ON THE SOURCE OF PROPAGATING SLOW MAGNETOACOUSTIC WAVES IN SUNSPOTS
S. Krishna Prasad
1
, D. B. Jess
1,2
, and Elena Khomenko
3
1
Astrophysics Research Centre, School of Mathematics and Physics, Queen ʼ s University Belfast, Belfast BT7 1NN, UK; krishna.prasad@qub.ac.uk
2
Department of Physics and Astronomy, California State University Northridge, Northridge, CA 91330, USA
3
Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain
Received 2015 August 15; accepted 2015 September 17; published 2015 October 9
ABSTRACT
Recent high-resolution observations of sunspot oscillations using simultaneously operated ground- and space-
based telescopes reveal the intrinsic connection between different layers of the solar atmosphere. However, it is not
clear whether these oscillations are externally driven or generated in situ. We address this question by using
observations of propagating slow magnetoacoustic waves along a coronal fan loop system. In addition to the
generally observed decreases in oscillation amplitudes with distance, the observed wave amplitudes are also found
to be modulated with time, with similar variations observed throughout the propagation path of the wave train.
Employing multi-wavelength and multi-instrument data, we study the amplitude variations with time as the waves
propagate through different layers of the solar atmosphere. By comparing the amplitude modulation period in
different layers, we find that slow magnetoacoustic waves observed in sunspots are externally driven by
photospheric p-modes, which propagate upward into the corona before becoming dissipated.
Key words: magnetohydrodynamics (MHD) – sunspots – Sun: atmosphere – Sun: oscillations – Sun: photosphere
Supporting material: animation
1. INTRODUCTION
Waves and oscillations are an integral part of sunspots. To
date, there have been many observational reports of oscillations
in the photosphere, umbral flashes and running penumbral
waves in the chromosphere, and propagating waves in the
corona (see, e.g., the review articles by Bogdan & Judge 2006;
Jess et al. 2015; Khomenko & Collados 2015). Oscillations
manifesting in photospheric sunspots usually display prominent
five-minute periodicities alongside traces of power in three-
minute bandpasses, albeit with relatively small amplitudes
compared to those present in the surrounding quiet Sun
(Bhatnagar et al. 1972; Abdelatif et al. 1984; Landgraf 1997;
Bellot Rubio et al. 2000). Umbral flashes (Beckers &
Tallant 1969) are approximately three-minute periodic bright-
enings in chromospheric umbrae that occur as a result of
upwardly propagating magnetoacoustic oscillations converting
into localized shock waves (Rouppe van der Voort et al. 2003;
Henriques et al. 2015).
Running penumbral waves are outwardly propagating
oscillations found in the chromospheric penumbrae of sunspots
(Giovanelli 1972; Zirin & Stein 1972). The periodicities of
these waves, which are on the order of a few minutes, increase
from the inner penumbra to the outer boundary, while the
associated phase speeds decrease (Brisken & Zirin 1997;
Christopoulou et al. 2000; Jess et al. 2013
). It is believed that
the “trans-sunspot” (i.e., outward) motion is apparent to a given
line of sight and that these oscillations actually represent the
upward propagation of field-guided magnetoacoustic waves
from the photosphere (Christopoulou et al. 2001; Kobanov
et al. 2006; Bloomfield et al. 2007; Jess et al. 2013). The
gradual change in inclination of the penumbral field lines
produces the observed changes in the oscillation periods and
phase speeds. Recently, Löhner-Böttcher & Bello González
(2015) identified the photospheric signatures of running
penumbral waves and found them to be consistent with the
upward propagation of magnetoacoustic waves predicted
previously. Reznikova et al. (2012) have even suggested
frequency fluctuations within umbrae itself indicate substantial
local variations in magnetic field inclinations.
Evidence for propagating waves along fanlike loop struc-
tures in the corona is in abundance. The fan loops associated
with sunspots are usually rooted in the umbra and display
propagating waves with periodicities approximately equal to
three minutes (De Moortel et al. 2002; Marsh & Walsh 2006;
Jess et al. 2012a; Reznikova et al. 2012). The amplitude of
these waves decreases rapidly as they propagate along the loop,
eventually disappearing after several thousand kilometers.
