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Attempts at improved quantitative results suer from arbitrarily tunable param-
eters.
Cyclonic convection is a means to generate poloidal eld from toroidal eld and
is thus important in many dynamo models (for a recent review see Charbonneau
2005). In these models, the sign of the kinetic helicity Hkin=hu(r^u)ide-
termines the strength (and sign) of this eect. Helioseismic measurements imply
that the kinetic helicity at supergranulation scales is negative in the northern
hemisphere (and positive in the south). This is an estimate rather than a direct
measurement because the horizontal components of the vorticity have not yet
been measured directly.
5.3 Evolution of Supergranulation Pattern
Gizon, Duvall & Schou (2003) studied the Fourier spectrum of long time se-
ries of maps of the horizontal divergence of the
ows at supergranulation scales,
measured using f-mode time-distance helioseismology. The observations reveal
surprising characteristics: the signal has wavelike properties (period around 6
days) and power is anisotropic (excess power in the prograde and equatorward
directions). These observations have been conrmed independently by Zhao (pri-
vate communication) and Braun (private communication) using p-mode helio-
seismology. The power peaks at a non-zero frequency that increases slightly with
horizontal wavenumber. Measurements of the Doppler shift of this apparent dis-
persion relation has provided a robust method for measuring the rotation and
meridional
ow of the solar plasma (Gizon, Duvall & Schou 2003; Gizon & Rem-
pel 2008). An interesting aspect of this work is that the inferred rotation and the
meridional
ow match the motion of the small magnetic features (e.g. Komm,
Howard & Harvey 1993a,b). On the other hand, correlation tracking measure-
ments applied to the divergence maps overestimate rotation and underestimate
the meridional
ow by large amounts (see Gizon & Birch 2005). The time evolu-
tion of the supergranulation pattern does not re
ect its advection by the plasma

ow, although the two can be decoupled in Fourier space.
We note that Hathaway, Williams & Cuntz (2006) demonstrated that the local
correlation tracking of Doppler features on the Sun gives biased estimates of the
rotation rate because of line-of-sight projection eects. This case, however, is
not directly comparable to the observations described above since helioseismic
divergence maps are not expected to be sensitive to line-of-sight projection eects
at supergranulation scales.
The helioseismic observations of the wavelike properties of supergranulation
are still calling for an explanation. Supergranulation may perhaps be related to
the traveling convection modes seen in idealized systems with rotation (e.g. Busse26 Gizon, Birch & Spruit
2007).
6 SUNSPOTS
In this section we discuss inferred
ows in the immediate vicinity of sunspots
(Section 6.2), the absorption of waves by sunspots (Section 6.3), and the sub-
surface structure of sunpots (Section 6.4). Recent reviews about sunspots are
provided by, e.g., Solanki (2003) and Moradi et al. (2009, submitted).
The absence of a suciently conclusive theory has allowed a wide range of
ideas about the origin and structure of sunspots to develop. These range all the
way from intuitive ideas directly inspired by the abundant observational clues,
to mathematically oriented ones that require ignoring almost all of these clues.
Some of the ideas should become testable if they make relevant predictions for
the relatively shallow layers below the surface that are accessible to local helio-
seismology methods.
6.1 The Anchoring Problem
The magnetic forces exerted by the spot on its surroundings are signicant. If
it were not in a quasi-stable equilibrium in its observable layers, a spot would
evolve on the time for the Alfv en speed to cross the size of the spot (on the order
of an hour), much shorter than the observed life times of spots (days to weeks).
The magnetic forces also make the sunspot plasma buoyant. Together, this gives
rise to an 'anchoring problem' (cf. Parker 1979). A sunspot cannot be just a
surface phenomenon since magnetic eld lines have no ends. The sunspot's eld
lines continue below the surface. In contrast with a scalar eld like pressure,
the magnetic eld of a sunspot cannot be kept in equilibrium simply by pressure
balance at the surface: the tension in the magnetic eld lines continuing below
the surface exerts forces as well. The magnetic tension acting at the base of
the spot keeps it together and prevents buoyancy from spreading it like an oil
slick over the solar surface. Sunspots also rotate faster than the solar surface,
indicating that they sense the increase of rotation with depth.
The question of sunspot equilibrium thus involves deeper layers, down to wher-
ever the eld lines continue. At which depth and by which agent is the sunspot

ux bundle kept together? A very stable location is the boundary of the convec-
tion zone with the stably stratied radiative interior of the Sun. A layer of mag-
netic eld
oating on this boundary becomes unstable only at a eld strength of
about 105G (Sch ussler et al. 1994). The existence of such a critical eld strength
was hypothesized by Babcock (1961). The subsequent rise to the surface is what
creates the observed bipolar active regions, as proposed by Cowling (1953). The
action of the Coriolis force on
ows in the magnetic eld associated with the
instability produces the poloidal eld of the next cycle, and is observable on theLocal Helioseismology 27
surface in the form of the systematic tilt of active region axes with respect to the
azimuthal direction (Leighton 1969). A boost of condence has been provided
by recent realistic 3D radiative MHD simulations of the last stages of the emer-
gence process of magnetic elds at the surface. These are beginning to look much
like real observations (Cheung et al. 2008). Though largely qualitative, the view
of the solar cycle developed by Babcock and Leighton appears to be the most
fruitful frame of reference for interpreting the solar cycle.
6.2 Moat Flow
In the photosphere, sunspots are typically surrounded by diverging horizontal
out
ows, termed moat
ows, with amplitudes of several hundred m s1. These
out
ows typically extend to about twice the radius of the penumbra. Moat

Attempts at improved quantitative results suer from arbitrarily tunable param-

eters.

