Periodicity of Twisting Motions in Sunspot Penumbral Filaments
We study the periodicity of twisting motions in sunspot penumbral filaments, which were recently discovered from space (Hinode) and ground-based (SST) observations. A sunspot was well observed for 97 minutes by Hinode/SOT in the G-band (4305 Å) on 12November 2006. By the use of the time – space gradient applied to intensity space – time plots, twisting structures can be identified in the penumbral filaments. Consistent with previous findings, we find that the twisting is oriented from the solar limb to disk center. Some of them show a periodicity. The typical period is about ≈ four minutes, and the twisting velocity is roughly 6 km s−1. However, the penumbral filaments do not always show periodic twisting motions during the time interval of the observations. Such behavior seems to start and stop randomly with various penumbral filaments displaying periodic twisting during different intervals. The maximum number of periodic twists is 20 in our observations. Studying this periodicity can help us to understand the physical nature of the twisting motions. The present results enable us to determine observational constraints on the twisting mechanism.
Periodicity of Twisting Motions in Sunspot Penumbral Filaments
, Wenda Cao
and Philip R. Goode
Purple Mountain Observatory, Nanjing 210093, P.R.China email:
Center for Solar Terrestrial Research, New Jersey Institute of Technology, Newark, NJ
Received ; accepted
Abstract. We study the periodicity of twisting motions in sunspot penumbral ﬁlaments,
which were recently discovered from both space (SOT/HINODE) and ground-based (SST)
observations. A sunspot was well-observed for 97 minutes by the SOT/HINODE in the
A ) on 12 November 2006. By use of the time-space-gradient applied to
intensity space-time plots, the twisting structures can be identiﬁed in the penumbral
ﬁlaments. Consistent with previous ﬁndings, we ﬁnd that the twisting is oriented from
the solar limb to disk center. Some of them show a periodicity. The typical period is
ab out ∼4 minutes, and the twisting velocity is roughly 6 km s
. However, the penumbral
ﬁlaments do not always show the periodic twisting motions during the time interval of
the observations. Such behavior seems to start and stop randomly with various penumbral
ﬁlaments displaying the periodic twisting during diﬀerent intervals. The maximum number
of the periodic twists is 20 in our observations. Studying this periodicity can help us to
understand the physical nature of the twisting motions. The present results enable us to
determine observational constraints on the twisting mechanism.
Keywords: Sunspot, Dynamics
Studying sunspot dynamics is one way to investigate the nature of sunspots.
Previous sp ectroscopic observations showed that sunspots exhibit a charac-
teristic ﬂow ﬁeld in the penumbra (e.g. Evershed 1909). This is the so-called
“Evershed ﬂow”, which is a nearly horizontal outward ﬂow of gas that takes
place in the photospheric layer of the penumbra. The Evershed ﬂow is ex-
plained as the siphon ﬂow based on the concept of interchanging convection
via magnetic ﬂux tubes (e.g. Jahn and Schmidt 1994). This proposal sub-
sequently demonstrated by simulations (e.g. Schlichenmaier and Collados
2002; Schlichenmaier and Solanki 2003). Recently, high-spatial resolution
observations from the Solar Optical Telescope (SOT) (Ichimoto et al. 2004;
Tsuneta et al. 2008) on HINODE (Kosugi et al. 2007) reveals new sunspot
structures and dynamics (Ichimoto et al. 2007), and similar ﬁndings are fur-
ther seen in ground-based observations from the Swedish 1-m Solar Telescope
(SST) (Zakharov et al. 2008). They found apparent motions of intensity
structures across penumbral ﬁlaments for several sunspots away from disk
center. These apparent motions are observed in the penumbra, which is
° 2009 Springer Science + Business Media. Printed in the USA.
09spt_twisting.tex; 15/04/2009; 10:56; p.1
2 Ning, Cao, and Goode
located in a direction perpendicular to the symmetry line connecting the
sunspot center and the solar disk center, and are hardly seen in the limb-side
and disc-center-side penumbra. The twisting motions are found to be always
in the direction from the limb toward disk center for both sides of the sunspot
and irrespective of whether the sunspot is East or West of the meridian.
This is the most striking recent discovery about the Evershed ﬂow. These
apparent twisting motions are neither an actual twist nor a helical motion
of individual penumbral ﬁlaments. Therefore, these observations are diﬃcult
to reconcile with (twisting) ﬂux tubes but are consistent with overturning
convective ﬂows in gaps (Spruit and Scharmer 2006). Such convective ﬂow
patterns are indeed seen in the simulations (Rempel, Schussler, and Knolker
The cause of the apparent twisting motions of the penumbral ﬁlaments is
still not clear. Observed properties of twisting motions should yield observa-
tional constraints on theories. For example, the properties of the periodicities
of the twisting motions. Ichimoto et al. (2007) mentioned such motions as
having a periodicity, which has been not explored in detail until this time.
