Statistical study of broadband whistler-mode waves detected by Kaguya near the Moon

Authors


Abstract

[1] Broadband whistler-mode waves in the frequency range from 0.1 to 10 Hz are detected near the Moon by the Lunar Magnetometer (LMAG) on board Kaguya. The generation process and statistical properties of the waves have not been understood yet. We analyze the distributions of their occurrence and reveal that most of the waves are generated by the solar wind interaction with lunar crustal magnetic field. We also clarify that the waves are observed when Kaguya is connected by the ambient magnetic field with the lunar surface. The statistical study indicates that the broadband waves are observed in the vicinity of the region where narrowband whistler-mode waves in the frequency of near 1 Hz are observed, showing the close relationship between them. The analysis of the wave vector directions suggests that these two types of waves are different views of the same waves propagating in the solar wind frame. The narrowband waves are possibly explained by a part of the broadband waves largely Doppler shifted in the spacecraft frame. The present results suggest a possible scenario of the generation process of the two types of waves through the solar wind interaction with the crustal magnetic field.

1. Introduction

[2] The Moon is generally characterized as an airless obstacle with no global magnetic field. When in the solar wind, or outside the magnetosphere, the Moon interacts with the solar wind. Obstruction of the supersonic plasma flow of the solar wind causes the formation of the lunar wake where plasma density is much lower than the solar wind. It is notable that the magnetic field remaining in the lunar crust interacts with the solar wind and form mini-magnetospheres [e.g.,Lin et al., 1998]. A variety of the solar wind interactions results in the complicated behavior of the plasma environment around the Moon.

[3] Broadband magnetic turbulence in the frequency range from 0.1 to 10 Hz has been detected around the Moon by Lunar Prospector [Halekas et al., 2008] and Kaguya [Nakagawa et al., 2011] at about 100 km altitude. Halekas et al. [2008] suggested that the waves are produced by the solar wind plasma interacting with crustal magnetic field and are associated with the shock formed near the crusts. Nakagawa et al. [2011]studied the characteristics of the broadband waves by considering properties of whistler-mode waves propagating in the solar wind frame of reference. While they discussed the possible generation process of the waves through resonant or non-resonant instability by ions reflected from the lunar surface, details of the generation process of the waves have not been clarified yet.

[4] Narrowband whistler-mode waves with frequencies close to 1 Hz have also been detected around the Moon by Lunar Prospector [Halekas et al., 2006a] and Kaguya [Tsugawa et al., 2011]. The waves are mostly left-hand polarized in the spacecraft frame, because of the large Doppler-shift effect on whistler-mode waves propagating in the solar wind frame of reference. The narrowband wave spectra can be explained by the Doppler-shift effect in the same way as “1 Hz waves” which have been observed upstream of planetary bow shocks [e.g.,Orlowski et al., 1995]. The association of the narrowband waves with the lunar crustal magnetic field has been revealed statistically [Tsugawa et al., 2011]. The generation process has not been clarified yet, because the wave source region has been unclear.

[5] In this paper, we conduct statistical analyses of the broadband waves observed by Kaguya to reveal the occurrence properties of the waves around the Moon. We also analyze a typical event in which the broadband and narrowband waves are detected simultaneously so as to discuss the relationship between the broadband and narrowband whistler-mode waves by comparing their wave properties and observation conditions.

2. Instruments and Observations

[6] Kaguya (SELENE) is a Japanese spacecraft, which orbited around the Moon in polar orbit at about 100 km altitude with a 2-hour period during December 2007–September 2008 as the constancy phase. We use data set obtained by the LMAG (Lunar Magnetometer) and PACE (Plasma energy Angle and Composition Experiment) on board Kaguya. LMAG has a triaxial ring-core type fluxgate sensor sampled at 32 Hz [Tsunakawa et al., 2010]. The noise level was attained to be less than 0.1 nT by the ground and in-orbit calibrations [Shimizu et al., 2008; Takahashi et al., 2009], and the electromagnetic compatibility conditions [Matsushima et al., 2010]. PACE contains ESA (Electron Spectrum Analyzer)-S1 and Ion Mass Analyzer (IMA) which face the Moon with a half-sphere field of view and detect upward electrons in the energy range from 5 eV to 10 keV and positive ions in the energy per charge range from 7 eV/q to 29 keV/q, respectively [Saito et al., 2008a]. We applied the fast Fourier transformation (FFT) to every 16 second time interval magnetic field data to obtain the wave spectra. For the waveform analysis, we estimated the wave normal direction by the minimum variance analysis (MVA) [Sonnerup and Cahill, 1967]. In addition, we divided the component of the waves oriented perpendicular to the mean field into right- and left-hand polarized wave components.

