PUBLICATIONS. Geophysical Research Letters

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1 PUBLICATIONS Geophysical Research Letters RESEARCH LETTER Key Points: Fast (a few tens of seconds) modulation of pulsating proton aurora was observed Fast modulations of pulsating proton aurora were related with subpacket structures of Pc1 pulsations The modulation frequency showed a correlation with Pc1 intensity based on a nonlinear theory Correspondence to: M. Ozaki, ozaki@is.t.kanazawa-u.ac.jp Citation: Ozaki, M., et al. (2016), Fast modulations of pulsating proton aurora related to subpacket structures of Pc1 geomagnetic pulsations at subauroral latitudes, Geophys. Res. Lett., 43, , doi:. Received 12 JUN 2016 Accepted 26 JUL 2016 Accepted article online 29 JUL 2016 Published online 14 AUG American Geophysical Union. All Rights Reserved. Fast modulations of pulsating proton aurora related to subpacket structures of Pc1 geomagnetic pulsations at subauroral latitudes M. Ozaki 1, K. Shiokawa 2, Y. Miyoshi 2, R. Kataoka 3,4, S. Yagitani 1, T. Inoue 1, Y. Ebihara 5, C.-W Jun 2, R. Nomura 6, K. Sakaguchi 7, Y. Otsuka 2, M. Shoji 2, I. Schofield 8, M. Connors 8, and V. K. Jordanova 9 1 Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan, 2 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan, 3 National Institute of Polar Research, Tachikawa, Japan, 4 Department of Polar Science, Graduate University for Advanced Studies (SOKENDAI), Tachikawa, Japan, 5 Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Japan, 6 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan, 7 National Institute of Information and Communications Technology, Koganei, Japan, 8 Center for Science, Athabasca University, Athabasca, Alberta, Canada, 9 Los Alamos National Laboratory, Los Alamos, New Mexico, USA Abstract To understand the role of electromagnetic ion cyclotron (EMIC) waves in determining the temporal features of pulsating proton aurora (PPA) via wave-particle interactions at subauroral latitudes, high-time-resolution (1/8 s) images of proton-induced N 2 + emissions were recorded using a new electron multiplying charge-coupled device camera, along with related Pc1 pulsations on the ground. The observed Pc1 pulsations consisted of successive rising-tone elements with a spacing for each element of 100 s and subpacket structures, which manifest as amplitude modulations with a period of a few tens of seconds. In accordance with the temporal features of the Pc1 pulsations, the auroral intensity showed a similar repetition period of 100 s and an unpredicted fast modulation of a few tens of seconds. These results indicate that PPA is generated by pitch angle scattering, nonlinearly interacting with Pc1/EMIC waves at the magnetic equator. 1. Introduction Hot ion temperature anisotropies excite electromagnetic ion cyclotron (EMIC) waves [Gendrin et al., 1984; Lin et al., 2014; Shoji and Omura, 2013, 2014] near the equator. EMIC waves in the Pc1 range (0.2 to 5 Hz) are a common phenomenon in the magnetosphere [e.g., Bossen et al., 1976; Anderson et al., 1992a, 1992b; Min et al., 2012]. The EMIC waves propagate along magnetic field lines from the equatorial source to the ionosphere. A part of the EMIC waves can be observed as geomagnetic pulsations on the ground [Kangas et al., 1998, and references therein]. The Pc1 pulsations on the ground become left-hand polarized in the vicinity of the ionospheric footprint connected to the magnetospheric source region by geomagnetic field lines [Kim et al., 2010; Nomura et al., 2011, 2012]. The polarization of the Pc1 pulsations far away from the footprint changes to linear or right handed due to the long path in the ionospheric waveguide. The EMIC waves may play a crucial role in the loss of relativistic (MeV energy) electrons from the radiation belts via wave-particle interactions [e.g., Miyoshi et al., 2008; Rodger et al., 2008; Usanova et al., 2014]. Also, EMIC waves are capable of scattering magnetospheric energetic ions (kev to 100 kev) [Erlandson and Ukhorskiy, 2001; Yahnina et al., 2003; Usanova et al., 2010]. A portion of the scattered energetic ions falls into the upper atmospheric loss cone, and the ion precipitation can then be observed as a proton aurora [Frey et al., 2004; Yahnin et al., 2007]. Isolated proton aurora and related Pc1 pulsations are simultaneously observed on the ground at subauroral latitudes [Sakaguchi et al., 2007, 2008; Miyoshi et