Periodicities and Colors of Pulsating Auroras: DSLR Camera Observations From the International Space Station
Abstract
We investigated the spatial characteristics of pulsating auroras (PsA) using digital camera measurements from the International Space Station. These measurements covered PsAs in 
5-h wide regions in the magnetic local time (MLT) direction in short time intervals (
10 min). Analyses of two events suggested that the periodicity of the main pulsation of a PsA does not exhibit any clear dependence on the magnetic latitude (63–
) and MLT (00–05). These results suggest that the periods are not controlled by the bounce time of trapped electrons but by local conditions such as gradients of temperature and/or density of electrons near the magnetospheric source region. We also analyzed the colors of PsAs as proxies for the energies of precipitating electrons. The blue and green channels of the digital camera are sensitive to the band emission of molecular nitrogen ions and the green line of oxygen atoms, respectively. Because the energy bands of precipitating electrons producing those two emissions are different, ratios of blue to green (B/G ratios) can be used as proxies for the energies of PsA electrons. The B/G ratio tends to be higher in the morning sector than in the midnight sector, which is consistent with the results of previous studies showing the MLT dependence of the energies of PsA electrons. This capability of estimating the energies of auroral electrons from digital camera images is expected to provide more opportunities for citizen scientists to contribute more deeply to auroral science.
Key Points
-
DSLR camera observations from the ISS revealed periodicities and colors of pulsating auroras over several thousands of kilometers
-
Periodicities of pulsating auroras analyzed for two events did not exhibit any clear dependence on magnetic latitude and local time
-
B/G ratios of DSLR camera images could be used as proxies for the energies of pulsating aurora electrons
1 Introduction
An aurora is an outstanding natural phenomenon in the Earth's upper atmosphere that emits colorful light when accelerated electrons precipitate from the magnetosphere into the ionosphere (e.g., Akasofu, 1965). Auroras have been classified into two broad categories: discrete and diffuse auroras. Discrete auroras emit bright light with distinct shapes such as arcs, curtains and curls. They sometimes appear in a wide altitude range, for example, from 90 to 300 km (Jones, 1971), which implies that electrons causing discrete auroras have a broad-band energy distribution. By contrast, diffuse-type auroras often show emissions only in a narrow range of altitudes, for example, from 80 to 110 km (Brown et al., 1976; Kataoka et al., 2013). Thus, the energies of electrons causing diffuse auroras tend to be higher than those producing discrete auroras. Such differences in the energies of incident electrons responsible for discrete/diffuse auroras often manifest in the colors of the auroras.
Discrete/diffuse electron auroras almost always show a greenish color at 557.7 nm, which is an emission of excited atomic oxygens. This most prominent oxygen emission is caused by typical auroral electrons with characteristic energies of a few keV and seen at 
110 km altitude. At higher altitudes above 200 km, the red-line emission of oxygen atoms at 630.0 nm is produced by the softer component of electron precipitation. Below the layer of the green-line emission, that is, near the bottom of auroral emission, e.g., below 100 km altitude, different emissions can be observed. Examples of these emissions include the first positive (1PG) band emission (650–700 nm: dark red) of nitrogen molecules (
) and the first negative (1NG) band emission (390–470 nm: bluish) of nitrogen molecule ions (
) (Jones, 1971, 1974). These emissions, often seen as white/pink auroras below the greenish emission, are known as indicators of more energetic electron precipitation, with energies that are sometimes higher than 10 keV. Thus, the altitude distribution of the colors of an aurora is known to represent the energy distribution of precipitating electrons in, at least, a qualitative manner.
Auroras show not only complicated spatial structures but also characteristic temporal variations in their brightness. Diffuse auroras often show quasi-periodic variations called ON–OFF switching and are commonly known as pulsating auroras (PsAs). PsAs are typically observed in the local time sector from the midnight to morning sector during the recovery phase of auroral substorms (Nishimura et al., 2020, and references therein). They are likely to occur under moderately disturbed conditions with a solar wind speed of 
500 km/s, an absolute IMF value of 
8 nT, and an AE index of 
400 nT (Partamies et al., 2017). Early ground-based observations of PsAs and VLF waves suggested that PsAs are caused by pitch angle scattering of energetic electrons by whistler-mode chorus waves (e.g., Ozaki et al., 2012; Tsuruda et al., 1981). After that, in a recent decade, several conjugate observations of PsAs with ground-based optical instruments and in-situ magnetospheric satellites revealed that the origin of a PsA is the interaction of energetic electrons with whistler-mode chorus waves in the magnetosphere (Hosokawa et al., 2020; Jaynes et al., 2013; Kasahara et al., 2018; Nishimura et al., 2010; Ozaki et al., 2018, 2019). The period of ON–OFF switching is known to be in the range from 2 to 40 s (e.g., Lessard, 2012; Nishimura et al., 2020; Yamamoto, 1988). Although the source of its periodicity is the quasi-periodic nature of VLF chorus waves (Sazhin & Hayakawa, 1992; Tsurutani & Smith, 1974), the mechanism to control the periodicity has not been identified yet. It may depend on some macroscopic parameters such as the lengths of local magnetic field lines, which are determined by the magnetic latitude (MLAT) and/or the magnetic local time (MLT), as suggested, for example, by Thomas and Rothwell (1979). To evaluate such dependence on MLAT and MLT, it is essential to observe PsAs in wide MLAT and MLT regions simultaneously.
In the ON phase of a PsA, because the higher-energy electrons are likely to precipitate (McEwen, Yee, et al., 1981; Miyoshi et al., 2010; Miyoshi, Saito, et al., 2015), the emissions of 1PG and 1NG become intense. Ono (1993) measured PsAs using a multi-wavelength photometer with a high temporal resolution (10 Hz) at the Syowa Station in Antarctica. He theoretically estimated the characteristic energies of PsA electrons from the emission-intensity ratios of 844.6 nm (O) and 427.8 nm (1NG) to 670.5 nm (1PG). However, because of the narrow field of view (FOV) of the photometer, it was impossible to observe the spatial distribution of the energies of PsA electrons. Thus, to investigate the characteristics of the energies of PsA electrons in detail, it is highly necessary to develop an easier way to perform such multi-spectral optical observations with sufficient spatial and temporal resolutions over a wide area.
