The Astrophysical Journal, 817:117 (16pp), 2016 February 1 doi:10.3847/0004-637X/817/2/117
© 2016. The American Astronomical Society. All rights reserved.
OBSERVATIONS OF OPPOSITELY DIRECTED UMBRAL WAVEFRONTS ROTATING IN SUNSPOTS
OBTAINED FROM THE NEW SOLAR TELESCOPE OF BBSO
J. T. Su1, K. F. Ji2, W. Cao3, D. Banerjee4, T. G. Priya1, J. S. Zhao5, X. Y. Bai1, J. Chen1, M. Zhang1, and H. S. Ji6
1 Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China; sjt@bao.ac.cn
2 Kunming University of Science and Technology, Kunming 650093, China
3 Big Bear Solar Observatory, 40386 North Shore Lane, Big Bear City, CA 92314, USA
4 Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India
5 Key Laboratory of Planetary Sciences, Purple Mountain Observatory, CAS, Nanjing 210008, China
6 Key Laboratory for Dark Matter and Space Science, Purple Mountain Observatory, CAS, Nanjing 210008, China
Received 2015 August 11; accepted 2015 December 11; published 2016 January 26
ABSTRACT
We study the umbral waves as observed by chromospheric imaging observations of two sunspots with the New
Solar Telescope at the Big Bear Solar Observatory. We find that the wavefronts (WFs) rotate clockwise and form a
one-armed spiral structure in the first sunspot, whereas two- and three-armed structures arise in the second sunspot
where the WFs rotate anticlockwise and clockwise alternately. All the spiral arms display propagation outwards
and become running penumbral waves once they cross the umbral boundaries, suggesting that the umbral and
penumbral waves propagate along the same inclined field lines. We propose that the one-armed spiral structure
may be produced by the WF reflections at the chromospheric umbral light bridge, and the multi-armed spirals may
be related to the twist of the magnetic field in the umbra. Additionally, the time lag of the umbral oscillations in
between the data of He I 10830Å and Ha - 0.4 Å is ∼17 s, and it is ∼60 s for that in between the data of 304Å
and Ha - 0.4 Å. This indicates that these disturbances are slow magnetoacoustic waves in nature, and that they
propagate upward along the inclined lines with fast radial expansions causing horizontal velocities of the running
waves.
Key words: Sun: chromosphere – Sun: magnetic fields – Sun: oscillations – sunspots
1. INTRODUCTION subsequent studies of umbral oscillations tried to find the
Intensity and velocity observations in various spectral lines eigenmodes of sunspot oscillations related to the photospheric
resonator under closed boundary conditions (Hasan 1991;
have revealed the existence of 5/3 minute oscillations (see
Hasan & Christensen-Dalsgaard 1992; Banerjee et al. 1995,
review by Thomas 1985; Lites 1992; Staude 1999; Bogdan & 1997, 2002; Gore 1997, 1998; Wood 1997) or open ones (Cally
Judge 2006 and references therein) in the umbral photosphere & Bogdan 1993; Cally et al. 1994; Bogdan & Cally 1997; Lites
(Bhatnagar & Tanaka 1972)/chromosphere (Beckers & Schultz et al. 1998) of one atmosphere permeated by a uniform
1972; Giovanelli 1972). The 5 minute oscillations are magnetic field aligned with the constant gravitational accelera-
predominantly a photospheric phenomenon. Their amplitude tion. Eigenmodes with periods from several tens of minutes
decreases with increasing height and they can hardly be (g-modes) to several tens of seconds (p-modes) have been
detected in the upper chromosphere and transition region. On found (Zhukov 2002). Another model, originally proposed by
the other hand, the oscillatory power in the 3 minute band Zhugzhda & Locans (1981) and recently improved by
shows a dominant peak in the sunspot chromosphere (e.g., Zhugzhda & Sych (2014), involves the resonant trapping of
Lites 1986; Yoon et al. 1995) and in the transition region slow-mode waves within a cavity located in the chromospheric
between the chromosphere and the corona (Gurman et al. umbra (a chromospheric resonator). In addition, some efforts
1982). A manifestation of chromospheric umbral oscillations is have been made toward reconciling photospheric and chromo-
umbral flashes (UFs), which were first discovered by Beckers spheric resonators (Lee & Yun 1987; Zhugzhda & Sych 2014)
& Tallant (1969) in Ca II H and K filtergrams and spectrograms and the oscillation eigenmodes and atmospheric wave filtering
of a sunspot. UFs appear in the form of narrow bright lanes (Zhukov 2005).
stretched along the light bridges (LBs) and around clusters of Running penumbral waves in velocity and intensity
umbral bright points (Yurchyshyn et al. 2015) when the observations were first reported by Giovanelli (1972) and Zirin
velocity amplitudes exceed a threshold, e.g., 5 km s−1 for the & Stein (1972). Later, they were found in the photosphere as
Ca II K line. UFs are rarely observed in Hα and perhaps only well (Musman et al. 1976), but there they appear to be more
when the velocity amplitude is large enough (e.g., Tziotziou intermittent and to have higher radial phase velocity
et al. 2007). (40–90 km s−1) than the waves in Hα. Whereas the velocity
In this paper, we concentrate on the chromospheric umbral amplitudes are less in the photosphere than in the chromo-
oscillations and the running waves associated with them. There sphere, the density is very low there and most of the wave
are several theoretical models for the nature of the 3 minute energy lies in the photosphere and subphotosphere. Larger
umbral oscillations. Scheuer & Thomas (1981) and Thomas & amplitudes on the disk-side penumbra demonstrate an align-
Scheuer (1982) proposed that the oscillations are driven by a ment of the oscillations along the magnetic field. Running
resonance of fast magnetoacoustic waves, located in the waves are also detected in the umbra, but the waves were
photosphere and subphotospheric layers, that are excited by believed to be unrelated to those in the penumbra (Kobanov &
overstable convection (a photospheric resonator). Many Makarchik 2004). In the chromosphere, the frequency of
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
travelling waves decreases as they propagate from the umbra running penumbral waves being upward-propagating slow-mode
into the outer penumbra (e.g., Lites 1988). A similar effect is waves guided by the magnetic field lines.