al., 2008; Nomura et al., 2012, 2016]. Isolated proton aurora can be displayed as an ionospheric projection of the location, duration, and evolution of the wave-particle interaction region in the magnetosphere [Sakaguchi et al., 2008, 2012]. Thus, the simultaneous observation of Pc1 pulsations and isolated proton aurora can be a good proxy for wave-particle interactions. Nomura et al. [2016] showed that the luminosity of pulsating proton aurora (PPA) oscillates with the same period between successive elements as the Pc1 pulsations, i.e., several tens of seconds. They did not report many faster luminosity modulations of PPA that may be related to the subpacket structures of Pc1/EMIC waves observed with amplitude modulations [Usanova et al., 2010; Nakamura et al., 2015]. Shoji and Omura [2014] have reported fast modulations of precipitating energetic protons of the order of seconds, nonlinearly interacting with the EMIC-triggered emissions, using hybrid code simulations. If such nonlinear pitch angle OZAKI ET AL. PPA AND PC1 PULSATIONS 7859

2 scattering occurs in a generation region, then rapid modulations of PPA may be observed with related Pc1/EMIC waves. However, the relationship between the subpacket structures of the Pc1/EMIC waves and PPA has not yet been identified, because the temporal resolution and the sensitivity of the low-light images have been insufficient. Moreover, the ground-based observations of Pc1/EMIC waves and precipitating protons generating PPA should include the dispersion effect in travelling from the magnetosphere to the ionosphere, which acts to smear their rapid variations. A recently developed electron multiplying charge-coupled device (EMCCD) camera can reveal the temporal relationship between the Pc1/EMIC waves and PPA with an enhanced sensitivity. This study is the first to examine how the subpacket structures of Pc1/EMIC waves relate to the temporal features of PPA. This relationship is key to understanding the dynamics of PPA origins in wave-particle interactions. 2. Instruments Geomagnetic pulsations and related phenomena are measured at Athabasca (ATH; 54.7 N, E; L 4.3) in Canada. Three components, H, D, and Z, of geomagnetic pulsations are measured by a three-axis induction magnetometer, where H and D are the horizontal components toward the geomagnetic north and east and Z is the vertical component. The quantization is 16 bit and the sampling frequency is 64 Hz. The details have been presented by Shiokawa et al. [2010]. This study uses excitations at N 2 + first negative bands in proton aurora [Eather, 1967, and references therein] to reveal rapidly varying PPA. To visualize proton precipitation into the upper atmosphere, two types of all-sky EMCCD cameras are used with 16-bit quantization. One records Hbeta (486.1 nm) emissions with a low time resolution (60 s) for detecting proton precipitation, and the other records N 2 + emissions with a high time resolution (1/110 s). A BG3 glass filter is used for N 2 + emission images to reduce the effects of slow auroral emissions (e.g., nm and nm emissions) [Semeter et al., 2008]. Hereafter, the BG3 images are treated as 1/8 s averaged images from the originals taken at 1/110 s to improve the signal-to-noise ratio. The BG3 images of proton aurora allow the visualization of the temporal relationship between Pc1 geomagnetic pulsations and PPA with an ever finer time resolution. These instruments are synchronized with one PPS signals from GPS receivers to guarantee a time accuracy of less than 1 ms. For the proton auroral events having long durations (over several tens of minutes), ground-based observations have better spatial and temporal coverages with a high time resolution at a fixed L value compared to satellite experiments. 3. Observations A PPA event was observed together with structured Pc1 pulsations at 07:40 to 08:40 UT on 12 November 2015, as shown in Figure 1. The typical energy range of protons responsible for exciting Pc1/EMIC waves is in kev to a few hundreds of kev [e.g., Erlandson and Ukhorskiy, 2001; Yahnina et al., 2003; Sakaguchi et al., , 2008; Miyoshi et al., 2008]. Our EMCCD camera captured the detailed behaviors of the PPA. The N 2 emissions observed at the same location as the Hbeta emissions are an indirect signature of proton precipitation. The observed Pc1 pulsations consist of fine structures of successive rising-tone elements in the He + band between He + and O + cyclotron