Several physical processes such as thermal conduction and
compressive viscosity are believed to dissipate such waves in
the corona (De Moortel & Hood 2003; Krishna Prasad et al.
2014). Jess et al. (2012a) found an association between three-
minute waves propagating along fan loops and simultaneous
amplitude enhancements in underlying photospheric umbral
dots. Their results suggest that magnetoacoustic waves
manifesting in the photosphere can propagate upward into the
corona where, ultimately, the energy they carry is dissipated.
As advancements are being made in solar instrumentation
and observations, it is becoming increasingly evident that all
the above phenomena detected in different layers of the solar
atmosphere are actually inter-connected and most likely
produced by the same upwardly propagating slow magnetoa-
coustic waves, which present themselves according to the local
physical conditions. Although it is often assumed that the
photospheric p-modes are the ultimate source of sunspot
oscillations, there is no clear evidence as to whether these
oscillations are externally driven by the p-modes or generated
in situ within the sunspots (e.g., through magnetoconvection).
In this Letter, we aim to address this issue by studying temporal
variations in the amplitudes of propagating slow waves
observed in a coronal fan loop that were not explored before.
We present the details on our observations, our analysis
methods, and results in the subsequent sections and finally
discuss the conclusions.
The Astrophysical Journal Letters, 812:L15 (7pp ), 2015 October 10 doi:10.1088/2041-8205/812/1/L15
© 2015. The American Astronomical Society. All rights reserved.
1
2. OBSERVATIONS
The Dunn Solar Telescope at Sacramento Peak, New
Mexico, was employed to observe active region NOAA
11366 on 2011 December 10 between 16:10 and 17:25 UT.
The Rapid Oscillations in the Solar Atmosphere (ROSA; Jess
et al. 2010) and the Hydrogen-Alpha Rapid Dynamics camera
(HARDcam; Jess et al. 2012a) instruments were employed to
simultaneously capture high-resolution images in four different
optical channels centered at the Hα line core (6562.8 Å),
Ca
II K line core (3933.7 Å), G-band (4305.5 Å), and blue
continuum (4170 Å) wavelengths, with filter bandpasses
corresponding to 0.25 Å,1Å, 9.2 Å, and 52 Å, respectively.
The pixel scale was 0
0696 for the ROSA channels, producing
a field of view equal to 69″ × 69″. For Hα images acquired by
HARDcam, the plate scale was 0
138 per pixel, providing a
marginally larger field of view of 71″ × 71″. Part of this data
set has been used previously by Jess et al. (2013), where the
authors detail the full speckle reconstruction and calibration
steps applied to the data. Following all image-processing steps,
the final cadences of the data are 2.11 s for the 4170 Å
continuum and G-band channels, 7.39 s for the Ca
II K
filtergrams, and 1.78 s for the narrowband Hα image sequence.
Seeing conditions remained excellent during the 75-minute
observation period. However, a few images were affected by
local and short-duration atmospheric fluctuations, which
resulted in slight image degradation in locations away from
the adaptive optics lock point. These images, corresponding to
an average duration not longer than a few seconds, were
replaced through interpolation. The co-alignment between the
different ROSA channels is achieved using a series of
collimated targets obtained immediately after the end of the
science observations.
The corresponding space-based data from the Atmospheric
Imaging Assembly (AIA; Lemen et al. 2012) and the
Helioseismic and Magnetic Imager (HMI; Schou et al. 2012),
on board the Solar Dynamics Observatory (SDO; Pesnell et al.