also found in measurements of the propagation velocity of Recently, Sych & Nakariakov (2014) detected umbral
travelling waves (Brisken & Zirin 1997; Sigwarth & Mattig wavefronts (WFs) with an evolving two-armed spiral that
1997; Alissandrakis et al. 1998; Kobanov & Makarchik 2004; rotated anticlockwise, suggesting that the umbral waves
Tziotziou et al. 2006, 2007). Generally, the waves decelerate propagate not only in the radial direction but also in the polar
from 40 km s−1 near the inner part of the penumbra to angle direction. In this work, utilizing the observations of the
10 km s−1 or less near the outer edge of the penumbra. More New Solar Telescope (NST, Cao et al. 2010; Goode & Cao
recently, from a multi-wavelength study including the coronal 2012), we find additional propagating patterns of the umbral
channels of the Atmospheric Imaging Assembly (AIA) on waves. We expect that the new results reported here could help
board the Solar Dynamics Observatory (SDO), Jess et al. to clarify some problems of sunspot oscillations, e.g., the
(2015) revealed the presence of a wide range of frequencies, source of the 3 minute oscillations and their connections with
with longer periodicities preferentially occurring at increasing the running penumbral waves. The remainder of this paper is
distance from the umbra. The phase speeds also tend to arranged as follows. Section 2 will discuss the observations of
decrease with increasing periodicity as the waves propagate target sunspots and the data reduction methods. Section 3 will
away from the umbral barycenter. These observations also explain the main results of the analysis. In Section 4 we further
suggest that these slow waves are driven by a regular coherent discuss the findings presented in the preceding section. Finally,
source. The physical nature of running penumbral waves has Section 5 summarizes the findings presented in the work.
been controversial. Some researchers have regarded them as
trans-sunspot waves originating from umbral oscillations since 2. DATA AND REDUCTION
they detected waves starting from the umbra and propagating
through the penumbra (e.g., Alissandrakis et al. 1992; Tsir- The NST observations were performed on two main
opoula et al. 1996, 2000). However, others suggest that the sunspots (see Figure 1) of NOAA active regions 12127
( ) (sunspot 1, located at S09E08 on 2014 August 1) and 12132trans-sunspot i.e., outward motion is apparent to a given line (sunspot 2, located at S19E04 on 2014 August 5). The data on
of sight, and that these oscillations actually represent the sunspot 1 were taken at 17:15 UT–17:55 UT, and the data on
upward propagation of field-guided magnetoacoustic waves sunspot 2 at 18:20 UT–19:20 UT. Chromospheric images were
from the photosphere (e.g., Christopoulou et al. 2000, 2001; acquired every 23 s by scanning of the Hα spectral line from
Georgakilas et al. 2000; Rouppe van der Voort et al. 2003; the blue wing −1Å to the red wing +1Å with a step of 0.2Å.
Bogdan & Judge 2006; Kobanov et al. 2006; Bloomfield et al. The field of view (FOV) is 70″ with a pixel size of 0.029.
2007; Jess et al. 2013, 2015). The gradual change in the Images of the TiO (7057 Å) line are used to identify the
inclination of the penumbral field lines is responsible for boundary between umbra and penumbra as this absorption line
changes in the oscillation periods and phase speeds. forms only at temperatures below 4000 K and it is well suited
The connection between the 3 minute umbral oscillations for observing the umbra. To study the effect of the inclination
and running penumbral waves is yet to be fully understood. of magnetic field on the wave period, we used the vector
Lites et al. (1998) observed a continuity of disturbances across magnetogram of sunspot 1 from the Spectropolarimeter of the
the umbra–penumbra boundaries of one sunspot. He proposed Solar Optical Telescope (Kosugi et al. 2007; Tsuneta et al.
that either the penumbral waves in the inter-penumbra are 2008) on board Hinode, and that of sunspot 2 from the
driven by the umbral oscillations or the umbral and penumbral Helioseismic and Magnetic Imager (HMI, Schou et al. 2012)
oscillations share a common physical basis. Tsiropoula et al. on board the SDO.