Recently, digital single-lens reflex (DSLR) cameras have been used for auroral observations, especially in the framework of citizen science (e.g., MacDonald et al., 2018; Palmroth et al., 2020). Because such DSLR cameras do not have narrow-band optical filters, they are not proper for multi-wavelength observations. However, Sigernes et al. (2008) suggested that the R, G, and B channel correspond to 630.0 nm and the 1PG band, 557.7 nm, and the 1NG band, respectively, by analyzing the relationship between the well-known emission lines of auroras and the transmission characteristics of RGB channels of several DSLR cameras. Although the accuracy may be lower than those of the optimized multi-wavelength observations, these transmission characteristics could allow us to estimate the energies of auroral electrons. If the color images are obtained with wide FOVs covering a variety of MLAT/MLT ranges, we can discuss the energy characteristics of auroral electrons in a wide region.
Nanjo et al. (2020) developed a method for projecting images captured using DSLR cameras onboard the International Space Station (ISS) onto the geographic coordinate system using the calibration method developed by Hozumi et al. (2016) for imaging parameters. They also confirmed that the ON–OFF switching of PsAs can be captured using projected images from these DSLR cameras because most of the cameras have temporal resolutions less than 1 s. The camera fixed to the ISS sweeps a wide area (
5 h in the MLT direction) in a short time interval (
10 min) because of the short orbital period of the ISS (
90 min). The images can then be used to investigate the spatial characteristics of (a) the periodicities of PsAs and (b) the energy of PsA electrons. In this study, using DSLR camera observations from the ISS, we derived the spatial distribution of the periodicity over a wide area and discuss its influencing factors. We also evaluated whether the energy characteristics of PsA electrons can be estimated from ratios of the RGB channels based on wide-FOV observations from the ISS.
2 Observations
2.1 Events
We analyzed two PsA events (referred to hereafter as Events 1 and 2) captured by a DSLR camera onboard the ISS during its excursion to high-latitude regions. Event 1 was observed for 
9 min, from 07:44 to 07:53 UT, on November 12, 2018, in which the ISS was on a pass from southern Alberta to southern Quebec, Canada, in the Northern Hemisphere. On the other hand, Event 2 was observed for 
8 min, from 18:07 to 18:15 UT, on August 18, 2018, when the ISS was above the Indian Ocean in the Southern Hemisphere. Figure 1 summarizes the background conditions of the geospace environment during Events 1 (left) and 2 (right). The top panels show the H component of the SYM index (Iyemori & Rao, 1996) in November 2018 and August 2018, respectively. These one-month plots of SYM-H indicate that both events did not occur during magnetic storms with clear initial, main, and recovery phases. At the same time, however, these were not always completely quiet intervals, as indicated by the slight decreases in the SYM-H index during the events. In particular, Event 1 had a minimum SYM-H index of 
nT, which corresponds to a weak magnetic storm, based on the definition by Loewe and Prölss (1997).
Background geomagnetic conditions for Events 1 (left) and 2 (right). Top panels show SYM-H indices for one month. Vertical dashed black lines mark days of Events 1 and 2. Second panels show SYM-H indices for one day. Third panels show interplanetary magnetic field in GSM coordinates. Black curves represent absolute values of the 
, and red curves represent 
component. Fourth panels show solar wind plasma densities. Fifth panels show solar wind speeds. Bottom panels show SuperMAG AE indices. Black curves represent SMU indices, and red curves represent SML index. Pairs of vertical solid black lines mark start and end, respectively, of Events 1 and 2.
The second to bottom panels of Figure 1 show one-day plots of various background parameters, such as SYM-H, interplanetary magnetic field (IMF) in the GSM coordinate system, solar wind density, solar wind speed, and SuperMAG auroral electrojet indices (Newell & Gjerloev, 2011). The pairs of vertical black lines mark the starts and ends of the events. Although no strong magnetic storms occurred in both Events 1 and 2, the SYM-H index fell to nearly a few tens of nT below zero. The IMF 
values were negative for several hours before the start of both events. The solar wind speed was high during Event 1, exceeding 600 km/s, whereas that during Event 2 was moderate, at 
500 km/s. The SuperMAG upper/lower (SMU/SML) indices indicate that small substorms occurred immediately before Events 1 and 2 and that the observations were made during the late recovery phases of those substorms. No clear differences in the background conditions were observed between both events, except only that the solar wind speed was higher during Event 1. However, based on the SYM-H index, Event 1 occurred during a very small storm, as already mentioned, implying that the background condition was relatively more disturbed during Event 1 than that during Event 2.
We used DSLR camera images obtained during both events, which are publicly available online with Photo IDs (Gateway to Astronaut Photography of Earth, 1995). The Photo IDs of the images from Event 1 range from ISS057-E-87611 to 88270, whereas those from Event 2 range from ISS056-E-146410 to 147974 and from 149138 to 149543. Although the Photo IDs for Event 2 have a gap, the images were obtained continuously without any data loss. During both events, Nikon D5, with AF-S NIKKOR 24 mm f/1.4 G ED lens for Event 1 and AF-S NIKKOR 28 mm f/1.4 E ED lens for Event 2, was used for the imaging. The settings of the imaging were as follows: the exposure duration was 0.20 s for Event 1 and 0.25 s for Event 2, the ISO speed rate was 12800 for Event 1 and 10,000 for Event 2, and the imaging interval was 0.67 s for Event 1 and 0.75 s for Event 2. Because the temporal variation of the ON–OFF switching of the main pulsation was a few to a few tens of seconds, these exposure durations and imaging intervals were sufficient for the periodicity analysis of the main pulsations of PsAs. To analyze the DSLR camera images as scientific data sets, we employed the mapping technique described by Nanjo et al. (2020). The auroral emission altitude was assumed to be 100 km in the mapping process.