2012), form the main part of the present study. Level 1.0 data
from both instruments were processed using the routines
aia_prep.pro and hmi_prep.pro available through
standard solar software (e.g.,
SSWIDL) pipelines. This involves
bringing all the data to a common center and plate scale, with a
final pixel scale ≈0
6. A subfield of 210″ × 210″ is then
carefully selected (by accounting for solar rotation) around the
target region from AIA 171, 131, 304, 1600, and 1700 Å
channels, in addition to HMI Dopplergrams covering the full
observational duration. The cadence is 12 s for the AIA 171,
131, and 304 Å channels, 24 s for the AIA 1600 and 1700 Å
channels, and 45 s for the HMI Dopplergram data, with each
image co-aligned to the first image using intensity cross-
correlation. HMI and ROSA (4170 Å) continuum images were
used to achieve the required co-alignment between ground- and
space-based data. We did not use the broadband 4170 Å
continuum channel for subsequent analyses since the ROSA
G-band data originate very close to the continuum level
(∼75 km height difference; Jess et al. 2012b) and have a better
signal-to-noise ratio than the ROSA 4170 Å continuum.
3. ANALYSIS AND RESULTS
Active region NOAA 11366 comprises a circularly sym-
metric sunspot with fanlike loop structures visible on one side
in the corresponding coronal channels (see Figure 1). A time-
lapse movie of the region, as seen through the AIA 171 Å filter
(available online), clearly shows outwardly propagating waves
in all of the fan loops. Figure 1 indicates a number of
preselected regions of interest, labeled as “A,”“B,” and “C,”
with the corresponding light curves extracted from location
“A” detailed in Figure 2. In this figure, the top panel displays
the original light curve (after binning over 3 × 3 pixel
2
), where
an oscillation of ≈3 minutes is visible along with other longer-
period components. The overplotted dotted line follows the
low-frequency background trend, which is subtracted to filter
such longer periods, with the resultant displayed in the middle
panel. The bottom panel displays the reconstructed light curve
obtained following Fourier filtration, allowing only a narrow
band (±50 s full width) of frequencies around three minutes.
All light curves show the persistent presence of three-minute
oscillations throughout the duration of the observing sequence.
An interesting aspect to note here is the amplitude of the
oscillations, which appears to increase and decrease over time.
This feature is visible in all the light curves, hence ruling out
the possibility that these are artifacts of the applied Fourier
filters. We also observed this behavior at other locations along
the wave propagation path.
The observed oscillations are similar to those previously
studied by many authors (e.g., De Moortel et al. 2002; Marsh &
Walsh 2006; Jess et al. 2012a; Krishna Prasad et al. 2012,
2014, to name but a few), in fanlike loop structures. There has
been a debate on whether these oscillations are due to waves or
high-speed quasi-periodic upflows (De Moortel & Nakariakov
2012), but it is widely believed that the three-minute sunspot
oscillations (as presented here) are the signature of propagating
slow magnetoacoustic waves. The disappearance of the
oscillations after a certain length along the structure further
confirms their propagating nature, and with temporal variations
in amplitude observed along their full propagation path, such
modulation may be a property of the source itself. In fact,
similar modulations were found in sub-coronal sunspot
oscillations by Beckers & Schultz (1972), Gurman et al.
(1982), Lites (1984), Thomas et al. (1987) , Fludra (2001),
Marsh & Walsh (2006), and Centeno et al. (2006, 2009). Thus,
an important aspect is to try and identify the wave source by
tracking these oscillations along the loop to its base, and
determining what feature(s) and atmospheric height(s) mod-
ulate the observed wave trains. It appears that the current fan
loop is rooted in the sunspot umbra, which explains the
prevalence of three-minute oscillations, and through visual
inspection this loop appears to be terminated at the location
marked “B” in Figure 1. Therefore, we constructed similar
Fourier-filtered light curves from location “B” near the coronal
footpoint of the loop (marked in Figure 1) in all channels
representing different layers of the solar atmosphere, with the
resulting light curves displayed in Figure 3. Although it is
generally assumed that magnetic field lines in the umbral
region are mostly vertical, an important aspect to consider is
whether location “B” corresponds to the same magnetic feature
when observed in all AIA channels. To determine the answer,
we used the vector magnetograms from this region and
employed nonlinear force-free field extrapolations (Guo et al.