(1996, 2000), Tziotziou et al. (2002), and Alissandrakis et al. To investigate the umbral oscillations in sunspot 2 at
(1992, 1998) provided clear evidence of waves originating different solar altitudes, in addition to the Hα data, we also
from oscillating elements inside the umbra and propagating used images of the narrow band (band-pass: 0.5 Å) of He I
through the penumbra. However, many authors have also 10830 Å of the NST with a pixel size of 0.078 and time
shown that the running penumbral waves are not an extension cadence of 15 s as observed on August 5, and the images of
of the 3 minute umbral waves (e.g., Kobanov & Makarchik 304 Å taken by theSDO/AIA. These lines allow us to study
2004; Kobanov et al. 2008). The measured propagation the umbral oscillations in the chromosphere (Hα line), in the
velocity of the umbral waves turned out to be much higher, upper chromosphere (He I 10830 Å line), and in the transition
40–70 km s−1. Whereas 3 minute umbral oscillations in the and lower corona region (304 Å line). For each sunspot, we
chromosphere are not considered as the source of the running used the first image at Ha - 1.0 Å as a reference to align all
penumbral waves (Christopoulou et al. 2000; Kobanov & the other images at the same passband. In this procedure, the
Makarchik 2004; Bloomfield et al. 2007), researchers realized relative shifts to the first image are kept, and are then used to
that the chromospheric oscillations in umbrae (UFs) and the align the Hα images in the other passbands (all the images
running penumbral waves might be different manifestations of observed every 23 s are assumed here to be already co-aligned).
the same phenomenon produced by a common source in the Similarly, with the reference image, it is not difficult to co-align
photosphere (Zhugzhda et al. 1984; Christopoulou et al. 2001; it with the images of other instruments.
Rouppe van der Voort et al. 2003; Bloomfield et al. 2007; The Ha - 0.4 Å images show that there are electric fan-like
Tziotziou et al. 2007). Their differences arise from the transmitted shadows emerging periodically and they rotate very fast around
wave power available for propagation along differently inclined the umbral centers of the two sunspots. Also, the direction of
field lines. Löhner-Böttcher & Bello González (2015) analyzed rotation of the shadows in sunspot 2 can alternate between
the Interferometric BIdimensional Spectropolarimeter (IBIS/ clockwise and anticlockwise. We attempt to use a phase-speed
DST) data and found signatures of running penumbral waves filter (see the Appendix) to extract these fast moving signals
in photospheric layers. This further supports the scenario of from the relatively quiet backgrounds. The filtered images of
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Figure 1. Left panels: TiO images of the sunspots in NOAA 12127 and NOAA 12132 as observed on August 1 and August 5, respectively. Three umbral regions of
sunspot 1 are marked as U1, U2, and U3. Two dotted lines mark two virtual slits (1 and 2) for further analysis. Right panels (b) and (e): power maps of the dominant
oscillation frequencies in the umbrae of sunspots 1 and 2, respectively. The red contours show the cosines of magnetic field inclinations with levels of 0.85, 0.95, and
0.99. Panel (c) and its inset show the Fourier power spectra and wavelet power corresponding to the averaged Ha - 0.4 Å intensity signals within the dotted square in
panel (b). The white contours on panels outline the umbral boundaries.
v > 14 km s−1 are used widely in this paper, and the physical side, on three umbrae marked as U1, U2, and U3. The left
reason is given in Section 3.1. umbra is often obscured by some peacock-like jets, so we do
In addition, we calculate the center of gravity of the Hα line not consider it for further analysis. Following Jess et al. (2013),
profile corresponding to each pixel to estimate the Doppler shift we generate a power spectrum (see technique details in
relative to the reference line center obtained by averaging over Scargle 1982; Horne & Baliunas 1986; Yuan et al. 2011)
the whole FOVs of sunspots 1 and 2 in Figure 1 (the blank corresponding to each spatial pixel for temporal sequences of
fields excluded in the figure). The passbands of the line have the Hα −0.4 Å intensity, and then extract the dominant
been expanded from 11 to 110 by interpolation to improve the oscillation (DO) frequency. Zero value is assigned at those
fitting for better velocity estimates. pixels where the DO frequency is less than the confidence
threshold of 0.95. Panels (b) and (e) show the DO frequency
3. RESULTS distributions (power maps) of Hα −0.4 Å for sunspots 1 and 2,
respectively.
3.1. Umbral Oscillations and Running Waves A part of U3 (marked by a white square in panel (b)) is
Figure 1 presents TiO images of sunspot 1 (panel (a)) and selected for further analysis. Corresponding to the averaged
sunspot 2 (panel (d)). For sunspot 1, we focus only on its right signal within this boxed region, the Fourier power spectrum
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 2. Velocities of the umbral and penumbral waves in sunspots 1 and 2. Panels (a) and (b) are the time–space diagrams corresponding to slits 1 and 2 as marked
in Figure 1, respectively. The solid lines mark the umbral and penumbral boundaries. Panel (c) is a histogram of the measured velocities in the umbral (red) and
penumbral (blue) regions.
and wavelet phase plots are shown in panel (c) and its inset. It (a) and (b) of Figure 2. Time–distance maps corresponding to
is clear that a frequency of ∼6.8 mHz (2.45 minutes) lasting for the two virtual slits crossing the umbrae of sunspots 1 and 2
about 35 minutes is dominant. The figure also exhibits some (see Figure 1) are shown. Umbral and penumbral boundaries
secondary frequencies around 5.5, 6.2, and 8.4 mHz. These are shown by the solid lines at Y = -4 and Y = 3 in panel
frequencies are consistent with the theoretical predictions of (a) and at Y = -5 and Y = 5 in panel (b). Although some
eigenmodes of photospheric umbral oscillation (Cally & umbral ridges are branching or merging (Chae et al. 2014) near
Bogdan 1993; Bogdan & Cally 1997; Zhukov 2005) and/or the boundaries, most ridges of penumbral waves extend from
chromospheric multi-passband filters for the slow waves the umbra to the penumbra, which indicates that they originate
(Zhugzhda 2008). In addition, the other umbrae (U1, U2, and in the umbra (Alissandrakis et al. 1992, 1998; Tsiropoula et al.
