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uctuations, with
amplitudes of5 m s1, in the meridional
ow that are associated with the but-
ter
y diagram (this pattern was seen in direct Doppler measurements by Ulrich
et al. 1988). As shown in Figure 21 , near the surface these local
uctuations
correspond to
ows converging towards the active latitudes (e.g. Gizon & Rem-
pel 2008, Gonz alez Hern andez et al. 2008). The exact depth where these
ows
change sign is not well known, but at depths of roughly 50 Mm, the component of
the meridional
ow associated with the torsional oscillations converges towards
the active latitudes (e.g. Beck, Gizon & Duvall 2002; Chou & Dai 2001). The
contribution of
ows around individual active regions to the torsional oscillations
and associated meridional
ows will be discussed in Section 7.
Sch ussler (1981) and Yoshimura (1981) suggested that the torsional oscillations
may be caused by the Lorentz force associated with migrating dynamo waves. A
turbulent mean eld dynamo model by Covas et al. (2000), tted to a butter
y
diagram of the solar cycle, shows a Lorentz force-induced torsional oscillation
pattern at the surface resembling the observations. As in other Lorentz-force
models, however, its amplitude increases strongly with depth, in contrast with the
helioseismic measurements. Kitchatinov et al. (1999), building on work by K uker,
R udiger & Pipin (1996), suggested that the torsional oscillations result from the
eect of the magnetic eld on the convective transport of angular momentum.
Another suggested explanation is the reduction of turbulent viscosity in active
regions (Petrovay & Forg acs-dajka 2002).
Spruit (2003) suggested that the torsional oscillations may be a result of
geostrophic
ows set up by enhanced surface cooling in regions of magnetic activ-
ity. Since the driving force in this explanation is at the surface, the velocity signal34 Gizon, Birch & Spruit
produced decreases with depth as observed. Rempel (2007) argued that such a
thermal forcing, rather than mechanical forcing as in the Lorentz-force based
models, is required to explain the observed deviation of the low-latitude torsional
oscillations from a Taylor-Proudman state (zonal velocity constant on cylinders).
Similarly, Gizon & Rempel (2008) suggested that the only current model for the
low-latitude branch of the torsional oscillations and associated meridional
ows
that is qualitatively consistent with the observations is the enhanced cooling
model of Spruit (2003). One complication for models that invoke thermal forc-
ing at the surface is to explain the presence of the torsional oscillations at solar
minimum (Gizon & Rempel 2008). It should be noted that the model of Rempel
(2007) does not require enhanced thermal forcing at high latitudes ( >50) to
explain the poleward-propagating branch of the torsional oscillations. The two
branches of the zonal torsional oscillations may have dierent physical origins.
8.4 Contribution of Active Region Flows to Longitudinal Aver-
ages
An interesting question is whether the localized
ows around active regions (Sec-
tion 7) contribute signicantly to the solar-cycle variation of the longitudinal av-
erages of the dierential rotation and the meridional
ow. The in
ows/out
ows
around active regions could aect the average meridional circulation around the
mean latitude of activity, while the vortical component of the
ows could aect
the average zonal
ows.
In order to study this question, Gizon (2003) selected all regions within 5
of all locations with strong magnetic eld and excluded these regions from the
longitudinal averages of the
ows. The zonal
ows are essentially unaected (ex-
cept for the fact that active regions rotate a little more rapidly than quiet Sun):
localized cyclonic
ows around large active regions do not provide a sucient
explanation for the torsional oscillations. This is not particularly surprising since
torsional oscillations exist at solar minimum, in the absence of active regions. The
torsional oscillations model of Spruit (2003) would have to rely on the thermal
disturbances caused by diuse small-scale magnetic elds, not localized active
regions. On the other hand, Gizon (2003) nds that the in
ows around active
regions appear to be largely responsible for the near-surface solar-cycle depen-
dence of the meridional
ow, at the level of a few m s1. This conclusion has
been challenged however by Gonz alez Hern andez et al. (2008), which indicates
that the answer depends sensitively on the selection of the regions of activity that
are removed from the longitudinal averages.
9 FARSIDE IMAGING
Lindsey & Braun (2000) introduced the concept of farside imaging, in whichLocal Helioseismology 35
observations of the solar oscillations made on the visible disk are used to infer
the presence of active regions on the farside of the Sun. Farside imaging has been
achieved using both holography-based methods (e.g. Lindsey & Braun 2000) and
time-distance helioseismology (Zhao 2007). Hartlep et al. (2008) have successfully
tested farside time-distance helioseismology with numerical simulations.
The conceptual ray geometry for farside imaging is shown in Figure 22a. In
the 2+2 skip geometry, wave packets leave the visible surface, make two skips
in the solar interior (this involves one re
ection from the surface), interact with
possible surface magnetic activity on the farside, make two more skips, and are
then seen again on the front side. The total travel time of the wave packet
is sensitive to the presence of large active regions on the farside. Travel-time
reductions of up to ten seconds are typically observed for large active regions.
By moving the farside target location, a map of the farside magnetic activity
can be constructed. The 2+2 skip geometry is suitable for mapping regions

uctuations, with

amplitudes of5 m s1, in the meridional

ow that are associated with the but-

ter

y diagram (this pattern was seen in direct Doppler measurements by Ulrich

et al. 1988). As shown in Figure 21 , near the surface these local

uctuations

correspond to

ows converging towards the active latitudes (e.g. Gizon & Rem-

pel 2008, Gonz alez Hern andez et al. 2008). The exact depth where these

ows

change sign is not well known, but at depths of roughly 50 Mm, the component of

the meridional

ow associated with the torsional oscillations converges towards

the active latitudes (e.g. Beck, Gizon & Duvall 2002; Chou & Dai 2001). The

contribution of

ows around individual active regions to the torsional oscillations

and associated meridional

ows will be discussed in Section 7.