In this paper, we statistically study the periodicity of twisting motions in
the diﬀerent penumbral ﬁlaments of a sunspot.
2. Observations and Measurements
The data that we use here are from the SOT aboard HINODE, which obtains
diﬀraction-limited images with a 50-cm aperture telescope from a Sun-
synchronous orbit. SOT allows us to observe sunspot dynamical activities
in the photosphere and chromosphere with stable diﬀraction-limited image
quality. We obtained image sequences of a sunspot in active region NOAA
10923 on 12 November 2006, taken by the SOT Broadband Filter Imager
(BFI) at 4305
A . The spatial resolution of the BFI is about 0.2 arcsec (or
150 km on the solar surface), and the temporal cadence is 20 s. This sunspot
was well observed from 08:37 UT to 10:14 UT (97 minutes) and shows
well-developed penumbral dynamics. Figure 1 shows the sunspot image at
08:37:32 UT. The sunspot center is located at E28S7 with a heliocentric angle
. Some of the data from this series of observations (blue continuum)
have been presented by Ichimoto et al. (2007).
Following Ichimoto et al. (2007), we also use space-time plots to show the
twisting motions in the penumbral ﬁlaments of the sunspots.As mentioned
before, these apparent motions of intensity ﬂuctuations in penum-
bral ﬁlaments are seen from the limb-side to the disk center-side
of ﬁlaments. So we ﬁrstly use a slit parallel to this direction, such as slit 1
in Figure 1. Figure 2 (top) shows space-time plots of the G-band intensity
at slit 1 for 97 minutes. The zero of the Y-axis indicates the limb
09spt_twisting.tex; 15/04/2009; 10:56; p.2
Sunspot penumbral dynamics 3
Figure 1. G-band image at 4305
A of the sunspot on 12 November 2006 obtained from
the SOT BFI on HINODE. Top and right are toward solar north and west, respectively.
The arrow at the center of sunsp ot indicates the direction toward the solar disk center.
Five slits were used in the paper, and the arrows represent the slit directions.
side end of the slit. More than 14 bright ﬁlaments were included, and
the apparent twisting structures can be seen, for example, at a height of 25
Mm. Because the slit points toward the disk center, the twisting motions are
expected from the slit bottom (solar limb) to top (toward the disk center).
The twisting motions start at one side of ﬁlaments, and end at another side.
Therefore, such structures are oblique in the space-time plots. However, the
problem is that the individual twisting structure is diﬃcult to discern from
such intensity plots. In order to study the periodicity of the twisting motions,
we ﬁrstly take the time derivative of the space-time plots. The bright and
dark ﬁlaments are displayed as before, as shown in the middle panel of Figure
09spt_twisting.tex; 15/04/2009; 10:56; p.3
4 Ning, Cao, and Goode
2. Then the space-gradient is performed in a direction from the slit bottom
to top, as shown in Figure 2 (bottom). The twisting motions are clearly
displayed, and each individual twisting structure can be identiﬁed. Thus, the
individual twisting structures are separated into two strips, the bright one is
beneath the dark one. The former indicates the edge of the intensity increase
from slit bottom to top, while the latter denotes the intensity decreasing to
Figure 2 (bottom) shows that ﬁve penumbral ﬁlaments exhibiting periodic
twisting motions, marked by G1, G2, G3, G4 and G5. Those are the ﬁve we
choose to study in detail here, and each individual twisting structure is in-
dicated by an arrow. It is clear that some ﬁlaments display twisting motions
without a periodicity. Note that the other three periodic twisting ﬁlaments
at heights of 40, 65 and 95 Mm are not studied here. Consistent with the
earlier ﬁndings by Ichimoto et al. (2007), the individual twisting
starts at the outside (limb-side edge) of the bright ﬁlament, and
ends at the inside (disk-center-side edge). When an individual twisting
ends, almost at the same time, a new twisting motion starts at the other
side of penumbral ﬁlament, as shown in the ﬁve samples identiﬁed. This
observation indicates that the apparent twisting motions in the penumbral
ﬁlaments are not a helical motion. In other words, the adjacent twisting
motions in the same penumbral ﬁlament represent the behaviors of diﬀerent
ﬂows of diﬀerent mass. Meanwhile, we have to pay attention to the fact that
these penumbral ﬁlaments do not show periodic twisting motions with the
same interval, and the number of periodic twisting structures are 5 (G1), 9
(G2), 5 (G3), 8 (G4) and 19 (G5), respectively. On the other hand, more
than 6 penumbral ﬁlaments in Figure 2 show twisting motions without a
periodicity, or irregularly, and even do not show twisting motions.
