Estimation of the emission altitude of pulsating aurora using the five-wavelength photometer

Using a ground-based five-wavelength photometer, which has been operative in Tromsø, Norway since February 2017, we have statistically analyzed the lifetime of O(1S) to reveal the emission altitude of pulsating aurora (PsA). For the statistics, we have extracted intervals of PsA using an EMCCD all-sky imager on 37 nights during 3 months from January to March, 2018. By performing a cross-correlation analysis between the time-series of 427.8 nm (N2+ first negative band) and 557.7 nm oxygen emissions, we derived the distribution of the lifetime of O(1S). The mean of the lifetime is 0.67 s and the mode is around 0.7 s. We estimated the emission altitude of PsA using the lifetime of O(1S) and then carried out a case study, in which we compared the temporal variations of the emission altitude with the peak height of E region ionization obtained from the simultaneous observation of the EISCAT UHF radar. We confirmed an overall agreement between the two parameters, indicating the feasibility of using the current method for estimating the energy of precipitating electrons causing PsA. In addition, we have derived the statistical characteristics of the emission altitude of PsA. The result shows that the emission altitude becomes lower in the morning side than in the midnight sector, which indicates that the energy of PsA electrons is higher in the later MLT sector. Especially, there is a decrease of the emission altitude at around 06 MLT. However, the model calculation infers that the energy of cyclotron resonance between magnetospheric electrons and whistler-mode chorus waves does not change so much depending on MLT. This implies that the observed change of the emission altitude cannot be explained only by the MLT dependence of resonance energy.


Introduction
Pulsating aurora (PsA) is a category of diffuse aurora, which is characterized by luminosity blinking with a periodicity ranging from a few to a few tens of seconds (Yamamoto 1988). Such a quasi-periodic luminosity variation is called the main pulsation [  and reference therein]. PsAs are generally observed in the morning side during the recovery phase of auroral substorms (Kvifte and Pettersen 1969). They often continue for a few hours or longer (Jones et al. 2011). The spatial structure of PsA is divided into the following two broad categories: (1) cluster of patches with irregular shapes (patch-type) and (2) bundles of arcs elongating mostly in the east-west direction (arc-type) (Royrvik and Davis 1977;Yamamoto 1988;Sato et al. 2004).
The temporal variation of PsA is associated with quasi-periodic precipitation of energetic electrons from the magnetosphere (e.g., Sandahl et al. 1980). Previous studies have suggested that such quasi-periodic precipitations are caused by the wave-particle interaction between whistler-mode chorus waves and ambient electrons whose energy ranges from a few to a few tens of Open Access *Correspondence: yukikawamura@uec.ac.jp 1 University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo 182-8585, Japan Full list of author information is available at the end of the article keV [e.g., (Miyoshi et al. 2010(Miyoshi et al. , 2015a]. Especially, it has been reported that there is a one-to-one correspondence between the amplitude variation of chorus waves and the luminosity modulation of PsA (Nishimura et al. 2010(Nishimura et al. , 2011. These observational results imply that PsA is the two-dimensional projection of the characteristics of chorus waves in the magnetosphere. Although recent literatures, which analyzed the simultaneous groundsatellite observations, have revealed the correspondence between PsA and chorus waves (e.g., Kasahara et al. 2018;Hosokawa et al. 2020), it is still unclear what factors control these periodic variations.
The emission altitude of PsA has been studied intensively since 1970s using optical data from ground-based all-sky video cameras (e.g., Brown et al. 1976). The altitude of PsA emission contains information about the energy of precipitating electrons, which allows us to infer the nature of wave-particle interaction process. Thus, there have been many studies investigating the altitude of PsA and the energy of precipitating electrons. Brown et al. (1976) estimated the lower cut-off altitude of PsA emission through triangulation of two all-sky TV cameras having a common field-of-view. They showed that the height of PsA emission ranges from 82 to 115 km; corresponding energy of electrons being from 50 to 5 keV, respectively, which is consistent with direct in situ observations of PsA electrons by sounding rockets (e.g., Sandahl et al. 1980). However, Brown et al. (1976) analyzed only 2 h of optical observations from 3 nights. Recently, similar analysis by Partamies et al. (2017) demonstrated that the height of PsA becomes slightly lower in the morning sector. But, it is still unclear whether this trend is statistically significant due to the limited amount of data available. Jones et al. (2009) estimated the energy of PsA electrons from ionospheric electron density observations by the Poker Flat Incoherent Scatter Radar (PFISR). More recently, Hosokawa and Ogawa (2015) studied the variation of electron density profile during PsA using the European Incoherent SCATter (EISCAT) radar. They demonstrated that the energy of PsA electrons, inferred from the altitude of ionization, tends to be higher in the morning side (i.e., in the later MLT sector). Miyoshi et al. (2015a) identified a few hundred keV electron precipitations during simultaneous measurements of PsA with EISCAT and Van Allen Probes. Then, they proposed a model explaining the scattering of electrons in a wide range of energy by considering the propagation of chorus waves toward higher latitudes.
As mentioned above, ionospheric electron density variations during PsA have been studied in detail using incoherent scatter radars. In the past, however, the MLT dependence of the altitude of PsA has not been examined using a sufficient amount of data. Thus far, the statistical properties of the energy of PsA electrons are still unknown. To solve this problem, we need a method that can derive the altitude of PsA emission in a statistical manner. Scourfield et al. (1971) proposed a procedure for estimating the emission altitude of PsA using the lifetime of O( 1 S) excited state atoms seen in the optical observations. Since the transition from O( 1 S) to O( 1 D) producing 557.7 nm emission is forbidden and its lifetime is about 0.70 s, time-series of the 557.7 nm emission exhibits a systematic time lag compared to that of an allowed transition emission such as 427.8 nm, whose lifetime is ~ 10 −8 s (Nozawa et al. 2018). Scourfield et al. (1971) estimated the altitude of the 557.7 nm emission from this delay time because the delay time is longer at higher altitudes. Their method has a potential to estimate the energy of PsA electrons. However, Scourfield et al. (1971) only proposed the above-mentioned method, which has not actually been used for the statistical analysis of the altitude of PsA.
In this paper, we performed a statistics by applying the method of Scourfield et al. (1971) to multi-wavelength photometer observations in Tromsø, Norway. This approach enables us to derive the statistical characteristics of the emission altitude of PsA, which provides fundamental information about the energy of PsA electrons and wave-particle interaction process in the magnetosphere.