Cyclonic convection is a means to generate poloidal eld from toroidal eld and

is thus important in many dynamo models (for a recent review see Charbonneau

2005). In these models, the sign of the kinetic helicity Hkin=hu(r^u)ide-

termines the strength (and sign) of this eect. Helioseismic measurements imply

that the kinetic helicity at supergranulation scales is negative in the northern

hemisphere (and positive in the south). This is an estimate rather than a direct

measurement because the horizontal components of the vorticity have not yet

been measured directly.

5.3 Evolution of Supergranulation Pattern

Gizon, Duvall & Schou (2003) studied the Fourier spectrum of long time se-

ries of maps of the horizontal divergence of the

ows at supergranulation scales,

measured using f-mode time-distance helioseismology. The observations reveal

surprising characteristics: the signal has wavelike properties (period around 6

days) and power is anisotropic (excess power in the prograde and equatorward

directions). These observations have been conrmed independently by Zhao (pri-

vate communication) and Braun (private communication) using p-mode helio-

seismology. The power peaks at a non-zero frequency that increases slightly with

horizontal wavenumber. Measurements of the Doppler shift of this apparent dis-

persion relation has provided a robust method for measuring the rotation and

meridional

ow of the solar plasma (Gizon, Duvall & Schou 2003; Gizon & Rem-

pel 2008). An interesting aspect of this work is that the inferred rotation and the

meridional

ow match the motion of the small magnetic features (e.g. Komm,

Howard & Harvey 1993a,b). On the other hand, correlation tracking measure-

ments applied to the divergence maps overestimate rotation and underestimate

the meridional

ow by large amounts (see Gizon & Birch 2005). The time evolu-

tion of the supergranulation pattern does not re

ect its advection by the plasma

ow, although the two can be decoupled in Fourier space.

We note that Hathaway, Williams & Cuntz (2006) demonstrated that the local

correlation tracking of Doppler features on the Sun gives biased estimates of the

rotation rate because of line-of-sight projection eects. This case, however, is

not directly comparable to the observations described above since helioseismic

divergence maps are not expected to be sensitive to line-of-sight projection eects

at supergranulation scales.

The helioseismic observations of the wavelike properties of supergranulation

are still calling for an explanation. Supergranulation may perhaps be related to

the traveling convection modes seen in idealized systems with rotation (e.g. Busse26 Gizon, Birch & Spruit

2007).

6 SUNSPOTS

In this section we discuss inferred

ows in the immediate vicinity of sunspots

(Section 6.2), the absorption of waves by sunspots (Section 6.3), and the sub-

surface structure of sunpots (Section 6.4). Recent reviews about sunspots are

provided by, e.g., Solanki (2003) and Moradi et al. (2009, submitted).

The absence of a suciently conclusive theory has allowed a wide range of

ideas about the origin and structure of sunspots to develop. These range all the

way from intuitive ideas directly inspired by the abundant observational clues,

to mathematically oriented ones that require ignoring almost all of these clues.

Some of the ideas should become testable if they make relevant predictions for

the relatively shallow layers below the surface that are accessible to local helio-

seismology methods.

6.1 The Anchoring Problem

The magnetic forces exerted by the spot on its surroundings are signicant. If

it were not in a quasi-stable equilibrium in its observable layers, a spot would

evolve on the time for the Alfv en speed to cross the size of the spot (on the order

of an hour), much shorter than the observed life times of spots (days to weeks).

The magnetic forces also make the sunspot plasma buoyant. Together, this gives

rise to an 'anchoring problem' (cf. Parker 1979). A sunspot cannot be just a

surface phenomenon since magnetic eld lines have no ends. The sunspot's eld

lines continue below the surface. In contrast with a scalar eld like pressure,

the magnetic eld of a sunspot cannot be kept in equilibrium simply by pressure

balance at the surface: the tension in the magnetic eld lines continuing below

the surface exerts forces as well. The magnetic tension acting at the base of

the spot keeps it together and prevents buoyancy from spreading it like an oil

slick over the solar surface. Sunspots also rotate faster than the solar surface,

indicating that they sense the increase of rotation with depth.

The question of sunspot equilibrium thus involves deeper layers, down to wher-

ever the eld lines continue. At which depth and by which agent is the sunspot

ux bundle kept together? A very stable location is the boundary of the convec-

tion zone with the stably stratied radiative interior of the Sun. A layer of mag-

netic eld

oating on this boundary becomes unstable only at a eld strength of

about 105G (Sch ussler et al. 1994). The existence of such a critical eld strength

was hypothesized by Babcock (1961). The subsequent rise to the surface is what

creates the observed bipolar active regions, as proposed by Cowling (1953). The

action of the Coriolis force on

ows in the magnetic eld associated with the

instability produces the poloidal eld of the next cycle, and is observable on theLocal Helioseismology 27

surface in the form of the systematic tilt of active region axes with respect to the

azimuthal direction (Leighton 1969). A boost of condence has been provided

by recent realistic 3D radiative MHD simulations of the last stages of the emer-

gence process of magnetic elds at the surface. These are beginning to look much

like real observations (Cheung et al. 2008). Though largely qualitative, the view

of the solar cycle developed by Babcock and Leighton appears to be the most

fruitful frame of reference for interpreting the solar cycle.

6.2 Moat Flow

In the photosphere, sunspots are typically surrounded by diverging horizontal

out

ows, termed moat

ows, with amplitudes of several hundred m s1. These

out

ows typically extend to about twice the radius of the penumbra. Moat