As in Figure 2, Figure 3 shows the space-time plots of intensity and the
space-time-gradient along slit 2, which is parallel to slit 1, but located at
the opposite side of the sunspot. Again the origin of the Y axis is the
limb side end of the slit. The time-gradient plots are not shown in Figure
3. In total, 15 ﬁlaments are included. Also, ﬁve samples of periodic twisting
penumbral ﬁlaments are chosen, and they are identiﬁed by G6, G7, G8,
G9 and G10. The apparent twisting motions are expected as before, along
the slit direction from the bottom to top (from the limb to disk center).
Each individual twisting is marked by an arrow. Note here that the other 4
periodic twisting ﬁlaments are not studied at heights of 27, 67, 85 and 110
Mm. As expected from the previous ﬁndings, the twisting direction
is from the limb to disk center again.
According to the ﬁndings of Ichimoto et al. (2007), the twisting motions
are hardly seen in the limb-side and disc-center-side penumbra. In order to
conﬁrm this result, we use another two slits, 3 and 4, at these two sides,
along the direction perpendicular to the line connecting the sunspot and
09spt_twisting.tex; 15/04/2009; 10:56; p.4
Sunspot penumbral dynamics 5
Figure 2. Space-time plots along slit 1 across the penumbral ﬁlaments. (a) G-band in-
tensity; (b) the time-derivative (or gradient) of intensity; (c) the space-time-gradient of
09spt_twisting.tex; 15/04/2009; 10:56; p.5
6 Ning, Cao, and Goode
Figure 3. Space-time plots along the slit 2 across the penumbral ﬁlaments. (a) G-band
intensity; (c) the space-time-gradient of intensity.
disc center. As in Figure 3, Figures 4 and 5 show the the space-time plots of
intensity and the space-time-gradient along slits 3 and 4, respectively. Only
one (G11) of the 11 penumbral ﬁlaments shows an apparent periodic twisting
motion, as indicated by arrows to each of the individual twisting structures,
although there are two ﬁlaments showing very weak twisting motions at
35 Mm (the time axis from 20 to 80 minutes) and 54 Mm (from 75 to 85
minutes) on the slit 3. Only two (G12 and G13) of 9 ﬁlaments on
the limb-side penumbra are found to show an apparent periodic
09spt_twisting.tex; 15/04/2009; 10:56; p.6
Sunspot penumbral dynamics 7
Figure 4. Same as in Figure 3, but along the slit 3 in Figure 1.
twisting motion in Figure 4. The twisting direction is from the
limb side to disk center again, i.e. from the slit top to bottom
along the slits 3 and 4.
The apparent periodic twisting motions are more frequently seen in the
penumbra located in the direction perpendicular to the symmetry line con-
necting the sunspot and disk center (slits 1 and 2) than the limb-side and
09spt_twisting.tex; 15/04/2009; 10:56; p.7
8 Ning, Cao, and Goode
Figure 5. Same as in Figure 3, but along the slit 4 in Figure 1.
disk-center-side penumbra (slits 3 and 4). Table-1 lists the parameters of the
penumbral ﬁlaments with the apparent periodic twisting motions, including
their duration, perio d, spatial scale and twisting velocities. The penumbral
ﬁlaments show various numbers of twists in their motions. We ﬁnd that the
maximum numbers of twisting motions is 20 (G7 in Figure 3) in our data
set. Here, the duration (4240 s) is the time interval, and it includes the 20
twisting structures. The periods are average values from the duration and
twisting numbers. Our results show this value is between 155 s and 330 s,
with an average value of 230 s. The spatial scale shows the width of the
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Sunspot penumbral dynamics 9
Figure 6. Same as in Figure 3, but along the slit 5 in Figure 1.
penumbral ﬁlaments along the slit direction as being from 1050 km to 1350
km. And the twisting velocity computed from the spatial scale and average
period is between 4.1 km s
and 7.7 km s
, with an average value of 5.6
We analyze the twisting motions of the penumbral ﬁlaments
along two opposite directions, i.e., parallel or perpendicular to the
direction from the limb to disk center. It is an interesting question
whether the twisting motions are able to be seen along an oblique
direction. Figure 6 shows the space-time plots along slit 5 that runs
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10 Ning, Cao, and Goode
Table I. Parameters of the twisting motions of the penumbral ﬁlaments.