We also used data from the RGB channels to estimate the energies of precipitating electrons. The sensitivity characteristics of each RGB channel of Nikon D5 were provided by de Miguel et al. (2019). According to their results, RGB sensitivity peaks at approximately 460, 540, and 610 nm, respectively, and the FWHM is 
100 nm. Their Figure 1 showed that the greenish emission at 557.7 nm corresponds to the G channel. Their data also implied that the band emissions of 
and 
(1NG and 1PG bands, which are responsible for more energetic electrons) correspond to R and B channels, respectively. However, because the R channel has its sensitivity at 630.0 nm, it is safer to use the B channel as a proxy for more energetic electron precipitation. Thus, we employ the B/G ratio as an index for the ratio of harder/typical electron precipitation, which is expected to represent the energies of PsA electrons qualitatively. The relevant datasets in NASA's website are available in two types: 8-bit JPEG images and 12-bit raw images (.NEF format). Because raw processing simply replaces the raw array with an RGB array using a Bayer filter pattern (Bryce, 1976), no adjustments of the black level or white balance were performed. After raw processing, a median filter was applied because there were many hot pixels in the raw images. We used JPEG images to show the spatial structures of the auroras in 2D, and employed raw images for more quantitative analysis of the time series and B/G ratios.
2.2 Time-Series Analysis
In this study, we intended to extract the periods of ON–OFF switching from successive DSLR camera images from the ISS through a time-series analysis. Because the FOV of the camera changed rapidly, we created a grid map with a resolution of 0.
/1.2 min in the MLAT/MLT covering the observed region and used the points, which continued to be in the FOV for at least 40 s, for the time-series analysis. The upper panel in Figure 2 shows an example of the time-series data from the camera in the region of the PsA. Characteristic temporal variations of the PsA, that is, successive ON–OFF switchings, are present in all RGB channels. Here, however, we used only the G channel data to extract the periods because the signal-to-noise ratio of the G channel is better than that of the two other channels. The color channels of Nikon D5 have wide band transmission characteristics (FWHM: 
100 nm); thus, the original time-series data contained large numbers of unwanted signals as compared to those in typical monochromatic observations using narrow band-pass filters (Grandin et al., 2017; Samara et al., 2012). To reduce contamination due to this effect, we used spline interpolation to smoothen the original signal and applied a low-pass filter to remove temporal variations with periods less than 2 s. In addition, because DSLR camera images from the ISS are captured in the direction of the rim of the Earth, the length of the optical depth changes depending on the looking direction. Because of this effect, the time-series data shown in Figure 2 include a decreasing trend. To remove this trend, we also applied a high-pass filter and subtracted the trend, which had a temporal variation longer than 20 s. This effect is discussed in detail in Section 4.2. The G channel curve after the aforementioned signal processing is shown in the figure as a lime-green curve (labeled “processed G”). The ON–OFF switching of the PsA remains in the processed G curve, whereas most of the unwanted signal and background trend has been removed from the original G curve.
After waveform processing, we applied a wavelet transform (Daubechies, 1990) to the processed G data to extract the period of the ON–OFF switching. A Mexican hat wavelet was used as a mother wavelet. The lower panel of Figure 2 shows the wavelet coefficient, which is an integral value of products of the time-shifted mother wavelet and the processed G. For reference, the processed G is overplotted with a white line in the same panel. The Mexican hat wavelet has an upward convex shape. Thus, when the wavelet coefficient is negative (positive), the waveform at that timing is downward (upward) convex, which would correspond to the OFF (ON) phase of the PsA. We identified such candidate times of the ON and OFF phases using positive and negative thresholds for the wavelet coefficient. The duration of the period can be regarded as the peak-to-peak length of the processed G. Thereby, the period is likely to correspond to the reciprocal of the frequency at which the wavelet coefficient reaches its local minimum. We also determined the start/end times of the period by subtracting/adding half the duration of the period to/from the time when the wavelet coefficient attains a local minimum. To improve the accuracy of the data, we used the periods that have their ON phases at both the start and end of the extracted period. The extracted periods and the local minimums of the wavelet coefficient are plotted in Figure 2 as black dotted lines and red stars, respectively. The start and end times of each black dotted line roughly correspond to the local maximum of the processed G, indicating that the periods were extracted correctly with an accuracy of a few seconds. According to the sampling theorem, periods of less than 1.3 and 1.5 s cannot be detected in Events 1 and 2, respectively. We have confirmed that the detected periods satisfy the sampling theorem. If periods that do not satisfy the theorem are detected, they should be excluded from the analysis. The signal processing described above was applied only to the periodicity analysis, and the unprocessed raw value was used for the B/G ratio analysis.
(Upper) Time-series data of PsA luminosities from 07:47:34 UT to 07:49:20 UT during Event 1. Each RGB curve corresponds to raw count in RGB channels of DSLR camera. Lime-green curve labeled “processed G” represents G-channel time series, which has been processed with method described in text. (Lower) Wavelet coefficient derived from wavelet transform. Black dashed lines show pulsation periods derived from local minimum values in wavelet coefficient.
3 Results
3.1 Spatial Distribution of Periodicities of PsA
Figure 3 summarizes the results of the periodicity analysis during Event 1. In the top panel, the estimated periods of the PsA are plotted as colored dots, which have been superimposed on the background full-color auroral image in the altitude-adjusted corrected geomagnetic (AACGM) coordinate system (Shepherd, 2014). As shown in Figure 2, multiple periods were sometimes extracted at a single location. In such cases, we simply plotted the median value of the extracted periods. Hereafter, we call this type of plot as a “banana plot.” Note that this background image was created via overplotting of all the images captured during Event 1 (more than 900) in descending order of Photo ID. Thus, the background image does not always represent the actual and instantaneous structures of the aurora, but demonstrates only the large-scale distribution of the aurora. An animation showing the full sequence of those images (not combined ones) accompanies the electronic version of this article (Movie S1). In these plots and movie, no dots are plotted when/where optical pulsations were not detected.
(Top) PsA observed from ISS during Event 1 in AACGM coordinate system. Color dots show median values of pulsation periods at each point. (Lower three) All extracted periods of PsA in MLAT ranges 65–
(second), 64–
(third), and 63–
(bottom). Red curves show median (dots) and interquartile range (error bars) for every half-hour in MLT.