Datasets
In the current statistical analysis, we employed the fivewavelength photometer (Nozawa et al. 2018) and Electron Multiplying Charged Coupled Device (EMCCD) all-sky camera both of which have been operative in Tromsø, Norway (69.6N, 19.2E, 66.7MLAT). The fivewavelength photometer has the field-of-view (FOV) of about 0.98 degrees and measures the auroral emissions in the field-aligned direction at 5 wavelengths simultaneously (427.8 nm, 557.7 nm, 630.0 nm, 777.4 nm, 844.6 nm). The original sampling rate is 400 Hz. The EMCCD all-sky camera mainly observes N 2 first positive band emissions with a temporal resolution of 100 Hz. These temporal resolutions are sufficiently high to detect the main pulsation of PsA whose periodicity ranges from a few to a few tens of seconds. In this study, we employed images from the all-sky camera to identify the appearance of PsA at the sensing point of the photometer.  Figure 1a shows an image from the all-sky camera at 03:02:30 UT. The red circle gives the FOV of the photometer. Figure 1b and c shows the time-series of the emission intensity from the photometer at the 427.8 nm and 557.7 nm wavelengths, respectively. Note that both the time-series have already been averaged with an integration time of 1 s to improve the signal-to-noise ratio. The quasi-periodic fluctuation, whose periodicity is about 5 s, is obvious in the time-series. It is also seen that there is a systematic time lag between the 427.8 nm and 557.7 nm emissions. By comparing data from these two optical instruments, we identified 37 nights of PsA events during 3 months from January to March, 2018, which were used for the current statistical analysis.

Methodology for estimating the lifetime of O( 1 S)
Before showing the statistical results, we introduce the methodology for estimating the lifetime of O( 1 S) using the case of PsA shown in Fig. 2. In this study, we calculate the lifetime of O( 1 S) every 1 min by performing cross-correlation analysis between the time-series of the 427.8 nm and 557.7 nm emissions. We decided to use relatively short (1 min) time intervals for the correlation analysis, to eliminate unwanted contributions of slower variations. Figure 2a and b again shows the time-series of the 427.8 nm and 557.7 nm emissions from the same interval shown in Fig. 1. It is clearly seen that the timeseries of 557.7 nm has a time delay of 1 s or less as compared to that of 427.8 nm. Here, we define the lifetime of O( 1 S) as a time lag giving the maximum cross-correlation coefficient. Note that the correlation coefficient is calculated by shifting the lag from 0 to 2 s with a resolution of 0.01 s, the time window of analysis being 30 s. The result of the correlation analysis is shown in Fig. 2c, where the dashed line gives the time-series of 557.7 nm and the solid line shows the time-shifted (i.e., delayed by the estimated time lag) variation of 427.8 nm. In this case, the lifetime of O( 1 S) is estimated to be 0.67 s as a lag giving a maximum correlation coefficient of 0.99. Figure 3a shows the distribution of lifetime of O( 1 S) derived by applying the above-mentioned procedure to 2856 events of PsA each of which has a duration of 1 min. The distribution has a prominent peak (mode) at around 0.7 s and the mean of the distribution is 0.67 s. Brekke and Henriksen (1972) also calculated the lifetime of O( 1 S) using a photometer which operated in Tromsø, Norway. In their result, the lifetime was distributed from 0.5 to 1 s and the mean was 0.80 s. Our result shows general agreement with that of Brekke and Henriksen (1972). In our case, however, the mean value is slightly shorter than that in their statistics. The time window for the cross-correlation analyses of Brekke and Henriksen (1972) was 5 min whereas the present study uses a window of 1 min duration. This difference might have introduced the slight difference between these two statistics. However, when we carried out the cross-correlation analysis using several different time windows, no significant differences were found; thus, the reason for the difference is still unclear at this stage.