the umbra in sunspot 2) are found with similar frequency 1996, 2000; Lites et al. 1998; Tziotziou et al. 2002).
distributions to U3 (not shown). Calculating the gradient of the ridges, we obtain the wave
In panels (b) and (e), cosine contours of field inclinations velocities as shown in panel (c). The histogram displays that
(deep red contours) are overplotted. Generally, they demon- the umbral waves have a velocity distribution from ∼15 to
strate that the DO frequency increases with the cosine of 50 km s−1, and the penumbral waves from 6 to 20 km s−1 with
inclination (Madsen et al. 2015). However, some regions are a peak at ∼10 km s−1. Based on the distributions, we somewhat
different, for example, in panel (b) around X = 0 and arbitrarily choose v=14 km s−1 to distinguish between umbral
Y = -3 (as compared to that around X = 0 and Y = 0), and penumbral waves, and v=4 km s−1 to distinguish
the higher-frequency (>7mHz) elements correspond to a between them and lower-speed waves.
smaller cosine of inclination. This may be due to the complex
topology and the strong inherent dynamics of sunspot 1.
Physical characteristics in such regions have so many 3.2. One-armed Spiral Structures in Sunspot 1
peculiarities that we should treat the obtained results with In Figure 3 we study the evolution of the spiral structure as
particular caution. seen within sunspot 1. It shows that at 17:49:06 UT, a dark
Evaluations of the propagating velocities of umbral and ribbon-like WF emerges at the north-east umbral boundary (the
penumbral waves in the two sunspots are displayed in panels red dotted contours). It moves subsequently in both radial (see
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 3. Formation of the one-armed spiral structure of one WF in U1 of sunspot 1 (seen in the phase-velocity filtering images of Ha - 0.4 Å with v > 14 km s−1.
The white solid circles highlight the propagating trajectory of the WF and the red dotted lines outline the umbral boundary. The black and white arrows indicate the
directions of propagation of the wave, and the blue arrows mark locations where the wave is reflected. Note that the bright patch in the top-left umbral boundary region
of panel (f) is caused by the dark WF in panel (b) radially expanding out of the region. However, the contrary is the case for the central region in panels (h) and (e),
where the WF just reaches here and then the region gets dark.
Figure 4. Similar to Figure 3, but for the same WF seen in the images of Hα Doppler velocity.
black arrows) and clockwise azimuthal (see white arrows) distance between the two black ribbons at 17:49:52 UT and
directions. The radial and azimuthal velocities are 17:50:14 UT (the WF shown by white arrows). The errors
vr = 20  10 km s
−1 at 17:51:00 UT (panel (f)) and come from the diffused WF profiles. At 17:51:22 UT (panel
va = 35  10 km s−1 at 17:50:14 UT (panel (d)), respectively. (g)), a one-armed spiral structure is formed. At 17:51:45 UT,
Specifically, for vr we measure the radial distance between the the next dark ribbon arises at the north-east umbral boundary
two arc ribbons at 17:49:29 UT and 17:51:00 UT (the WF again, suggesting that the previous period of umbral oscillation
shown by black arrows). For va we measure the azimuthal ended (with P = 2.6  0.4minutes).
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Figure 5. Similar to Figure 3, but in U2.
Figure 6. Similar to Figure 3, but in U3.
The one-armed spiral structures are also found in umbrae U2 directions of propagation abruptly at some locations (see the
(Figure 5) and U3 (Figure 6), which show radially expanding blue arrows at 17:49:52 UT and 17:51:00 UT in U1, 17:54:01
and clockwise rotation as well. The timescale for formation of UT and 17:54:47 UT in U2, and 17:48:21 UT, 17:49:29 UT,
the spiral structure is about 2.6 minutes in U2 and 2.3 minutes and 17:50:14 UT in U3). It appears that the WFs are reflected at
in U3. The typical radial and azimuthal velocities are the above locations. We also find these locations of reflection
vr = 18  5 and v = 50  15 km s−1a in U2, and near the photospheric umbral boundaries (marked by blue
vr = 20  10 and va = 35  10 km s
−1 in U3. These time- arrows in Figures 3, 5, and 6), which might be acting as natural
scales and velocities are of the same order as those in U1. barriers to partially prevent WFs escaping from the umbrae.
How do the propagating WFs develop into such a one-armed However, we are aware that the given boundary refers to the
spiral pattern? We find that they would change their azimuthal deep photosphere while the studied oscillations refer to the
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Figure 7. Temporal sequence of the two-armed spiral of one WF in sunspot 2. As usual, the red dotted lines outline the umbral boundary and the white solid circles
highlight the WF trajectory. The black arrows display outward expansion of one spiral arm and the white ones show the WF core rotating anticlockwise.
chromosphere (the height difference is 1500–2000 km). More- reflecting surface for the umbral waves propagating toward
over, according to general views, in the chromosphere, waves them. But the question is why the waves (after being reflected)
propagate along magnetic field lines. Thus, we attempt to check travel in the azimuthal direction as shown in the figures. Are
Doppler velocity in the Hα spectral line to find out more there some azimuthal magnetic channels for the reflected
information about the direction of propagation of umbral waves? To understand this further we need to study similar
waves. Figure 4 shows such maps of Doppler velocity in U1. high-resolution observations, which we hope to perform in the
As compared to Figure 3, the WF seen in them is more diffused near future.
with a bias toward blueshift enhancement of the line. This is a Here we conjecture that the trajectories of umbral WFs may
feature of upward-propagating quasi-periodic intensity pertur- contain two different parts: preceding and following. The
bations (Verwichte et al. 2010). In Section 3.4, we will show preceding part is likely reflected back into the umbra, creating
that the umbral oscillations of Doppler velocity and intensity of the azimuthal motion. The following part propagates only in
Hα are in or out of phase, suggesting that the waves propagate the radial direction, and becomes the penumbral waves after
along the field lines. Therefore, we infer that the above radially crossing the umbral boundaries. These two parts may have
transverse motions (vr) of WFs are likely produced by the effect common sources located in the photosphere and/or below the
of expansions of field line as the waves propagate upward photosphere, but with different wavelength or period.
along them.