In the top panel of Figure 3, the colors of the dots are mainly greenish and yellowish, indicating that the periodicity of the PsA during Event 1 was 
10–20 s, which is most clearly observable in the local time sector before 03 MLT. However, the red dots are dominant in the late MLT sector (
03 MLT), which indicates that the periodicity becomes shorter 
5–10 s in the late-morning side. To visualize the dependence of periodicity on MLT in more detail, we plotted all extracted periods as a function of MLT in the lower three panels. Here, we have sorted the data points into three latitudinal ranges: 65–
(top), 64–
(middle), and 63–
(bottom) MLAT, with which we may determine an MLAT dependence of the periodicity. The median (dots) and interquartile range (error bars) (i.e., 25th–75th percentile) are plotted with red color for every half-hour in MLT. The red curves in the lower three panels demonstrate a gradually decreasing trend in periodicity for later MLT, with some exceptions (e.g., small peaks at 03 MLT in the bottom two panels). This trend is consistent with the existence of reddish points in the later MLT (after 03 MLT) in the banana plot. However, if we examine the full distribution of the periods in the lower three panels in detail, short periods are observed in the midnight sector (a certain number of 
5 s points before 02 MLT) and, conversely, longer periods in the morning sector (
10 s points after 03 MLT). Namely, even at a single location, there was a wide variety of periodicity, indicating that the period of the PsA was highly diverse.
The same periodicity analysis was applied to Event 2 from the Southern Hemisphere, which is summarized in Figure 4 in the same format as that of Figure 3. During Event 2, auroras were already visible in earlier local time sectors. However, the PsA was observed only after 23 MLT; thus, only the data from 23 to 05 MLT are displayed in the banana plot. The background full-color image of the auroras reveals several discrete arcs in the higher latitude part of the FOV (mostly poleward of the 
MLAT circle). Signatures of PsA are seen over a wide MLT range, from 23 to 04 MLT, at the lower latitude part (
MLAT). Details of the behavior of the auroras, especially the temporal variation of the PsA, in this interval are more clearly shown in an animation compiling all the images from this sequence (Movie S2). During this interval, the optical signatures of the PsA were relatively dimmer than those in Event 1; however, the time-series analysis was able to extract their periods. In contrast to that in Event 1, the periodicity had no clear dependence on MLT, that is, there were no systematic changes in the colors of the dots. The lower three panels show the periodicity with respect to MLT in three MLAT ranges: 
to 
(top), 
to 
(middle), and 
to 
(bottom) MLAT. The total number of extracted periods was a few times lower in Event 2 than that in Event 1. As already inferred from the banana plot, the periodicity had no systematic dependence on the MLT and MLAT. However, the periods sometimes changed in a few seconds even for small differences in MLT. For example, at 
1.5 MLT, as shown in the middle panel, the median of the periods became longer than that in the surrounding MLT sectors, and there were a few samples with periods shorter than 10 s. Although Events 1 and 2 had differences in terms of their periodicities exhibiting (or not exhibiting) dependence on MLT, the results are similar in that the periodicities were highly diverse and had broad distributions even at single locations.
(Top) PsA and discrete aurora observed from ISS during Event 2 in AACGM coordinate system. Color dots show median values of pulsation periods at each point. (Lower three) All extracted periods of PsA in MLAT ranges 
to 
(second), 
to 
(third), and 
to 
(bottom). Red curves show median (dots) and interquartile range (error bars) for every half-hour in MLT.
3.2 Spatial Distribution of B/G Ratio
Here, we evaluate the feasibility of using RGB-color DSLR images for estimating the energies of precipitating electrons using the blue-to-green ratios (B/G ratios) of the ISS images. If the assumption that the B and G channels are respectively sensitive to the 1NG emission and the green-line, is true, then the higher the B/G ratio means the higher the energy of PsA electrons. The validity of this assumption is discussed in detail in Section 4.2. The banana plot in Figure 5 shows the B/G ratios calculated from the raw RGB images of Event 1. The B/G ratio values are displayed with a color scale from 0.3 to 0.8, where values in the regions without auroral emissions are colored black. The FOV of a single image is traced using a dashed white line in the banana plot. This fan-shaped FOV swept the entire area as the ISS progressed with its orbit; thus, the data shown in the banana plot contain both temporal and spatial variations and this type of plot can be used only for visualizing large-scale distributions of the parameter. The distribution of B/G ratios in the MLAT and MLT coordinate system exhibited an increasing trend from the midnight to morning sector, which is shown by the reddish points in the equatorward part of the oval in the 04–05 MLT sector.
(Top) B/G ratios of PsA observed from ISS during Event 1 in AACGM coordinate system. White dashed fan-shaped region shows FOV at 07:49:28.9 UT (corresponds to middle panel). Blue contour lines show the solar elevation angle at 07:53 UT. (Middle) RGB image (left) and B/G ratios (right) of PsA observed at 07:49.28.9 UT. White dashed box shows region magnified in bottom panel. (Bottom) Magnified images from middle panel.
The middle panels show the RGB image (left) and B/G ratio image (right) at 07:49:28.9 UT. These are not combined images but, rather, snapshot images captured within the FOV shown by the dashed white lines in the banana plot. Detailed spatial structures of PsA patches are outlined with white solid lines, which are quite different from what is shown in the banana plot. From these snapshot data, patches of the PsA were observed only on the equatorward part of the aurora oval, in which the B/G ratio was significantly higher. This tendency is more clearly demonstrated in a movie compiling the data from the entire sequence, which accompanies the electronic version of this article (Movie S3). To compare the spatial structures of the PsA patches and B/G ratios more directly, the data in the white dashed boxes in the middle panels are shown magnified in the bottom panels. According to the image, the B/G ratio increased up to 
0.7 within the brighter region (pinkish and whitish patches in the RGB image). By contrast, within some darker regions (dim areas in the RGB image), the B/G ratio decreased below the background level at 
0.5.