frequencies (1.5 Hz and 0.37 Hz) at the equator calculated using the Tsyganenko 2002 (hereafter referred to as T02) model [Tsyganenko, 2002a, 2002b]. Based on the ionospheric footprint accuracy using coordinated observations between pulsating electron aurora (PEA) and chorus waves [Nishimura et al., 2011], the T02 model was used in this study. Another proton aurora was seen at the eastern edge of the keograms. The Pc1 pulsations could include the Pc1/EMIC waves coming from other magnetospheric sources. As a result, the Pc1 pulsations showed a few groups in the frequency domain (e.g., frequency gap at 0.6 Hz in Figure 1c). The frequency sweep rate is about 200 to 1000 s/hz. The structured Pc1 pulsations mainly have a left-handed (blue in the figure) polarization. This means that the ionospheric footprint of the magnetic field line connecting to the magnetospheric source region (possibly the equator) is close to the observation site [Kim et al., 2010]. A high correlation between the Pc1 and BG3 intensities was observed in this event. The spatial distribution of the high correlation (over 0.75) is concentrated around a proton spot, as shown in Figures 2a 2c. The Pc1 intensity was calculated by integrating over the frequency range from 0.35 to 0.90 Hz. The BG3 intensity variation of the proton aurora shows a very significant correlation with the Pc1 pulsations in Figure 2d. The BG3 intensity was calculated by averaging the luminosities at the proton spot shown in Figure 2c. Both OZAKI ET AL. PPA AND PC1 PULSATIONS 7860

3 Figure 1. Ground-based observations of a PPA and associated Pc1 pulsations during 07:40 to 08:40 UT on 12 November (a and b) East to west keograms extracted from the BG3 and Hbeta images. (c and d) Dynamic spectrum ((H 2 + D 2 + Z 2 ) 1/2 ) and the polarization of the Pc1 pulsations. The white line indicates the equatorial O + cyclotron frequency, which is calculated by using the T02 model. Red indicates right-handed, white linear, and blue a left-handed polarization, and gray is for uncertain polarization due to low SNR. (e) Variations in the AE index. Pc1 and BG3 intensities were calculated with a time resolution of 3 s to clearly show the quasiperiodic oscillations. The maximum cross correlation between the Pc1 and BG3 intensities is when the BG3 intensity is time shifted by 66 s. The negative time lag means that the energetic protons arrived at the ionosphere later than the associated Pc1/EMIC waves. Mende et al. [1980] showed almost the same time lag of 42 s in the simultaneous ground-based observations of N + 2 emissions and related Pc1 pulsations at Siple Station in Antactica (L = 4.2). On the other hand, Nomura et al. [2016] pointed out a 3 min delay of Pc1 start time from the start time of one of the proton aurora spots in other PPA event at ATH. The time lag depends on the energy spectra of precipitating protons and the propagation characteristics of Pc1/EMIC waves in the magnetospheric conditions (e.g., wave dispersion relation and configuration of the ambient magnetic field). The Pc1 and BG3 intensities have a clear periodicity of 100 s, as shown in Figure 2e. Another peak was seen at Hz in the Pc1 repetition period, which was likely caused by the contamination of the Pc1/EMIC waves coming from other magnetospheric sources. Nomura et al. [2016] used panchromatic images for the PPA including slow emissions (e.g., lifetimes of 0.74 s and 110 s for nm and nm lines) with a time resolution of 3 s. However, it is difficult to analyze fast modulations of PPA using panchromatic images because of the smearing effect of slow emissions. Figures 3a and 3b present a dynamic spectrum and waveform of the H component from 08:06:00 to 08:10:00 UT. The Pc1 waveform (black curve) is band-pass filtered over the frequency range from 0.35 Hz to 0.90 Hz to extract only the rising-tone structures. Figure 3b also shows the amplitude envelope of the Pc1 pulsations (red curve) and the BG3 intensity (blue curve) at the proton spot, which have a time resolution of 1/8 s. The fine structures of the Pc1 wave packets are seen in accordance with successive discrete elements. In previous works, coordinated ground and satellite observations showed that structured Pc1 pulsations in the magnetosphere can propagate to the ground with no significant frequency dispersion [Mursula et al., 2001; Usanova et al., 2010; Paulson et al., 2014]. Thus, the observed amplitude modulation of the Pc1 wave packet would be equivalent to subpacket structures of EMIC waves. The time resolution of 1/8 s for a PPA is the best to our knowledge and 24 times faster than the previous study by Nomura et al. [2016]. When the BG3 intensity was time shifted by 53 s, the cross correlation between the Pc1 amplitude envelope and the BG3 intensity took on its maximum value (0.59) in this time interval. The cross correlation between OZAKI ET AL. PPA AND PC1 PULSATIONS 7861