Furthermore, additional inferences can be drawn from
Figure 4. At 17:49:06 UT, the area of a LB on the right side 3.3. Multi-armed Spiral Structures of WFs in Sunspot 2
of U1 shows a small additional redshift, but from then on it In sunspot 2 several dark ribbons of one WF emerge
becomes more blueshifted due to the arrival of the WF. simultaneously, and then rotate in a coordinated manner to
Moreover, there is a disconnection in the dark trajectory of the form a two-armed spiral structure as shown in Figure 7. The
WF at the lower-left corner of Figure 3(h), which is likely central patch marked by white arrows in panels (b) and (c)
caused by a part of the WF leaking away along the open field rotates anticlockwise and expands radially. Meanwhile, two
lines (produced by the jets) emanating from another LB seen spiral arms (e.g., one arm marked by black arrows) expand
nearby in Figures 4(e)–(g). radially. When the spiral arms cross the umbral boundary,
It is believed that the field lines of LBs form a magnetic penumbral WFs are generated (see bottom parts of panels (e)–
canopy structure where the field strength increases and the (h)). Moreover, the two-armed spiral structure occurs periodi-
inclination decreases with height in all parts of LBs, and in the cally in sunspot 2. For example, following the first two-armed
narrow parts it acquires values that are similar to those in the spiral structure shown in panels (a)–(e), the second one
surrounding umbra (Jurčák et al. 2006). Thus, the physical emerges gradually in panels (f)–(h). The period of appearance
parameters of these narrow parts, e.g., temperature and density, is nearly 2.7±0.4 minutes, which is the time interval
are also different from their surroundings. By further checking between panels (a) and (h). The radial velocity of the two
the so-called reflected positions of the WFs, we find that they spiral arms is nearly 20±10 km s−1 inferred from panels
are located at such chromospheric umbral boundaries that are (a)–(e), and the azimuthal velocity of the central patch is nearly
adjacent to a LB of two umbrae. The LBs might constitute a 60±20 km s−1 inferred from panels (b) and (c).
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 8. Similar to Figure 7, but for a clockwise rotating three-armed spiral evolving into a two-armed spiral rotating anticlockwise.
Anticlockwise rotation of the central patch becomes 3.4. Spectral Features of the Umbral WFs
clockwise rotation after 18:55:43 UT. Figures 8(a)–(f) display Figure 9 compares the filtered images at Ha - 0.4 Å in
this rotating motion. A dark ribbon arises at the left side of the panels (a) and (d) with those at Ha + 0.4 Å in panels (b) and
umbral boundary of sunspot 2 in panel (a). Its head then (e) for U3 of sunspot 1 and sunspot 2. It appears that the blue
rotates clockwise, and jumps to the umbral center as shown in wing images are negative images of the red wing. The figure
panels (b) and (c) (see white arrows). The shifting velocity is
−1 also presents the Hα profiles averaged over the abovemore than 100 km s , which is too large to believe that this is respective entire FOVs and their filtered profiles averaged
a real rotating motion. Finally, a three-armed spiral structure over the regions, i.e., r1 and r2 in panel (c) and r3 and r4 in
emerges as shown in panel (e). However, we find that the panel (f). For the Hα profiles, the intensities in red wings are
three-armed structure is not a periodic phenomenon. It slightly higher than those in blue wings. The filtered profiles
evolves toward an opposite pattern (anticlockwise rotation) are antisymmetric, analogous to those of Stokes V-profiles. The
after 1.5 minutes as shown in panel (g). Also, the three-armed LOS velocities averaged over r1 and r3 are −2.4 and
spiral structure turns into a two-armed structure. In panel (i), a −2.8 km s−1, and those over r2 and r4 are −0.4 and
dark bump (shown by the white arrow) emerges. Its core +0.6 km s−1, respectively. This indicates that the black (bright)
exhibits fast rotation with a speed of ∼90 km s−1 during patches in the filtered Ha - 0.4 Å (Ha + 0.4 Å) images are
19:00:53 UT–19:01:16 UT. Finally, another two-armed strongly associated with the perturbations in the region of
spiral structure appears in the umbra as shown in panel (l). upward compression, while the bright patches do not always
Hence, we show again that the two-armed spiral structure correspond to the perturbations in downward compression (see
arises periodically. In this case, the appearance period further discussions in the Appendix).