The top and middle panels of Figure 6 display the B/G ratio data of Event 2 in the same format as that of Figure 5. An animation showing the full sequence of the middle panels of Figure 6 accompanies the electronic version of this article (Movie S4). The bottom panel of Figure 6 shows the B/G ratio along the cross-section at 
MLAT in the banana plot as a function of MLT. The red curve represents the median calculated for every half-hour in MLT. In the banana plot, two L-shell aligned regions are visible, which may be a signature of a double oval (Elphinstone et al., 1995). The one at the high-latitude side was a discrete aurora; the B/G ratio was mostly low in this region. However, the B/G ratio was locally high in the pre-midnight sector poleward of 
MLAT. This reddish area could correspond to the lower-altitude border of the discrete aurora, which appears in pink in the RGB image (see Figure 4). This localized enhancement was introduced because we mapped the rim-direction images onto the horizontal plane, which cautions us not to recognize the altitude variation in emission color as a horizontal spatial structure. The effects of the rim-direction observation are discussed in detail in Section 4.2.
(Top) B/G ratios of PsA and discrete aurora observed from ISS during Event 2 in AACGM coordinate system. White dashed fan-shaped region shows FOV at 18:10:41.0 UT (corresponds to middle panel). White dashed line shows cross section plotted in bottom panel. Blue contour lines show the solar elevation angle at 18:15 UT. (Middle) RGB image (left) and B/G ratios (right) of PsA observed at 18:10:41.0 UT. (Bottom) B/G ratios on white dashed line in top panel (at 
MLAT) as function of MLT.
The other oval feature at the low-latitude side is fully composed of diffuse auroras; the B/G ratio was higher than that in the discrete aurora at the higher latitude. These trends can also be observed in the middle panels, where snapshots of the RGB and B/G ratios are shown. Moreover, the pre-midnight sector shows some high B/G ratio values at 
MLAT, but the optical emission was dim in that region, which implies that, when using the B/G ratio, we should check whether the aurora is sufficiently bright in the region of interest. Furthermore, the B/G ratio becomes slightly higher in the morning sector than in the midnight sector. This tendency was observed during Event 1 and was also identified for Event 2, in the bottom panel of Figure 6. In the region of the PsA, which belongs to the main oval, it was difficult to identify the brighter and darker regions from single images (i.e., in the middle panels). However, the B/G ratio exhibits a slightly increasing trend in the top and bottom panels; the B/G ratio attains a minimum (
0.6) before 00 MLT and a maximum value (
0.7) at 
04 MLT. Although distinguishing the brighter and darker regions of the PsA in Event 2 was difficult, the B/G ratio tended to be higher in the morning sector than in the midnight sector for both Events 1 and 2.
4 Discussion and Conclusions
4.1 Spatial Distribution of Periodicities of PsA
Thomas and Rothwell (1979) measured the periodicities of PsAs at two sites: Poker Flat (
MLAT), Alaska; and Andøya (
MLAT), Norway. Their results showed that the periodicity is longer at higher latitudes, and that the pulsating periods are close to the bounce period of a few keV electrons. They therefore suggested that the periodicity of a PsA is associated with the bounce period of trapped electrons in the magnetosphere. Duncan et al. (1981) operated photometers at four sites in Canada and performed a similar analysis of the latitudinal dependence of the periodicity. Their results also showed that the period was longer at higher latitudes, but the dependence was observed only in a limited period range of less than 10 s. Both sets of data were obtained at different times and locations with insufficient FOVs not covering the entire region of the PsA; thus, it was difficult to investigate the spatial (i.e., latitudinal) dependence of the periodicity in detail. In this study, we examined the spatial (MLAT and MLT) dependence of the periodicity under almost the same geomagnetic conditions by capturing entire regions of the PsAs in a quiet, short time interval. This type of large-scale observations of PsAs may provide us clues regarding the factors influencing periodicity.
Both the banana plot and scatter plots in Figure 3 show that, for Event 1, the periodicity of the PsA exhibited no monotonic dependence on MLAT, but tended to be shorter in the morning sector. At the MLAT from 64 to 
, the median period was 14 s in 1.5 MLT and was shortened to 7 s in 4.5 MLT. To confirm whether this trend reflects the change in the bounce period of the trapped electrons, we calculated the lengths of the magnetic field lines using the T04 model (Tsyganenko & Sitnov, 2005). At 64.
MLAT, the length of the field lines was 13 
for both 1.5 and 4.5 MLT, and the bounce period of electrons with 3-keV energy was 5.3 s. The change in the bounce period was less than 0.1 s for the 3-hr difference in MLT, and there was no trend for the bounce period to shorten by 8 s in the morning sector. The typical period derived from our analysis was 10 s. If this pulsation period is determined by the bounce period of the trapped electrons, the energy of the electrons was 800 eV, which is exceedingly low to explain quasi-periodic optical emissions of PsA at lower than 100 km reported in Partamies et al. (2017). In contrast to Event 1, which exhibited a shorter pulsating period in the morning sector, Event 2 demonstrated no monotonic spatial dependence on MLT, as shown in both the banana plot and scatter plots in Figure 4. Three scatter plots show that the typical pulsation period was 
15 s, and that the energy of electrons with a bounce period of 15 s at 
MLAT was 
500 eV at both 00 and 03 MLT, which was also lower than the typical energy band of electrons causing the main pulsation. Therefore, the results of this study do not lead the theory that the periodicity of a PsA is influenced by the bounce period of the trapped electrons.
