Generalization of the results
In this section, we generalize the results and emphasize some details, which are useful for result interpretation.
We analyzed a series of seven on/off events that represent a typical PsA of an arc-like auroral structure demonstrating both main (a few seconds periodicity) and internal (a few Hz) modulations of luminosity. Two cameras (KRN and TJA) were located approximately along the meridian at a separation ~ 60 km and provided all-sky images of auroras with 1-s resolution. The arc was located in the KRN–TJA common field of view. This location allowed us to make a tomographic reconstruction of the altitude profile of arc luminosity so as to investigate the evolution of arc altitude over the course of the main pulsation. The third all-sky camera (TJA-R) provided the data at a higher time resolution (100 frames per second), and we used these data to study the internal modulation.
Intensity variations in the arc, averaged over squares of 10 × 10 pix, are shown in Fig. 8. We put the square at the place where the arc is crossed by the black profile in Fig. 2. While the few-second variations look like quasi-sinusoidal oscillations, the internal modulation represents a rather irregular sequence of peaks with different time intervals between them. The mean value of the time interval, T, corresponds to frequency f = 1/T ~ 2 Hz. This is consistent with the result of a statistical investigation by Nishiyama et al. (2014), who showed that the occurrence probability of rapid modulation is localized between 2.0 and 2.5 Hz.
Fast scintillations are observed only during the “on” phase of the main pulsations. Fig. 8 shows the sequence of peaks, corresponding to a few Hz modulation, which is highlighted in gray. There was no modulation in the background luminosity (before ~ 01:16:07 UT) or between the pulses except at approximately 01:16:22 UT, when the next pulse of the main pulsation started just after the previous pulse (see, as well, Fig. 3). These facts are important for a possible explanation of fast scintillations, which will be discussed in the next section.
The altitude of the arc changes. Regarding the examined arc as a homogeneous structure, we have found the following features of its behavior (see Fig. 3). The “arc altitude”, defined by us as the position of the luminosity maximum, was lower within the switch-on intervals than between them. The altitude changes by 1.5–3 km, which is larger than the spatial resolution of the optical tomography method (~ 500 m). To the authors’ knowledge, earlier observations of PsA showed no indication of changes in the height of the lower border during the lifetime of a single pulsation (e.g., Brown et al. 1976). This is probably due to the lower spatial resolution of the triangulation method, which is traditionally used in such investigations. The decrease in arc altitude means that the energy of precipitating particles increases.
Of the two closely spaced arcs, internal modulation took place only in the lowest arc. In addition to the high spatial resolution (in comparison with triangulation), one more merit of optical tomography is its ability to distinguish the fine structure of the auroral arc, whereas on ordinary all-sky images, this may be masked by neighboring structures (see Fig. 5). A more careful analysis of the original frames of the rapid camera TJA-R showed that the structure considered actually consists of two thin arcs, at least at the beginning of the interval (Fig. 6a). This allowed us to calculate the variation in luminosity in each arc separately (Figs. 6, 7). The comparison with tomographic reconstructions showed that internal modulation appears in the arc which has lower altitude during the “on” phase. One can say that the result is consistent with the early study by Royrvik and Davis (1977), who showed that in many cases, 3 ± 1 Hz modulation is detected only near the form boundary. Later, Whiter et al. (2010) found that the energy of flickering electron precipitation was higher than the energy of non-flickering auroral electrons.
Two approaches for interpretation of PsA features: pitch-angle scattering
One widely accepted primary process for PsA is pitch-angle scattering of electrons in the magnetosphere (Li et al. 2012, and references therein). Another process was proposed by Sato et al. (2004), who showed that time variations of the field-aligned potential drop may cause the pulsating aurora. In what follows, for brevity, we will refer to these approaches as scattering and accelerating approaches.
Both approaches are based on satellite measurements, and the generation mechanism of some PsA features is still not fully understood due to a lack of in situ observations. Indeed, cases of successful location of satellites with respect to PsA patterns are very rare events by themselves, and not all such events allow the correct association of satellite measurements with optical pulsations in the ionosphere. To reduce the uncertainty in locating a satellite’s magnetic footprint, special methods should be applied (e.g., Hosokawa et al. 2020). Because of this, we do not give preference to any of the above approaches and show below that our results regarding the brightening pulsating arc can be explained in the frame of both approaches.
We have shown that the altitude of the emission is lower during the “on” phases of PsA, which means that the energy of precipitating electrons is higher at these moments. In the frame of the scattering approach, the result can be explained by the model of Miyoshi et al. (2015). They demonstrated that PsA during the “on” phase is caused by scattering of electrons due to the lower/upper band chorus. The upper (lower) band resonates with lower (higher) energy electrons. Both higher- and lower-energy electrons are detected during the “on” phase, whereas only lower-energy electron precipitation, caused by the upper band, is seen during the OFF phase. Such precipitation causes relatively higher-altitude emissions. One other possible explanation is that variations in cold plasma density that potentially correspond to the on–off pulsations of the pulsating aurora would change the resonant energy of chorus-electron scattering (e.g., Li et al. 2012).