~2.7  0.4 minutes according to the time interval between The top panels of Figure 10 show the temporal evolution of
panels (g) and (l), and the radial velocity ~17  5 km s−1 the Hα line, which is obtained by averaging over regions r1
(shown in panel (j)) is nearly the same as those values in and r3 (in Figure 9). Both the original and filtered signals show
Figure 7. the same sawtooth behavior, that is, a slowly increasing redshift
In summary, from Figures 3–8, the WFs display a common followed by a rapid blueshift. This indicates the presence of
character in which the outer arms of the spiral structures upward-propagating magnetoacoustic shock waves (e.g.,
expand radially and they become the penumbral waves upon Lites 1986; Centeno et al. 2006; Chae et al. 2014; Tian et al.
travelling across the umbral boundaries. Therefore, our 2014; Yurchyshyn et al. 2014). The middle two panels display
observations support the view that both umbral and the corresponding temporal sequences of the averaged Hα
intensity and LOS velocity over the same regions, where the
penumbral waves have a common source in the photosphere
velocities also show the sawtooth patterns (Centeno et al. 2009;
and/or subphotosphere (Zhugzhda et al. 1984; Christopoulou Bard & Carlsson 2010; Tian et al. 2014; Yuan et al. 2014).
et al. 2001; Rouppe van der Voort et al. 2003; Bloomfield The cross-correlation in panel (h) shows that there is a
et al. 2007; Tziotziou et al. 2007). However, our studies do dominant peak at the time lag of 0 minutes, suggesting that
not support a prevalent view that the difference between the major oscillation signals of intensity and Doppler velocity
them arises from their propagation along differently inclined are in phase. Thus, the major waves in r3 of sunspot
field lines. Figures 3–6 clearly show that they propagate 2 are upward-propagating. However, in panel (g) there are
together and separate only at the wave reflection points close four peaks with nearly the same correlation at the lag times of
to LBs. This indicates that they propagate along the same −2.3, −1.0, 0.0, and 1.5 minutes. The averaged oscillation
inclined field lines in the umbrae of the two sunspots. period is ∼2.4 minutes in r1 of sunspot 1 seen from panel (e).
Furthermore, their radial propagation velocities are likely to Thus, the positive peaks indicate that the waves upward are
be introduced by the disturbances propagating upward along propagating (with phase delays of ∼2π or 0), while the negative
the inclined field lines, which expand quickly in the radial peaks indicate that the waves are downward-propagating (with
direction. phase delays of ∼π).
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 9. v > 14 km s−1 filtered signals as seen from the blue wing −1 Å to the red wing +1 Å of the Hα spectral line. The filtered images at Ha - 0.4 Å are shown
in (a) and (d), and those at Ha + 0.4 Å in (b) and (e). The blue/red contours represent the Hα LOS velocity with levels of −2.5 and −2.0 km s−1/+0.5 and
+1.0 km s−1. (c) and (f) show the respective Hα profiles averaged over the overall FOVs of panels (a) and (d) (black), and the filtered profiles averaged over the
square regions of r1 and r3 (blue) and over r2 and r4 (red).
3.5. The Properties of the Umbral WFs at Different Heights chromosphere (T = 104 K) and 33 km s−1 in the transition
4.7
In the ltered v > 14 km s−1 images of He 10830 Å in region (T = 10 K for 304Å), we can estimate the differencefi I
in height of line formation between Ha - 0.4 Å and He I
sunspot 2, we also find spiral structures of the umbral WFs. The
10830 Å~ dh = 260 km, and the difference between He I
same is found in the difference images of the 304 Å channel of 1
/ ( 10830 Å and 304Å ~ dh2 = 1500 km.SDO AIA which have been filtered with a frequency window
) Above a sunspot, White & Wilson (1966) estimated that theof 3 mHz centered at 5.55 mHz . Figure 11 presents such an Hα spectral line forms at a height of 1500 km. Recently, the
example as seen at different lines: Ha - 0.4Å, He I 10830Å, average formation height of Hα was found to vary between
and 304 Å in the umbra of sunspot 2. 1100 and 1900 km depending on the local optical depth
Following Sych & Nakariakov (2014), we also study the (Leenaarts et al. 2012). The sunspot umbra is dark and well
phase relationship among the WFs at three altitudes by defined, suggesting that the opacity is greatly reduced and that
calculating 2D cross-correlation functions of the selected eight the formation height may be as low as 1100 km (Jess
pairs of Ha - 0.4 Å and He I 10830 Å images, and eight pairs et al. 2013). With the two lines of Si I 10827Å and He I
of He I 10830 Å and 304 Å images in the period of 18:36 UT– 10830 Å Centeno et al. (2009) detected that the height
18:60 UT, which is shown in Figure 12. This shows that the difference between the umbral photosphere and chromosphere
gradient between Ha - 0.4 Å and He I 10830 Å is larger than is 1000 km. Therefore, if the formation height of Hα above the
that between Ha - 0.4 Å and 304 Å. We obtain two sets of umbra of a sunspot is taken as 1100 km (even lower at
time-lag data (corresponding to the local maxima of the 2D Ha - 0.4 Å), then we infer that the He I 10830 Å line may
correlation function) of the umbral waves propagating from the form at ∼1360 km in the umbral chromosphere, which is
formation height ofHa - 0.4 Å to that of He I 10830Å then to slightly less than the 1500 km obtained by Centeno
304 Å. The averaged values are obtained by computing their et al. (2009).
means and variances, which are dT1 = 17  6 s between
Ha - 0.4 Å and He I 10830 Å and dT2 = 62  9 s between
Ha - 0.4 Å and 304 Å. The time lags are consistent with a 3.6. Distribution of Power Within the Spiral Structure
scenario of upward-propagating slow waves. In addition, With a Morlet wavelet (Torrence & Compo 1998) applied to
assuming that the propagating velocities vp ∼ 15 km s−1 in the the Ha - 0.4 Å images, we obtain the spatial distributions of
9
The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 10. Shock waves in the central patches of umbrae. The wavelength–time maps of the Hα spectral line averaged over r1 and r3 in Figure 9 are shown in panels
(a) and (c) for sunspots 1 and 2, respectively, and their filtered maps of v > 14 km s−1 are shown in panels (b) and (d). The temporal sequences of the averaged Hα
intensity and LOS velocity over r1 and r3 are shown in panels (e) and (f), respectively, and the corresponding cross-correlation coefficient of the two as a function of
time lag is shown in panels (g) and (h).