2012) to reveal that the central pixel position of location “B”
laterally shifts by less than 3 AIA pixels over a height of
3600 km above the photosphere, thus justifying our choice of a
3 × 3 pixel
2
binning region for all channels. For ROSA and
HARDcam channels, we used equivalent macro-pixels to
2
The Astrophysical Journal Letters, 812:L15 (7pp ), 2015 October 10 Prasad, Jess, & Khomenko
construct the corresponding light curves. The AIA 171 Å light
curve from location “A” is also shown in this figure for
comparison. Interestingly, the dominant oscillation period at
location “B” is ≈5 minutes in the photospheric channels, even
within the umbra, which is similar to that reported earlier by
several authors (Bhatnagar et al. 1972; Soltau et al. 1976;
Thomas et al. 1981). The normalized Fourier power spectra
generated from the corresponding original light curves are
shown in left panels of Figure 3, where the numbers listed in
each panel represent the peak periodicity value in seconds. The
positions of the three-minute and five-minute periods are
marked by vertical dashed red lines for comparison. It is
evident that the oscillation power peaks near three minutes for
formation heights above that of the AIA 1700 and 1600 Å
channels, which form near the temperature minimum region,
before shifting to periodicities of ≈5 minutes in lower atmo-
spheric regions. The ROSA G-band and HMI Dopplergrams
form approximately 100 km above the photosphere (Fleck et al.
2011; Jess et al. 2012b). It is noted that ≈5 minute peaks in
G-band imaging and HMI Dopplergrams are accompanied by
Figure 1. Left: active region NOAA 11366 and its surroundings observed in the AIA 171 Å channel (top) and an HMI Dopplergram (bottom). The dotted box
encloses the subfield region shown as a series of stacked images on the right. Right: the sunspot as seen in different imaging channels: (from bottom to top) HMI
Dopplergram, ROSA G-band, AIA 1700 Å, AIA 1600 Å, ROSA Ca
II K, HARDcam Hα , AIA 304 Å, AIA 131 Å, and AIA 171 Å. Locations labeled “A,”“B,” and
“C” are also marked, which are used to study wave propagation in subsequent figures. A time-lapse movie of the active region in AIA 171 Å channel can be found
online.
(An animation of this figure is available.)
3
The Astrophysical Journal Letters, 812:L15 (7pp ), 2015 October 10 Prasad, Jess, & Khomenko
multiple closely spaced peaks (similar to those at ≈3 minutes in
the other channels), yet there is no significant enhancement at
three minutes in these channels. Therefore, to accommodate
this frequency shift, the reconstructed light curves displayed in
Figure 3 are Fourier-filtered around five minutes for these two
photospheric channels. The frequency band used in each
channel to produce the filtered light curves is marked in gray
over the corresponding power spectra. Furthermore, to check
the nature of propagation of these oscillations from the
photosphere to the corona, we estimated phase angles (f) for
the light curves at location “B,” taking information from the
HMI Dopplergram, AIA 1700 Å, and AIA 304 Å channels as
reference points. The obtained values are listed in Figure 3.
Some channels cannot be used as a reference for photospheric
and chromospheric propagation since the periodicities are
different. As the observations enter an optically thin regime, the
AIA 304 Å channel is chosen as a reference to indicate the
coronal propagation of the waves.
From Figure 3 it is clear that all light curves show a similar
modulation in amplitude with time, indicating a possible
connection between the five-minute photospheric oscillations
and their slow magnetoacoustic counterparts observed in the
corona. To extend this further and check the possible
connection with photospheric p-modes, we identified a location
(marked as C in Figure 1) outside the sunspot where the
average absolute magnetic field strength is <20 G and
constructed a similarly Fourier-filtered time series correspond-
ing to that location. This light curve is shown in the bottom
right panel of Figure 3 and, interestingly, also displays a similar
modulation in its oscillatory amplitude. In order to quantify the
observed variation in amplitude, we employed wavelet analysis
over the filtered light curves and extracted the amplitude
variation (i.e., correlated with the wavelet power) as a function
of time. The obtained amplitudes are shown in Figure 4.By
applying wavelet analysis to the obtained amplitudes, we
estimated the dominant period at which the amplitudes vary.