In the banana plot and median of scatter plots in Figure 3, the pulsation period of the PsA tended to shorten toward the morning sector. However, in Figure 4, no such noticeable shortening trend was observed in the MLT direction. Since this paper conducted the event study, the results may not exhibit universal characteristics of PsA. In both Events 1 and 2, however, the pulsation period had broad distributions that could exceed 20 s even at a single point (e.g., at 03 MLT in the middle scatter plot in Figure 3). Hence, a single indicator such as the median may not be the best parameter to describe spatial dependence. Even in Event 1, the shortening trend was not necessarily monotonous, because there was a location at 
03 MLT where the period became locally longer. Based on these observations, it would be appropriate to infer that the periodicity of a PsA does not have a clear and monotonic spatial dependence on MLT/MLAT and that their beats change locally. Thus, the periodicity of PsA should depend on some local parameters, such as the gradient of magnetospheric electron density and temperature, rather than on parameters that change monotonically in large scales, such as the bounce period of trapped electrons or the magnetic field intensity. In support of inconsistent with the length of the magnetic field line, Li et al. (2011) reported the modulation of chorus waves is related to the electron density variation. Ozaki et al. (2015) reported that the periodicities of PsAs and chorus waves change with the curvature of the magnetic field line at the equatorial source region. Our results also suggest that the periodicities of PsAs are a result of the generation of chorus waves controlling by the local parameters (density, temperature, and gradient of the magnetic field line, etc.) in the magnetosphere. Davidson (1979) has suggested the relaxation-oscillation model as an origin of the periodicity of PsA. Demekhov and Trakhtengerts (1994) have suggested the flow-cyclotron maser model to explain the periodicity. Such spontaneous process should be essential to control the periodicity of PsA.
4.2 Validity of B/G Ratio as Proxy for Energy of PsA Electron
McEwen, Duncan, and Montalbetti (1981) performed multi-wavelength optical observations with a ground-based photometer and direct simultaneous observations of the precipitating electrons with a sounding rocket. They compared the values of characteristic energy (
) from the rocket observations with that estimated from the intensity (Rayleigh) ratios of the 557.7- and 427.8-nm emissions. Both 
values were high during the ON phase of the PsA and low during the OFF phase, and agreed quantitatively within 1 keV. Steele and McEwen (1990) also performed simultaneous observations of discrete and diffuse auroras using particle observations from a low-altitude orbiting satellite and optical observations with a photometer. They determined a negative correlation between the intensity ratio 5577/4278 and 
, and inferred that 
is expressed by the following equation: 
. Note that their ratio has an inverted numerator and denominator to the B/G ratio. Although they suggested that the estimation of 
using the 6300/4278 ratio was more accurate than that using the 5577/4278 ratio, the lifetime of the 630.0-nm emission (
110 s (Jones, 1971, 1974) is exceedingly long to infer the energies associated with auroras that have fast temporal variations (i.e., shorter than several tens of seconds). Hence, the 5577/4278 ratio is more suitable than the 6300/4278 ratio for estimating the energies of PsA electrons.
Because our analysis used a DSLR camera with wider transmission characteristics than those of a typical photometer, we should not simply regard the B channel as the 427.8-nm emission and the G channel as the 557.7-nm emission without evidence. Since the DSLR camera used in this study is mounted on the ISS, it is not possible to conduct a calibration experiment and derive transmission characteristics of RGB channels. However, de Miguel et al. (2019) derived the transmission characteristics of the same model of the DSLR camera used in this study (Nikon D5). According to their Figure 1, the band where the relative response of the B channel exceeds 10% is 400–520 nm. According to Jones (1974), there are many other emission lines of auroras in this bandwidth besides 427.8 nm, but all emission lines, which are brighter than 10% of those of the 427.8-nm emission, belong to the 1NG band. The auroral spectra in Svalbard, Norway, as measured by Sigernes et al. (2008) (their Figure 7), also showed that there are no bright emission lines in this band other than the 1NG band. However, because the emission intensity at 557.7 nm is 6–7 times greater than that at 427.8 nm, contamination of the green-line should be considered separately. In the transmission characteristics of the B channel of de Miguel et al. (2019), the relative responses for the 427.8- and 557.7-nm emission are 60% and 5%, respectively. Thus, when the ratio of the emission intensities at 427.8 and 557.7 nm is 1:6, the ratio of their contributions to the B channel is 2:1. Since 33% of the total is due to the emission at 557.7 nm, we cannot conclude that the B channel detects only the 427.8-nm emission. By contrast, applying the same procedure, the ratio of the contribution in the G channel is calculated to be 1:180, indicating that the G channel is almost entirely composed of the 557.7-nm emission. Therefore, compared to the G channel, the B channel has a larger contribution of the 1NG band, including 427.8 nm, and is more sensitive to the high-energy electrons precipitation. Although the G channel contains the emission at 630.0 nm, its contribution was found to be less than 1% by applying the same calculation. This estimation is based on a theoretical calculation using the results of the previous studies, but in the upper panel of Figure 2, the peak of the intensity in the B channel occurred a little (
1 s) earlier than that in the G channel at some points (e.g., at 7:47:45 and 7:48:27). The 1NG band is emitted immediately after excitation, whereas the emission at 557.7 nm is delayed by 0.7 s from excitation (Jones, 1971, 1974). Therefore, the timing difference in the emission peaks of the B and G channels suggests that they are sensitive to the 1NG band and the 557.7-nm emission, respectively.
Due to its wide bandwidth, the DSLR camera receives a wide variety of background light besides auroras. These include, for example, airglow, city lights, and reflected light from the ground and clouds. However, these may not have systematic dependence on the B/G ratio. In the current cases, there were no city lights in the auroral region. The banana plots in Figures 3 and 4 also show that the non-auroral region is in almost completely dark. Therefore, the contamination of reflection light and airglow on the B/G ratio could be small. Comparing Figure 1 in de Miguel et al. (2019) with the spectrum of the night airglow (Broadfoot & Bellaire Jr., 1999; Krassovsky et al., 1962), there are no bright emission lines in the B channel band. The G channel band contains emissions at 557.7 nm (OI) and at 589.6 nm (NaD). The intensity (Rayleigh) of the OI emission is 
10% of the PsA emission at 557.7 nm, and the NaD emission is several times fainter than the OI emission. Through the above, the contribution of the G channel is mostly (
90%) due to the PsA emission at 557.7 nm, and the B channel has almost no atmospheric light effect, thus the qualitative features of the B/G ratio are not interfered with by the non-auroral emissions. In addition to the background light, in the morning sector, the purple aurora often appears due to the resonant scattering by sunlight (Shiokawa et al., 2018, 2019). Such a purple emission is seen in the higher-altitude parts of discrete auroras. Although it has not been reported that a PsA is also colored purple due to the resonant scattering, we have drawn contours of the solar elevation angle at an altitude of 100 km in the banana plots in Figures 5 and 6 to evaluate the effect of sunlight. In the aurora oval in Event 1, the solar elevation angle took a maximum of 
at 5 MLT. Since the astronomical twilight ends at a solar elevation angle of 
, the oval is unlikely to be affected by sunlight. The oval in Event 2 also has solar elevation angles less than 
, which supports that the sunlight does not affect the increasing trend of the B/G ratio.