Statistics of distribution of the lifetime of O( 1 S)
We In addition, when focusing on the shape of the distribution, the weight is shifted to the shorter area in the morning side. In particular, for the 05-08 MLT case (Fig. 3d), there is a significant population having a lifetime of about 0.60 s, which is not seen before 05 MLT (Fig. 3b, c). In the following section, we will estimate the altitude of PsA emission from these values of lifetime.

Calculating the effective altitude of pulsating aurora
Here, we introduce a method to derive the altitude of the 557.7 nm emission from its lifetime (Scourfield et al. 1971). There are three routes through which an oxygen atom in the excited state transits to the ground state.
Here, we define I as the intensity of 557.7 nm emission, which can be expressed as follows (Brekke and Henriksen 1972): where A 31 and A 32 are the probability of radiative transition from O( 1 S) state to O( 1 D) and O( 3 P) states, respectively. d 3 is the probability of collisional transition of O( 1 S) state. Q 0 is the excitation rate of O( 1 S) state. Using these parameters, the lifetime of O( 1 S) state is calculated as follows: In this equation, the values of A 31 and A 32 have been estimated experimentally and those are 1.28 s −1 and 0.078 s −1 , respectively (Brekke and Henriksen 1972). Since we are able to estimate τ from actual observations of PsA, the collisional transition probability d 3 can be derived for each case of PsA. Assuming that there is no collisional transition of O( 1 S) state, the lifetime is about 0.74 s. Therefore, when estimating the emission Here, we assumed that the collisional transition is due to O 2 and N 2 , and then d 3 can be expressed as follows: where q O2 and q N2 are the quenching rate coefficient of O 2 and N 2 and n(O 2 ) and n(N 2 ) are the density of O 2 and N 2 , respectively. Using the theoretical value of q O 2 and q N 2 which are 3.0 × 10 −13 cm 3 s −1 (Zipf 1969) and < 10 −17 cm 3 s −1 (Hunten and McElroy 1966), the collisional transition due to N 2 can be ignored. Thus, d 3 can simply be expressed by the following equation (Scourfield et al. 1971): Using the theoretical value of q O 2 , we can determine the density of O 2 and then estimate the emission altitude of PsA by comparing the obtained value of n(O 2 ) with that from the neutral atmosphere model [Mass Spectrometer and Incoherent Scatter: MSIS (Hedin 1991)] sampled every 1 km. The emission layer of PsA can be measured by incoherent scatter radar observations such as EISCAT, and its thickness is about 20 km (Jones et al. 2009;Hosokawa and Ogawa 2015). However, our method cannot directly estimate the lower cut-off altitude of the optical emission as well as the thickness of the emission layer. This is simply because it is difficult to obtain the height profile of the emission from the optical observations. Therefore, we need to bear in mind that the emission altitude estimated in this study is the volume altitude which roughly means the center of the emission layer rather than the lower cut-off altitude.

