal dierential rotation and

the increase of rotation with depth in the top 35 Mm of the convection

zone (near-surface shear layer). Flows in meridional planes have been mea-

sured by local helioseismology in the top 50 Mm. For latitudes less than

45, the longitudinal component of the

ow is poleward, with a maximum

amplitude of 15 m s1. It is not clear whether the meridional

ow can be

detected reliably deeper or at higher latitudes.

4. The solar-cycle variation of rotation has been conrmed: bands of faster

and slower rotation ( 10 m s1) migrate in latitude with magnetic activity.

In addition, local helioseismology has revealed that the longitudinal-average

of the meridional

ow also varies with the solar cycle ( 5 m s1), i.e. by

a signicant fraction of its mean value. Near the surface, the time residu-

als are consistent with a North-South in

ow around the mean latitude of

activity. At a depth of 50 Mm, the residuals are consistent with a small

out

ow.

5. On intermediate scales ( 20) weak horizontal in

ows ( 50 m s1) have

been detected around complexes of magnetic activity, near the surface. If

conrmed, these

ows may explain the time evolution of the longitudinal

average of the meridional

ow. At greater depths ( >10 Mm) the horizontal

ows appear to switch sign and diverge from centers of magnetic activity

(50 m s1). In addition, the surface in

ows are associated with cyclonic

vorticity.

6. Farside helioseismology works. Large active regions can be detected on

the invisible hemisphere of the Sun, thus providing advanced warning of

energetic particle events, days before they occur on the front side.

FUTURE ISSUES

1. The most pressing issue in local helioseismology is how to interpret mag-

netic eects, which requires new methods of analysis. This is illustrated by

the fact that the standard methods of analysis yield con

icting inferences

regarding sunspot structure and dynamics (see e.g. Figure 16 ). The way

forward is to develop methods that incorporate appropriate physical mod-

els of the interaction of waves with strong magnetic elds near the surface.

Surface magnetic eects must be accounted for before we can detect and

study the magnetic eld below the photosphere.

2. Instrumental artifacts often dominate realization noise and hamper the

study of weak perturbations in the Sun. Ever-improving instrumenta-