In addition to the wide wavelength bands, the observations from the ISS have a different spatial resolution as compared to the typical ground-based observation. Because the camera captures auroras in the rim direction and then we project the image onto the horizontal plane, there is a spatial distortion in the shape of auroras. This effect is smaller if an aurora is thinner in the altitude direction. As shown by Nanjo et al. (2020), because PsAs are generally thinner than discrete auroras, patches of PsAs whose lengths are several tens of kilometers can be projected and resolved with similar accuracy to observations by ASIs.
The incident angle of the line-of-sight (LOS) vector depends on the location in the ISS image. Therefore, the B/G ratio can be biased in some locations. The incident angle is larger at the back of FOV (often at the morning side) and smaller at the front of FOV (i.e., closer to the camera). Because it also depends on the projected altitude of the aurora, further attention is needed when the blue and green emissions are emitted at different altitudes. According to Jones et al. (2009), the altitudinal thickness of a PsA is 15–25 km; thus, we assumed that the 1PG was emitted at 90–100 km (B layer) and that the green line was emitted at 100–115 km (G layer). In Event 1, because the difference between the incident angle at 100 km and that at 115 km was small (less than 
), the difference in the incident angle between the two layers was not considered. The thicknesses of the B and G layers were assumed to be 10 and 15 km, respectively. Therefore, the LOS vector penetrated the B and G layers with distances of 
and 
km, respectively. Here, 
is the incident angle. Because the value of 
/
is equal to 10/15, the B/G ratio does not depend on the incident angle of the LOS vector.
Because the PsA patches were not large in most cases, it was not clear whether the LOS vector penetrated the auroral emission layer all the way from the top to the bottom. The horizontal size of a patch is several thousands of 
(Humberset et al., 2018; Partamies et al., 2019), and the vertical thickness is 15–25 km (Jones et al., 2009). As an example, let us consider an aurora that is 100 km in the horizontal direction and 25 km in the vertical direction. A LOS vector that penetrates the emission layer from the top to the bottom has an incident angle of 
(
) or less. Because the incident angles of the LOS vectors in the middle panel of Figure 5 range from 30 to 
, this effect can be canceled at least at one point of each PsA patch in FOV. Near the edges of the patches, however, it was unlikely that the LOS vector penetrated from the tops to the bottoms of the patches. In this case, a single LOS vector may penetrate the patch and background precipitation regions, but the background precipitation will not affect significantly because the flux is 
1/10 of the ON phase of the patch (Miyoshi, Saito, et al., 2015). This effect would be small based on the averages of B/G ratios inside the patches. Therefore, because of the influence of the incident angle, B/G ratios in rim-direction observations should be used to estimate energy variations in wide areas of more than a few hundred kilometers, rather than to estimate the fine-scale energy variation in a single patch.
The above geometric problems do not have to be concerned if both layers were distributed at the same altitude, as in Figure 7 in Partamies et al. (2017). However, because the same altitudinal distribution means that there is little difference in the energy of PsA electrons, the B/G ratio may not work as an index of the energy of PsA electrons. By contrast, if PsA electrons have relatively high energy and the quenching of the 557.7-nm emission occurs, the B/G ratio will be higher. Therefore, the B/G ratio might be more effective in moderate to severe events where the auroral color changes than in quiet ones where no quenching of the 557.7-nm emission occurs at all regions and times.
4.3 Spatial Distribution of B/G Ratio
Hosokawa and Ogawa (2015) investigated the ionospheric 
region electron density profile for 21 intervals of a PsA using data from the European Incoherent Scatter (EISCAT) radar. The results suggested that the peak altitude becomes lower and that the peak electron density becomes higher in the morning sector. Later, Partamies et al. (2017) analyzed the peak emission altitude for 
400 cases of a PsA using the all-sky cameras of the Magnetometers–Ionoshperic Radars–All-sky Cameras Large Experiment (MIRACLE) network. They concluded that there is no significant MLT dependence of the altitude of PsAs before 6 MLT. Tesema et al. (2020) combined ground-based optical observations and particle observations from the low-Earth orbiting satellites DMSP and POES to derive the MLT dependence of the flux of PsA electrons. They found no overall MLT dependence in the flux, but they also noted a slight increase in the flux after 6.5 MLT at higher energy band (
30 keV) at the same time. Kawamura et al. (2020) measured a lifetime of oxygen atoms that produce the 557.7-nm emission by a photometer at Tromsø, Norway. They calculated an altitude of PsAs by using the measured lifetime. Their result exhibited that the altitude decreased in the morning sector, especially after 6 MLT. A common implication of these studies is that the energy of PsA electrons increases after 6 MLT.
In this study, the B/G ratio increased from 3.5 MLT in Event 1 and from 3.0 MLT in Event 2. Although there is a 3-hr difference in the timing of the increase between the previous studies and the present study, the qualitative increasing trend in the morning sector is consistent. The difference in the timing may be due to the fact that the present study is a case study while the previous studies are statistical studies. Another possible cause is the difference in latitude. Hosokawa and Ogawa (2015) and Kawamura et al. (2020), who suggested the increase in the energy of PsA electrons, performed their observations in Tromsø, Norway (MLAT: 66.
). The increase in the B/G ratio observed in Event 1 started at an earlier MLT at lower MLAT, and it started at 3.5 MLT in regions with the MLAT lower than 
. The increase in the B/G ratio at 66.