Accuracy of estimating of the emission altitude
To evaluate the validity of the current method, here we compare the emission altitude of PsA estimated from the lifetime of O( 1 S) and the altitude profile of the electron density from the EISCAT UHF radar whose FOV is ~ 0.7°. The raw electron density (i.e., power profile data) was obtained with the altitude resolution of about 0.6 km. During 2.5 h from 00:30 to 03:00 UT on February 19, 2018, intense PsA and corresponding ionization were observed respectively by the five-wavelength photometer and the EISCAT UHF radar located in the same place. Figure 4a shows the variation of the ionospheric electron density from the EISCAT UHF radar. In this time interval, especially after 01:00 UT, PsA was observed by the photometer almost continuously. However, the lowaltitude cut-off of ionization varied in time, which means that the characteristic energy of precipitating electrons was not uniform during this episode. Figure 4b plots the time-series of the emission altitude of PsA derived from the lifetime analysis (blue line) and h m E (peak height of the E region electron density enhancement: red line). h m E has been derived directly from the altitude profile of the electron density shown in Fig. 4a. Although there is a slight difference mainly due to the limited altitude resolution of h m E, the altitude ranges of PsA emission and h m E are similar. In particular, during the 30 min from 02:30 to 03:00 UT, they show rather good agreement. This indicates that the emission altitude of PsA can be a good proxy for the energy of precipitating electrons during PsA. Figure 5a shows the MLT distribution of the occurrence of PsA events. Most events are distributed from the magnetic midnight to 08 MLT and the mode of distribution is located around 04 MLT. This distribution has good agreement with past studies of the occurrence distribution of PsA (e.g., Jones et al. 2011). Figure 5b shows the MLT variation of the emission altitude of PsA estimated in this study. Each dot corresponds to the emission altitude derived for each PsA interval. The red cross marks indicate the averages calculated every 1 h bin of MLT, and the red bars give the standard deviation of the distribution. The emission altitude becomes lower in the morning sector, especially after 06 MLT, while the central altitude stays high at around 108 km in the earlier MLT sector. After 06 MLT, the minimum emission altitude is as low as ~ 95 km, which corresponds to the energy of precipitating electrons of 30 keV.

Discussion
As shown in Fig. 5b, the emission altitude of PsA is distributed in altitudes from 95 to 115 km, which corresponds to precipitation of 5-30 keV electrons (Turunen et al. 2009). This result is consistent with several early observations of PsA electrons by sounding rockets (Sandahl et al. 1980;Yau et al. 1981). Miyoshi et al. (2010Miyoshi et al. ( , 2015b also identified, using simultaneous particle and optical data from the Reimei satellite, precipitation of a few keV electrons causing PsA. Hosokawa and Ogawa (2015) investigated the variation of ionospheric electron density profile during PsA using the EISCAT radars and indicated that the energy of PsA electrons tends to be higher in the morning side. This tendency is actually seen in Fig. 5b, where the emission altitude drastically decreases after 06 MLT. This systematic change is consistent with the MLT variation of the E region peak height (h m E) demonstrated by Hosokawa and Ogawa (2015). Similar MLT dependence has been reported by Partamies et al. (2017) who showed the MLT dependence of the emission layer of PsA.
Here, we discuss why the emission altitude of PsA decreases after 06 MLT. One of the possible explanations is the MLT change of the background magnetic field intensity in the magnetosphere because the resonance energy of electrons in the first-order cyclotron resonant scattering with the chorus waves is proportional to the square of the ambient magnetic field intensity (Kennel and Petschek 1966): where B is the ambient magnetic field intensity, μ 0 the permeability of a vacuum, N thermal plasma density, f ce the cyclotron frequency, and f the frequency of chorus wave. Note that this approximation is valid when we assume f pe /f ce ≫ 1 or f/f ce ≪ 1 (Kennel and Petschek 1966). Hosokawa and Ogawa (2015) have already calculated the magnetic field intensity and discussed the MLT variation of resonance energy. However, they have not yet evaluated the contribution of the thermal plasma density to the resonance energy.
Here, we calculated the magnetic field intensity at the conjugate point of Tromsø using the Tsyganenko 89 magnetic field model (Tsyganenko 1989) and the thermal plasma density using the model of Sheeley et al. (2001) for the PsA event on 19 February 2018. However, the calculated value of resonance energy was almost uniform in MLT, implying that the drastic decrease of emission altitude cannot be explained only by the MLT change in the ambient parameters. Recently, Miyoshi et al. (2015a) pointed out that the resonance energy increases as the chorus wave propagates to higher latitude. If chorus waves propagate to higher latitude in the morning sector, more energetic electrons can be precipitated by the cyclotron resonance. Hence, the energy of PsA electrons should be discussed by considering both the ambient parameters (magnetic field intensity and thermal plasma density) and the propagation characteristics of chorus waves along the field line.

Conclusion
In this study, we estimated the emission altitude of PsA using the lifetime of O( 1 S) derived from the five-wavelength photometer in Tromsø, Norway. The main results are summarized as follows: 1. We have statistically analyzed the emission altitude of PsA using the observed value of lifetime of O( 1 S). The distribution of the lifetime has a strong peak at around 0.70 s and the mean lifetime is 0.67 s. These automatically estimated time constants are in good agreement with those derived by the previous studies, implying the feasibility of the method for estimating the lifetime. 2. Through comparison of the emission altitude of PsA with the peak height of the E region ionization obtained by the EISCAT UHF radar, we demonstrated that the peak height of electron density (i.e., peak of ionization) roughly matches the central emission altitude of PsA. 3. There is a tendency that the emission altitude is significantly lower in the morning side after 06 MLT, suggesting that the energy of precipitating electrons should be higher at later MLT sector.