Duration is the time interval over which the twisting motions are identi-
ﬁed; Spatial scale shows the width of p enumbral ﬁlaments along the slit
Filaments Numbers of Duration Period Spatial Velocity
Twisting (s) (s) scale (km) (km s
G1 5 620 155 1200 7.7
G2 9 1740 218 1350 6.2
G3 5 760 190 1050 5.5
G4 8 2000 286 1500 5.2
G5 19 4060 213 1200 5.6
G6 5 1000 225 1350 6.0
G7 20 4240 223 1350 6.1
G8 14 2860 220 1200 5.5
G9 8 1840 263 1350 5.1
G10 2 220 220 1200 5.5
G11 14 3240 249 1050 4.2
G12 7 1980 330 1350 4.1
G13 7 1240 207 1200 5.8
across 8 inner penumbral ﬁlaments obliquely. It is parallel to the
South-North direction. As expected from the previous ﬁndings,
it is possible that the twisiting motions could be seen along the
slit 6. Using the same method as before, however, we do not ﬁnd
apparent twisting motions with periodicity in these 8 penumbral
4. Conclusions and Discussions
We studied the periodicity of the recently discovered twisting motions of
sunspot penumbral ﬁlaments. Among the SOT data set, a sunspot was well-
observed for 97 minutes on 12 November 2006. Using space-time-gradient
plots of the G-band intensity, the individual periodic twisting structures were
identiﬁed. Firstly, our results are consistent with the previous ﬁndings of
twisting directions being from the solar limb to the disk center. Such behav-
ior is neither an actual twisting nor a helical motion. The adjacent motions
are almost head-on-end. In other words, all of the twisting ﬂows appear on
the same side of the penumbral ﬁlaments, and disappear on the other side.
As a twisting-ﬂow just ends, a new one starts simultaneously at
09spt_twisting.tex; 15/04/2009; 10:56; p.10
Sunspot penumbral dynamics 11
the other side of the ﬁlament. Secondly, some apparent twisting motions
display periodicity, where the average period is about 4 minutes. The twist-
ing motions have a mean velocity of 6 km s
. A penumbral ﬁlament does
not show periodic twisting motions over all of its lifetime. The start and end
times of periodic twisting behavior are diﬀerent for the various ﬁlaments.
Thirdly, the apparent periodic twisting motions are hardly seen in both
limb-side and disk-center-side of sunspot. According to our observations,
only 3 of 20 ﬁlaments located at these two sides exhibit periodic twisting
motions. To the contrary, more than half (17 of 29) ﬁlaments at slits 1 and 2
display periodic twisting structures. We do not ﬁnd a fundamental diﬀerence
between the periodic twisting motions for the penumbra on diﬀerent sides
of the sunspot.
The nature and origin of the apparent motions is still unclear. An in-
terpretation of the twisting motions is an upﬂow of overturning convection,
viewed from the side (e.g. Ichimoto et al. 2007; Zakharov et al. 2008). There-
fore, the twisting motion being always from the limb to disk center must be
an eﬀect of viewing angle. With the limb-side part of these ﬁlaments hidden
from view, such ﬂows will always appear to be in the direction of sun
center direction when they are observed away from the disk center.
However, our result for the periodicity of twisting motions is an observational
contrast to their theory. As noted earlier, the periodic twisting motions could
represent a typical behavior of Evershed ﬂows. Our observations that not
all of twisting motions show a periodicity, and the periodic twisting motions
start or end randomly in the penumbral ﬁlaments, suggest a stochastic
nature of the Evershed ﬂow.
Physical connection to the 4-min in penumbral ﬁlaments is not
clear at all. It is possible that this periodicity contains physical in-
formation about the origin of the twisting. This observational property
should be considered by the theorists in constructing their models. The 4-
min periodicity is between the 3-min and 5-min perio ds, which are generally
thought to be related the period of acoustic standing waves inside of the
HINODE is a Japanese mission developed and launched by ISAS/JAXA,
with NAOJ as domestic partner and NASA and STFC (UK) as international
partners. It is operated by these agencies in co-operation with ESA and NSC
(Norway). W. Cao gratefully acknowledges the support of NSF through
ATM-0847126, ATM-0745744, and NASA through NASA-NNX08BA22G.
This work is also supported by NSF of China under grants 10603014, 10843005,
09spt_twisting.tex; 15/04/2009; 10:56; p.11
12 Ning, Cao, and Goode
10833007, 40804034, 973 Program under grant 2006CB806302, and CAS
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