4 Figure 2. Observed high correlations between the structured Pc1 pulsations and a PPA. (a and b) Averaged BG3 and Hbeta images from 08:02 to 08:12 UT. (c) Spatial distribution of correlation (color scale) between the Pc1 and BG3 intensities in Figure 2a. (d) Variations of the Pc1 and BG3 intensities at the proton spot over an hour. The BG3 intensity was time shifted by 66 s to maximize the cross correlation (+0.93) between them. (e) Repetition periods of the structured Pc1 pulsations and PPA obtained by Fourier analysis. their quasiperiodic oscillations was a very high value of 0.93, but the cross correlation between their fast modulations was a moderately high value of It is expected that either the difference in the time resolution for the correlation analysis (3 s and 1/8 s) or the velocity dispersion of precipitating protons cause the decrease in the correlation coefficient. The BG3 intensity variation clearly shows the fast modulations on a time scale of a few tens of seconds, which can be related with the subpacket structures of the Pc1 pulsations. The fast modulations of the PPA and the subpacket structures of the Pc1 pulsations are shown in Figures 3c and 3d. The dynamic spectrum of the intensity variations of the subpacket structures was calculated from the amplitude envelope of the H component. The BG3 and Pc1 intensity variations were high-pass filtered above a frequency of 0.03 Hz to clearly show their fast modulations. Then, a short-time Fourier transform was performed over every 60 s duration with a Hanning window function having 95% overlap. From the comparison between Figures 3c and 3d, the fast modulations of the BG3 intensity are similar to those for the Pc1 intensity variations of the subpacket structures. The fast modulations in both intensities were clearly seen in the frequency range from 0.05 Hz to 0.2 Hz during 07:50 to 08:20 UT. The BG3 intensity ratio of the fast modulation component (Figure 3c) to the 100 s oscillation component (blue curve shown in Figure 2d) was approximately 2%. An interesting point is that the upper cutoff frequencies of the fast modulations for the BG3 intensity and of the subpacket structures gradually increase with the Pc1 intensity (red curve in Figure 2d) at 07:50 to 08:04 UT, while their upper cutoff frequencies subsequently decrease with the Pc1 intensity. Additionally, the fast modulations of the subpacket structures were weak at 08:00 UT, which was the same time for the minimum Pc1 intensity as shown in Figure 2d. The OZAKI ET AL. PPA AND PC1 PULSATIONS 7862

5 Figure 3. Observed subpacket structures of Pc1 pulsations and fast modulations of a PPA. (a) Dynamic spectrum of the H component of the Pc1 pulsations over a 4 min interval. (b) Waveform (black) and the amplitude envelope (red) of the H component and the time-shifted BG3 intensity (blue) of the PPA. (c and d) Dynamic spectra of the BG3 intensity variation and amplitude envelope variation of subpacket structures of the Pc1 pulsations. Pc1/EMIC waves may have a threshold for their intensities to transit to the nonlinear process as suggested by Omura et al. [2010]. The observation results of the fast modulations imply that their modulation frequencies have a relation with the Pc1 intensity. The effect of Pc1 intensity on the modulation frequency is discussed in the next section. 