The internal modulation may also be explained in the frame of the scattering approach. Hosokawa et al. (2020) demonstrated a direct association between the multiscale temporal variations in chorus wave power detected onboard the Arase satellite and aurora luminosity inferred from ground optical measurements. Namely, they showed correlations between chorus bursts and the main optical pulsations, as well as between discrete chorus elements embedded in a burst and internal modulation embedded in an impulse of main pulsations (a Matryoshka doll configuration).
Hosokawa et al. (2020) noted that the energy of precipitating electrons responsible for pulsating auroras often ranges from a few to several tens of keV. Due to different time-of-flight from the magnetosphere to the ionosphere, significant spreading in time of the electron flux appears. In such a case, the sub-second modulation in the chorus tends to be smeared out, and ground-based optical instruments do not see the corresponding internal modulation in the PsA emission. If the resonance energy is higher (in our case, this means that the corresponding auroral arc has lower altitude), the dispersion effect would be smaller, and sub-second (internal) modulation would be able to survive in the optical data.
Periodic acceleration as a possible mechanism for internal modulation
In this section, we present a simple physical model that explains all three of our findings—the decrease in the arc altitude in the course of its brightening, internal modulations inside the brightening arc, and absence of internal modulation in the arc located higher than the arc with sub-second pulsations.
By using the Swarm satellite, Gillies et al. (2015) identified upward field-aligned current (FAC) throughout the interior of the PsA (pulsating patches). It is widely assumed that aurora brightening is due to an increase in the flux of precipitating particles, which may mean an increase in FAC. In the course of its increase, the FAC can exceed the threshold for electrostatic ion-cyclotron instability (EIC instability) resulting in anomalous resistivity and yielding a field-aligned potential drop (e.g., Papadopoulos 1977). The potential drop accelerates the precipitating electrons along the magnetic field line and the altitude of the corresponding arc decreases during the “on” phase. Signatures of electron acceleration were found in FAST satellite data by Sato et al. (2004). We leave the reason for current enhancement at the beginning of each switch-on pulse of main pulsations as beyond the scope of our study and consider the further possible evolution of the current during the “on” phase.
Safargaleev (1996) showed that the value of the EIC instability threshold inside the anomalous resistivity area decreases due to a change in some plasma parameters in the course of instability development. After the appearance of the anomalous resistivity, the FAC should decrease following Ohm’s law. When the FAC becomes less than the new threshold, then the anomalous resistivity and potential drop turn off, the FAC starts to increase again, and the on/off process becomes quasi-periodic. Earlier, the idea of excitation of periodic events in a circuit with a double layer was suggested by Alfven (1981). Later, quasi-periodic oscillation of anomalous resistivity was discussed by Pilipenko et al. (1999) as an additional possible mechanism for the generation of geomagnetic pulsations in the few Hz range. In our case, the periodic switch on/off of a field-aligned potential drop may lead to oscillation of the flux of precipitating particles either directly or via the periodic launch of VLF waves, which then periodically scatter the electrons into the loss cone (Liatskii and Safargaleev 1985).
The stabilization time of the FAC inside the layer of anomalous resistivity is determined by the parameters of the layer. Alfven waves are one of the basic mechanisms for energy and current transport in near-Earth plasmas. Connecting the stabilization of the current with the propagation of an Alfvén wave across the layer, for a rough estimation of the pulsation period, T, we can put T ~ 2b/VA. Here, VA is the Alfvén velocity at the place of anomalous resistivity development, and b is the width of the layer along the magnetic field line. Although the expression is very simple, both parameters are unknown. Let us assume that VA does not change dramatically along the magnetic field line and, according to Kim et al. (2018), reaches a value of ~ 1500 km/s in the postmidnight sector where our observations occur. Then, to obtain the frequency of potential drop oscillations ~ 2 Hz, one needs to take the other unknown parameter b to be approximately 400 km. To the author’s knowledge, only the dimension along the meridian (i.e., across the magnetic field lines) is known for areas where field-aligned acceleration presumably took place (Torbert and Mozer 1978). In particular, the authors noted that the geometry of accelerating structures is similar to that of auroral arcs.
The absence of internal modulation in the upper arc (arc 2 in Figs. 5, 6) may simply mean that the arc-related field-aligned current does not achieve the threshold value due to, for example, different conditions for the development of EIC instability above the arcs.
In many papers related to pulsating auroras, there is no direct indication of exactly what auroral form is under consideration, although the generation mechanisms for pulsating patches and pulsating arcs may be different. In accordance with Sato et al. (2015), applying the field-aligned electric field modulation model to elongated pulsating arcs may be more reasonable than the pitch-angle scattering approach if one takes into account the analogy to ordinary auroral arcs. Ordinary arcs are enhanced via field-aligned electric field accelerations, as is widely accepted due to in situ observations (e.g., Torbert and Mozer 1978).