the narrow-band powers of the spiral structures of umbral WFs power patches (marked by the white arrows) gradually get
for sunspots 1 and 2 as shown in Figures 13 and 14, enhanced (before P=4.4 minutes) with distance in the
respectively. The 95% confidence threshold is used for the direction opposite to the trajectory of WF propagation (in a
time series of periods at each pixel. Note that the power maps clockwise direction). We propose that short-period waves
are further smoothed over a smoothing width of 30 pixels for evolve into shock waves over much smaller distances than
the FOVs of 420×420 pixels in sunspot 1 and 600×600 long-period waves. With the high-frequency power dissipation,
pixels in sunspot 2. the lower-frequency oscillations dominate.
The power distributions of umbral oscillations are quite Figure 14 shows another example in the umbra of sunspot 2.
complicated and each has its own features. In Figure 13, we The first two panels show that the high-frequency
take U3 of sunspot 1 as one example to show the power maps (P < 2.0 minutes) oscillations do not appear in the central
of a one-armed spiral structure at different frequencies. Panels patch of the two-armed spiral structure (marked by the white
(a) and (b) show that the WF head and tail (marked by the two arrows) or in their spiral arms. This is not consistent with the
arrows in panel (a)) have stronger power in the high-frequency study of Sych & Nakariakov (2014), who reported that the
(P < 2minutes) oscillations. With frequency decreasing, some central patch of one two-armed spiral of a WF corresponds to
10
The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 11. WF spiral structures at different heights as seen in the filtered images. Left and middle panels: the phase-speed filtered images of v > 14 km s−1 taken at
Ha - 0.4 Å and the He I 10830 Å spectral lines, respectively. Right panels: the difference images of AIA 304 Å, which have been filtered with a frequency window
of 3 mHz centered at 5.55 mHz.
Figure 12. 2D cross-correlation function for the selected eight pairs of Ha - 0.4 Å and He I 10830 Å images, and eight pairs ofHa - 0.4 Å and 304 Å images in the
period of 18:36−18:60 UT.
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 13. Spatial distribution of the narrow-band power of one WF spiral structure in U3 of sunspot 1 at 17:49:29 UT on August 1. The red dotted lines have the
same meaning as before, and the white circles outline the trajectory of the WF, with white arrows marking its head or tail.
Figure 14. Similar to Figure 13, but for sunspot 2 at 18:39:25 UT on August 5.
high-frequency oscillations (e.g., P=1.7 minutes). Panels panels (g) and (h), as expected, the spiral structure in the umbra
(c)–(e) of Figure 14 show that the power of the spiral is unrelated to the lower-frequency (P > 4.0 minutes)
structure is mostly associated with the 3 minute oscillations oscillations.
(~P = 2.4  0.5minutes). However, stronger power is con-
centrated not in its central patch, but in its arms or the regions
marked by the two arrows in panel (d) (where the brightening 4. DISCUSSIONS
regions shown in panel (b) of Figure 7 are). In particular, panel
(e) shows four patches (marked by white arrows) concentrating In this study we have mainly utilized high-speed (v >−1
near the umbra–penumbra boundary, whose distribution is 14 km s ) filtered images to investigate some properties of
analogous to magnetic oscillations with the signature of a umbral oscillations. The validity of this filtering method has
whispering gallery-like mode of slow body waves in a thick been tested with observed data as shown in the Appendix. We
magnetic flux tube (Zhugzhda et al. 2000; Staude 2002). In have chosen the critical velocity vc = 14 km s−1 so that we can
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The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 15. Rotations of sunspot 2 in two days (through August 5−6). Panel (a): a HMI white-light map for the sunspot. Panels (b) and (c): two time–azimuth diagrams
for the two virtual slits (the white circles on panel (a)) in the umbral and penumbral regions, respectively.
distinguish the umbral and penumbral waves in the velocity sunspots between the proposed monolithic (Cowling 1953) and
distribution. spaghetti models (Parker 1979). The two- or three-armed
One of our important findings is that one-armed spiral (uniform) structures of the WF trajectories in sunspot 2 indicate
structures of the umbral WFs are found in sunspot 1 and two- that they are produced by the interaction between multiple
and three-armed ones in sunspot 2. We have tried to discover strands of flux tube and the slow magnetoacoustic waves under
the relationship between the spiral structures and the twist of the photosphere. Those in the three umbrae of sunspot 1
magnetic field. For sunspot 1, by checking the HMI white-light displayed that the waves propagated and sometimes were
data we find that the four umbrae move as a whole and rotate reflected, likely in the three monolithic flux tubes. Rempel
anticlockwise, while their individual behaviors differ; for (2011) suggested that sunspots that present light bridges and
example, U1 and U2 rotate anticlockwise and U3 rotates signs of flux separation are more spaghetti-like than those
clockwise. Because sunspot 2 has only one umbra, we can without LBs. Therefore, we conjecture that the main umbra of
clearly see its motion in the time–space diagrams as shown in sunspot 1 may also consist of multiple strands.