4. Discussion The proton density mapping at the magnetic equator (L = 4.9) along the field line was 111 particles/cm 3 from the plasmaspheric model, which was calculated under the realistic geophysical conditions (moderately high) using the observed Kp, F 10.7, and Ap indices for the convection model and the thermosphere/ionosphere models in the simulation [Rasmussen et al., 1993; Miyoshi et al., 2006]. The source region would be located in the vicinity of the plasmapause, which is consistent with previous observations of isolated proton aurora at subauroral latitudes [Frey et al., 2004; Sakaguchi et al., 2007, 2008, 2012; Yahnin et al., 2007; Usanova et al., 2010]. To evaluate the minimum kinetic energy of the protons required for the wave-particle interaction by the linear growth theory [Kennel and Petschek, 1966], the parallel resonant energy of the protons was calculated using the T02 model and plasmaspheric model. The parallel resonant energy of the protons interacting with the parallel propagating EMIC waves (0.35 Hz to 0.90 Hz) was in 44 kev to 3.3 kev. The calculated minimum resonance energy range can contribute to the Hbeta emissions and the N + 2 emissions [Eather, 1967]. The observed Pc1 pulsations can therefore be a driver for the generation of PPA. In previous studies, the amplitude modulation mechanisms for Pc1 pulsations were classified into two types, the beating effect in the ionosphere [Pope, 1964; Nomura et al., 2011; Jun et al., 2014] and the propagating effect in the magnetosphere along the magnetic field line [Obayashi, 1965; Guglielmi et al., 1996; Mursula et al., 1999]. However, the observed high correlation between the Pc1 and BG3 (aurora) intensities suggests that rather than these mechanisms, the quasiperiodic Pc1 amplitude modulations are generated at the waveparticle interaction region in the magnetosphere. The bouncing wave packet (BWP) model is well known as an important theoretical model for the generation of Pc1 pulsation in the magnetosphere [Obayashi, 1965]. In the BWP model, the quasiperiodic modulation of Pc1 pulsations over a few minutes is demonstrated as being the result of bouncing between forward and backward traveling waves along a magnetic field line reflected at the ionosphere on both hemispheres. While other theoretical models propose the effect of wave growth rates at the source region modulated by ULF waves [e.g., Loto aniu et al., 2009], these models cannot explain the generation of the subpacket structures of Pc1 pulsations. Recently, Shoji and Omura [2013] proposed a generation process for subpacket structures of EMIC-triggered emissions based on the nonlinear wave growth theory [Omura et al., 2010]. In their proposed model, subpacket structures result in a superposition of EMIC emissions repeatedly nonlinearly triggered at different locations near the equator. In the nonlinear OZAKI ET AL. PPA AND PC1 PULSATIONS 7863

6 Figure 4. Upper cutoff frequencies (a) for the subpacket structures of Pc1 pulsations and (b) for PPA intensity variations as a function of Pc1 intensity for each discrete Pc1 element during 07:50 to 08:15 UT. wave growth theory, the duration of the nonlinear triggering process is characterized by a nonlinear transition time T N, which is defined as [Shoji and Omura, 2013] 1 m 2 H T N ¼ τt tr ¼ 2πτ (1) kv 0 q H B w where τ is a proportionality coefficient, T tr is a nonlinear trapping time, m H is the rest mass of proton, q H is the charge of proton, k is the wave number of Pc1/EMIC wave, V 0 is the perpendicular velocity of resonant protons, and B w is the magnetic amplitude of Pc1/EMIC wave at the generation region. Thus, the time span of each subpacket structure of the EMIC-triggered emissions is also characterized by a nonlinear transition time, which is inversely proportional to the square root of the wave amplitude. Nakamura et al. [2015] showed using Time History of Events and Macroscale Interactions during Substorms (fleet of five satellites) satellite observations that the subpacket structures of EMIC-triggered emissions are in good agreement with the nonlinear transition time, supporting the model of Shoji and Omura [2013]. If such a successive nonlinear triggering process is in effect in the wave-particle interaction region for the generation of subpacket structures, related modulations can be observed for PPA, resulting in nonlinear pitch angle scattering. The shortest time interval of fast modulations for the BG3 intensity can be related with the nonlinear transition time. Figure 4 shows the upper cutoff frequencies for the subpacket structures of Pc1 pulsations and BG3 intensity variations with respect to the Pc1 intensity (red curve in Figure 2d) for each discrete Pc1 element during 07:50 to 08:15 UT. The upper cutoff frequencies were determined by the criterion that the power spectra be larger than 3 times the standard deviation based on the previous study by Kataoka et al. [2012]. Their upper cutoff frequencies, which are equivalent to the inverse of the shortest time interval of the fast modulations during each