Sch ussler (1981) and Yoshimura (1981) suggested that the torsional oscillations

may be caused by the Lorentz force associated with migrating dynamo waves. A

turbulent mean eld dynamo model by Covas et al. (2000), tted to a butter

y

diagram of the solar cycle, shows a Lorentz force-induced torsional oscillation

pattern at the surface resembling the observations. As in other Lorentz-force

models, however, its amplitude increases strongly with depth, in contrast with the

helioseismic measurements. Kitchatinov et al. (1999), building on work by K uker,

R udiger & Pipin (1996), suggested that the torsional oscillations result from the

eect of the magnetic eld on the convective transport of angular momentum.

Another suggested explanation is the reduction of turbulent viscosity in active

regions (Petrovay & Forg acs-dajka 2002).

Spruit (2003) suggested that the torsional oscillations may be a result of

geostrophic

ows set up by enhanced surface cooling in regions of magnetic activ-

ity. Since the driving force in this explanation is at the surface, the velocity signal34 Gizon, Birch & Spruit

produced decreases with depth as observed. Rempel (2007) argued that such a

thermal forcing, rather than mechanical forcing as in the Lorentz-force based

models, is required to explain the observed deviation of the low-latitude torsional

oscillations from a Taylor-Proudman state (zonal velocity constant on cylinders).

Similarly, Gizon & Rempel (2008) suggested that the only current model for the

low-latitude branch of the torsional oscillations and associated meridional

ows

that is qualitatively consistent with the observations is the enhanced cooling

model of Spruit (2003). One complication for models that invoke thermal forc-

ing at the surface is to explain the presence of the torsional oscillations at solar

minimum (Gizon & Rempel 2008). It should be noted that the model of Rempel

(2007) does not require enhanced thermal forcing at high latitudes ( >50) to

explain the poleward-propagating branch of the torsional oscillations. The two

branches of the zonal torsional oscillations may have dierent physical origins.

8.4 Contribution of Active Region Flows to Longitudinal Aver-

ages

An interesting question is whether the localized

ows around active regions (Sec-

tion 7) contribute signicantly to the solar-cycle variation of the longitudinal av-

erages of the dierential rotation and the meridional

ow. The in

ows/out

ows

around active regions could aect the average meridional circulation around the

mean latitude of activity, while the vortical component of the

ows could aect

the average zonal

ows.

In order to study this question, Gizon (2003) selected all regions within 5

of all locations with strong magnetic eld and excluded these regions from the

longitudinal averages of the

ows. The zonal

ows are essentially unaected (ex-

cept for the fact that active regions rotate a little more rapidly than quiet Sun):

localized cyclonic

ows around large active regions do not provide a sucient

explanation for the torsional oscillations. This is not particularly surprising since

torsional oscillations exist at solar minimum, in the absence of active regions. The

torsional oscillations model of Spruit (2003) would have to rely on the thermal

disturbances caused by diuse small-scale magnetic elds, not localized active

regions. On the other hand, Gizon (2003) nds that the in

ows around active

regions appear to be largely responsible for the near-surface solar-cycle depen-

dence of the meridional

ow, at the level of a few m s1. This conclusion has

been challenged however by Gonz alez Hern andez et al. (2008), which indicates

that the answer depends sensitively on the selection of the regions of activity that

are removed from the longitudinal averages.

9 FARSIDE IMAGING

Lindsey & Braun (2000) introduced the concept of farside imaging, in whichLocal Helioseismology 35

observations of the solar oscillations made on the visible disk are used to infer

the presence of active regions on the farside of the Sun. Farside imaging has been

achieved using both holography-based methods (e.g. Lindsey & Braun 2000) and

time-distance helioseismology (Zhao 2007). Hartlep et al. (2008) have successfully

tested farside time-distance helioseismology with numerical simulations.

The conceptual ray geometry for farside imaging is shown in Figure 22a. In

the 2+2 skip geometry, wave packets leave the visible surface, make two skips

in the solar interior (this involves one re

ection from the surface), interact with

possible surface magnetic activity on the farside, make two more skips, and are

then seen again on the front side. The total travel time of the wave packet

is sensitive to the presence of large active regions on the farside. Travel-time

reductions of up to ten seconds are typically observed for large active regions.

By moving the farside target location, a map of the farside magnetic activity

can be constructed. The 2+2 skip geometry is suitable for mapping regions