Figure 15, where two circular slits are marked in panel (a). We
can see that there is no apparent rotation in the umbra, whereas
in the penumbra both clockwise and anticlockwise rotations are 5. CONCLUSIONS
found at the polar angles of 0 and 150, respectively, which
may come from tiny disturbances in the umbra where some The principal aim of this work was to investigate the running
imprints are seen at the corresponding positions. waves in the two sunspots observed on 2014 August 1 and 5.
Since WFs in the umbrae U1 and U2 are always clockwise The main results are as follows.
rotations, which are opposite to the umbrae’s own antic- (1) The phase-speed filters are used to extract the fast
lockwise rotations, this indicates that the twist has little or no rotating structures in the Hα images (mainly at the −0.4Å
effect on the one-armed spiral structure in U1 and U2. passband). We demonstrate that the filtered images of v > 14
−1
However, it is hard to draw the same conclusion for U3 km s may be suitable for studying umbral waves and the
because the rotation and twist directions are the same. We have images of 4 < v < 14 km s
−1 for studying penumbral waves.
already shown that in sunspot 1 the change in the WF direction (2) The umbral WFs emerge and propagate both radially and
occurs at the reflection points near those umbral–penumbral azimuthally in sunspots 1 and 2. When the WFs arrive at the
boundaries close to LBs (blue arrows in Figures 3–6). umbral boundaries, some of them may become the penumbral
Therefore, we conjecture that the spiral structures in sunspot waves and continue to propagate in the radial direction. We
1 are produced by their inward reflections at the umbral LBs. conjecture that the umbral and penumbral waves are possibly
However, we should treat this conjecture with particular excited by a single common source.
caution as the topology of sunspot 1 was quite complex. (3) The one-armed spiral structures of the WFs in sunspot 1
In sunspot 2, the multi-armed spiral structures alternate may be produced by waves reflected at the LBs. The multi-
between clockwise and anticlockwise rotation. This opposite armed spiral structures in sunspot 2 are likely related to the
rotation may come from the opposite vortices relating to the twist of the magnetic field under the photosphere. Moreover, its
magnetic fields. At least, we cannot exclude the association of stronger oscillating power prefers to concentrate at the umbral–
the multi-armed spiral structures with the twist of the magnetic penumbral boundaries.
field. This result is different from the result of Sych & (4) The spiral structures of WFs appeared sequentially at
Nakariakov (2014), who found no twisted magnetic field in a different heights in the solar atmosphere, which confirms
two-armed spiral structure. previous studies that the 3 minute umbral disturbances are p-
One should note that the WF spiral structures in the umbrae mode waves propagating upwards along magnetic field lines in
of the sunspots provide a clue to discern the constitution of the umbra of a sunspot.
13
The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
Figure 16. Test of the phase-speed filters with the data from 2014 August 1. Panels (a)–(d) in order: A Ha - 0.4 Å image and its filtered images of v < 4,
4 < v < 14, and v > 14 km s−1, respectively. Panel (e): a difference image of the two Ha - 0.4 Å images at 17:52:08 UT and 17:51:45 UT, on which the inset is a
comparison plot for the filtered and difference signals. Panel (f): Hα LOS velocity.
However, the complex topology of sunspot 1 means that we A vertical cone symmetric about the ω axis can cut off all
need observations with higher resolution and higher cadence to velocity components outside the cone and leave unchanged all
confirm our results. components inside. The Butterworth filter is applied to reduce
ringing and wrap-around error, and its low- and high-pass
We thank the anonymous referee for his/her valuable functions are given by
comments, which have enabled us to improve the quality of
the presentation. This work is supported by the strategic priority H low ( 1v, v ) = , (1)
research program of CAS with Grant No. XDB09000000 and c ⎡ v ⎤2n
the other Grants: National Basic Research Program of China 1 + ⎣⎢ ⎥⎦
under grant 2011CB8114001, XDB09040200, 11373040, vc
11373044, 11273034, 11303048, 11178005, 11573012, AGS-
0847126, and NSFC-1142830911427901. BBSO operation is and
supported by NJIT, US NSF AGS-1250818, and NASA 1
NNX13AG14G, and NST operation is partly supported by the Hhigh (v, vc) = , (2)2n
Korea Astronomy and Space Science Institute and Seoul ⎡ v1 + c ⎤
National University, and by the strategic priority research ⎢⎣ v ⎦⎥
program of CAS.
respectively, where vc is the cut-off velocity and n is the order.
If we are interested in some special components within
APPENDIX a certain speed range, then a band-pass filter is needed,
PHASE-SPEED FILTER whose function is H (v, vc1, vc2) = Hhigh (v, vc1) ´ H low (v, vc2),
created by combining a low-pass filter with a high-pass
A filtering method that works in the frequency–wavenumber
(w - k) domain is used to extract the wave signals of interest filter. Finally, with an inverse transform of the FFT, the
from the analyzed temporal sequences of Hα images. required images in the spatial domain are obtained. In the
Specifically, a three-dimensional time–space matrix generated paper, the temporal sequences of images are filtered according
by one image sequence is transformed to the w - k domain to the following three speed regimes: v < vc1 = 4 km s
−1
using the three-dimensional Fourier transform. The wave phase (high-pass), 4 km s-1 < v < 14 km s−1 (band-pass), and
velocity, v, is equal to the ratio of ω and k in the w - k domain. v > v = 14 km s−1c2 (low-pass).
14
The Astrophysical Journal, 817:117 (16pp), 2016 February 1 Su et al.
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