MLAT was observed from 
4.5 MLT, which is still different from the timing in the previous studies, but the difference in the MLAT may explain the gap. Based on the above, the B/G ratio, which can be a proxy for the energies of precipitating electrons, becomes higher in the morning sector, suggesting that the energies of PsA electrons are higher in the morning sector.
Sandahl et al. (1980) launched a sounding rocket into a PsA and observed the characteristic temporal variations of electron energy spectra. Their in-situ observation showed that pulsation in the electron energy spectrum occurs only in the energy range above 3–4 keV. More recently, Miyoshi, Saito, et al. (2015) compared in-situ energy spectra from the REIMEI satellite with simultaneously obtained optical data at the magnetic footprints of the satellite. They determined that the ON–OFF switching of optical pulsation is caused by energetic electrons above 3 keV and that continuous (i.e., without pulsation) background precipitations occur below 1 keV which has been known as drizzle precipitations (Evans et al., 1987). In our analyses, the behavior of the B/G ratio is in good agreement with the aforementioned energetic characteristics of PsA electrons. That is, the energy is higher within the brighter (white/pink) regions than in the background regions. Furthermore, we observed stable, faint-green emissions in areas where optical pulsation was not detected (i.e., areas without dots in the banana plot of Figures 3 and 4), which may correspond to the background continuous precipitations suggested by Miyoshi, Saito, et al. (2015).
Brown et al. (1976) set up two video cameras 10 km away from each other and tried to estimate the lower cut-off altitude of PsA and discrete aurora emissions. The altitude of PsAs was then determined to be relatively lower than that of discrete auroras. In some cases, the altitudes were less than 90 km. More recently, Kataoka et al. (2013) conducted a similar experiment using two DSLR cameras 8 km away from each other. They estimated the altitude distributions of PsAs and discrete auroras by producing an altitude map of the emissions in 2D. Through this approach, they demonstrated that discrete auroras with ray structures exhibit broad altitude distributions mainly 100–130 km and, sometimes, up to 
250 km, whereas optical emissions of PsAs are distributed in a narrow altitude range, from 80 to 90 km. The results of these previous studies indicated that the energies of precipitating electrons are higher during a PsA than during a discrete aurora. In our study, the B/G ratio was demonstrated to be higher in the region of the PsA compared with that of the discrete aurora. This result is in good agreement with those of previous studies because a high B/G ratio may be a sign of higher-energy electron precipitation causing auroral emissions at lower altitudes.
As shown in the banana plot of Figure 5, in the morning sector of Event 1, the B/G ratio increased significantly in the equatorward part. By contrast, the B/G ratio distribution in Event 2 did not exhibit a similar characteristic. This tendency may be explained by the precipitation of high-energy electrons from the radiation belt, as reported by Miyoshi, Oyama, et al. (2015) and Miyoshi et al. (2020, 2021). As shown in the banana plots of Figures 3 and 4, the aurora oval was located 
MLAT equatorward in Event 1 as compared with that in Event 2. From Figure 1, the SYM-H index decreased more and the solar wind speed was higher in Event 1 than in Event 2. From the difference in background conditions between the two events, the radiation belt may have been more active in Event 1 than in Event 2, and more energetic electrons may have been precipitated into the ionosphere. This could be a reason for the higher B/G ratio in the equatorward side of the morning sector during Event 1.
In conclusion, the characteristics of B/G ratios derived from DSLR camera data are qualitatively consistent with those of the energy of PsA electrons reported in previous studies. This result confirms the feasibility of estimating electron energies from full-color DSLR camera images. In recent years, citizen science has been practiced with DSLR cameras, which has contributed to scientific studies on auroras (e.g., MacDonald et al., 2018; Palmroth et al., 2020). However, most of these methods have been employed only for identifying the forms and locations of auroras, and their usages remain limited at this stage. In the future, we plan to evaluate the possibility of using B/G ratios as more quantitative proxies for the energies of precipitating electrons, which will contribute to the further development of citizen science with DSLR cameras.
5 Summary
10 min, during the midnight to morning sector (23–05 MLT). The results are summarized as follows:
-
The periodicities of the examined PsAs did not exhibit a systematic spatial dependence on MLAT or MLT, which was inconsistent with previous studies (Duncan et al., 1981; Thomas & Rothwell, 1979).
-
The periodicities of the examined PsAs varied widely from location to location, suggesting that local conditions in the magnetosphere, rather than the large-scale structure, contribute to the determination of periodicity.
-
B/G ratios were higher in the morning sector than in the midnight sector, and higher in brighter regions than in darker regions, which are consistent with characteristics of PsA electrons reported by previous studies (Hosokawa & Ogawa, 2015; Miyoshi, Saito, et al., 2015). This result implies that B/G ratios could be used as proxies for the energies of precipitating electrons in a qualitative manner.
-
In the morning sector, an increase in the B/G ratio in the equatorward part of the aurora oval was identified during a small magnetic storm, suggesting the precipitation of more energetic electrons from the radiation belt in the region of the PsA.
These results demonstrate that conjugate observations with satellites measuring of the temperatures and densities of electrons will enable us to discuss deeply the factors that influence the periodicities of PsAs. Moreover, although it was suggested that B/G ratios are a valid proxy for the energies of PsA electrons, further experiments are necessary for its use in more quantitative estimation.
Acknowledgments
This work was supported by Grants-in-Aid for Scientific Research (15H05747, 15H05815, 16H06286, 17H00728, 18KK0100, 20H01959, 20H02162, 21H04518, and JPJSBP120194814) from the Japan Society for the Promotion of Science. The authors acknowledge NASA Goddard Space Flight Center's Space Physics Data Facility's OMNIWeb services for providing solar wind data and magnetic indices, which are available at https://omniweb.gsfc.nasa.gov/. The authors would like to thank the Johns Hopkins University Applied Physics Laboratory for the use of SuperMAG indices, which are available at http://supermag.jhuapl.edu/.
Open Research
Data Availability Statement
The auroral photographs obtained from the ISS are courtesy of the Earth Science and Remote Sensing Unit, NASA Johnson Space Center. The photographs obtained from the ISS are available at https://eol.jsc.nasa.gov/.