This value is listed at the bottom left corner of each panel in
Figure4. The amplitude fluctuations appear to have a
reciprocating nature with mean values on the order of
20–27 minutes. It may be noted that since the amplitudes are
extracted from the narrowband Fourier-
filtered light curves, the
observed fluctuations purely represent the variations in
amplitude of three (or five) minute oscillations and thus have
distinguished themselves from the the usually present long-
period sunspot oscillations (see Figure 2, top panel). To verify
if other loops in the coronal fan system behave in a similar way,
we performed identical analysis at all pixel locations in the AIA
171 Å channel that displayed prominent three-minute oscilla-
tions (∼600 pixel locations), as well as all pixel locations in the
HMI Dopplergrams that contained average absolute magnetic
field strengths <20 G (over 12,000 pixel locations), and
calculated their corresponding amplitude modulation periods.
The results are displayed in a histogram plot shown in Figure 5,
which reveals peak modulation periods of 27.0 minutes and
29.1 minutes (modal values) in the HMI and AIA channels,
respectively, thus strengthening our hypothesis that the global
p-mode oscillations and the propagating waves found in
coronal loop systems are related.
4. DISCUSSION AND CONCLUSIONS
Propagating slow magnetoacoustic waves observed in fan-
like loop structures are found to exhibit temporal variations in
their amplitude. We employed multi-wavelength and multi-
instrument data to track the oscillations along the length of the
loop structure. Similar modulations in the wave amplitudes are
observed at all atmospheric heights, including at the base of the
photosphere. The amplitude fluctuations appear to be modu-
lated with a periodicity on the order of 20−27 minutes across
all bandpasses. Despite the fan loops being anchored in the
sunspot umbra, the dominant oscillation period at its base shifts
from three to five minutes close to the photosphere, while the
Figure 2. Light curves from location “A” (see Figure 1) as captured by the AIA 171 Å channel. The top panel displays the original light curve after 3 × 3 pixel
2
binning. The low-frequency background trend is overplotted using a dotted line, which is subsequently subtracted from the original time series to produce the
detrended light curve shown in the middle panel. The bottom panel displays the reconstructed light curve following narrowband Fourier filtration around
three minutes.
4
The Astrophysical Journal Letters, 812:L15 (7pp ), 2015 October 10 Prasad, Jess, & Khomenko
amplitude modulation period remains the same. The five-
minute Doppler oscillations from a non-magnetic region
outside the active region also show similar variations in wave
amplitude across the same period range. This behavior is also
observed in other parts of the fan loop system, which show a
good correlation in amplitude modulation periods with that of
non-magnetic regions outside the sunspot in HMI Doppler-
grams. These results highlight a possible connection between
the photospheric p-modes and the propagating slow magne-
toacoustic waves observed in the corona.
Amplitude modulation has previously been observed in
sunspot oscillations by several authors (Beckers &
Figure 3. Left: normalized Fourier power spectra of original light curves from different SDO and ROSA/HARDcam channels. The peak periodicity identified is listed
in each plot in seconds. The two vertical dashed red lines mark the locations of three-minute and five-minute periodicities. Regions in gray denote the corresponding
frequency band used to produce the filtered light curves shown on the right. Right: Fourier-filtered light curves from the footpoint of the fan loop (location “B” in
Figure 1), plotted as a function of atmospheric height. An AIA 171 Å light curve from location “A” and an HMI Dopplergram time series from location “C” are also
shown for comparison. The obtained phase angles (f) for the light curves at location B, taking the HMI Dopplergram, AIA 1700 Å, and AIA 304 Å channels as a
reference (indicated by superscript “1”) are also listed.
5
The Astrophysical Journal Letters, 812:L15 (7pp ), 2015 October 10 Prasad, Jess, & Khomenko