discrete Pc1 element, showed a positive correlation (0.55 and 0.34 for the Pc1 and BG3 modulation frequencies) with respect to the Pc1 intensity. As written in equation (1), this is believed to be due to the relationship between the inverse of the nonlinear transition time and the square root of the wave amplitude when the wave number and the perpendicular velocity of the protons are almost constant at the source region. The positive correlation for the BG3 modulation frequency was slightly weak compared to that for the Pc1 modulation frequency. This is because the precipitating protons resonated with the EMIC waves propagating in the opposite direction. The Pc1/EMIC waves are generated around the equator regions and propagate toward the ionosphere in both hemispheres. The Pc1/EMIC waves are resonated with counterstreaming energetic ions. Thus, to investigate more detailed behavior of PPA, geomagnetically conjugate observations of PPA using high-speed imagers lead to an important step for understanding the EMIC instability. Additionally, the BG3 intensity variations may include the dispersion effect due to the long path along the field line in the magnetosphere. Ray tracing analysis of Pc1/EMIC waves and time-of-flight analysis of energetic protons using realistic magnetospheric conditions are the subject of a future study to investigate the generation mechanism of fast modulations of PPA in more detail. Even though such factors for the smearing effects on the BG3 images would be included, the observed fast modulations of the PPA related with the Pc1 OZAKI ET AL. PPA AND PC1 PULSATIONS 7864

7 intensity support an origin due to nonlinear effects of energetic protons (which later precipitate) via the wave-particle interaction. 5. Conclusions This study presents the first ground-based observations of fast modulations of PPA related with structured Pc1 pulsations. This study analyzed the temporal features of PPA in detail from high-time-resolution (1/8 s) auroral images for N 2 + emissions caused by proton precipitation. The key findings of this study are as follows: 1. Isolated proton aurora is generated by a bundle of Pc1/EMIC waves with a duration of several tens of minutes (cf. Figure 1). 2. Each PPA event exhibits a quasiperiodic oscillation on the time scale of a few minutes (cf. Figure 2e), which is related to the intervals of successive discrete elements of Pc1/EMIC waves. 3. The quasiperiodic oscillations of PPA include fast modulations associated with the subpacket structures (a few tens of seconds) of the Pc1/EMIC waves (cf. Figure 3). 4. The upper cutoff frequencies for the time interval of the fast modulations of the BG3 intensity and for the subpacket structures of Pc1 pulsations are correlated with the Pc1 intensity (cf. Figure 4). This proportional relation supports the importance of a nonlinear effect on the rapid pitch angle scattering by the EMIC waves in the generation process of PPA at subauroral latitudes. These findings contribute to understanding nonlinear processes in the wave-particle interactions between ions and EMIC waves in the same manner as electrons and chorus waves. High-speed auroral observations lead to a new auroral microphysics by visualizing never-before-seen state of the wave-particle interaction. Pulsating electron aurora caused by chorus waves [Li et al., 2012; Miyoshi et al., 2015a, 2015b, and references therein] is a similar phenomenon to PPA interacting with Pc1/EMIC waves. The modulation frequency of PEA correlates with the auroral intensity, which is indirectly proportional to the chorus intensity, based on nonlinear wave growth theory [Nishiyama et al., 2014]. The chorus waves have subpacket structures with a duration of about several tens of milliseconds. Therefore, PEA would show very fast modulation related with the subpacket structures of chorus waves, similar to PPA as suggested by Kataoka et al. [2012]. Acknowledgments This work was supported by Grants-in- Aid for Scientific Research ( , , 15H05747, 15H05815, and 16H06286) from the Japan Society for the Promotion of Science. The observations at the Athabasca University Geospace Observatory were supported by the Canada Foundation for Innovation, and the authors wish to thank Kyle Reiter of Athabasca University Geospace Observatory for his helpful support in the operation of the induction magnetometer and optical observations. 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