[7] Figure 1shows an example of broadband whistler-mode waves detected by Kaguya. Broadband magnetic waves up to ∼10 Hz were seen from about 12:10 to 12:40 UT in FFT spectra (Figure 1a) derived from LMAG data set. The ellipticity of the waves is variable in this period (Figure 1b). The frequency range and no preferred polarization of these waves correspond to the whistler-mode waves in the solar wind frame of reference [Nakagawa et al., 2011]. During this event, since the angle between the ambient magnetic field and the lunar surface (B-surface angle) was greater than about 19°, which corresponds to the minimum angle for the traced straight field line connected to the lunar surface (Figure 1c), the spacecraft is considered to be connected to the lunar surface by magnetic field lines. Figures 1d and 1eshow the differential energy fluxes of upward electrons and ions from the Moon detected by ESA-S1 and IMA, respectively. The electrons were energized during 12:10–12:40 UT. The large flux of ions during 11:30–11:50 and 12:40–13:00 UT correspond to the solar wind ions came into the field of view of IMA [Saito et al., 2008b]. The enhanced flux of ions during 11:50–12:40 UT corresponds to the reflected ions from the Moon, especially reflected by the crustal magnetic field during 12:10–12:40 UT. In this period, the spacecraft orbited over the region of the largest magnetized crusts in the South Pole Aitken (SPA) basin (Figure 1f). The broadband waves are observed simultaneously with the electron energization and the ion reflection just above the magnetized crusts. Furthermore, most of the waves are also observed only on the dayside (Figure 1g). Figures 1f and 1g suggest that the geometrical condition to observe the broadband waves at altitude of 100 km from the lunar surface is to locate above the magnetized crusts and on the dayside of the Moon. In the following section we conduct statistical analyses in order to reveal detailed properties of the waves.

Figure 1.

The broadband waves detected by Kaguya on March 9, 2008. (a) The fast Fourier transform (FFT) spectrum of magnetic field, (b) ellipticity spectrum, (c) magnetic field strength (∣B∣), angle between the magnetic field and the lunar surface (B-surface angle), and differential energy fluxes of (d) electrons and (e) ions. Ellipticity is defined as (R − L)/(R + L), where R and L represent the right- and left-hand polarized component of the intensity of the waves, respectively. Spacecraft trajectories during 11:00–13:00 UT and magnetic field vectors (f) in the selenographical (Mean Earth/polar axis, ME) coordinates and (g) in the Selenocentric Solar Ecliptic (SSE) coordinates. East longitude is adopted in ME coordinates. SSE longitude corresponds to local time (e.g., 0° longitude in SSE corresponds to local noon), SSE latitude almost corresponds to selenographical latitude because of the small (a few degrees) inclination of the Moon's axis. The black contour in Figure 1f indicates 20 nT surface magnetic field strength obtained from LP observations (courtesy of J. S. Halekas). The color contours in Figure 1g indicate SZA of every 20°. The thick red arrows superposed on the trajectories represent the period during 12:10–12:40 UT indicated by a red bar just below Figure 1a.

3. Statistical Properties

3.1. Event Selection

[8] We have analyzed the LMAG data set during the constancy phase of 10 months. To limit our investigation to the period when the Moon was outside the Earth's magnetosphere and to discard waves originating from the Earth's bow shock, we selected the period when the azimuth of the spacecraft position in the Geocentric Solar Ecliptic (GSE) coordinates ranged from −135° to 135°, which is the same period used in Tsugawa et al. [2011] for the narrowband waves. The data set of the analyzed period has enough spatial coverage around the Moon.

[9] In the present study, we define the broadband whistler-mode waves near the Moon as the waves appeared in the frequency range from 0.5 to 10 Hz with the integrated power greater than 6.4 nT2. The lower limit of the frequency range corresponds to the proton gyro-frequency for the magnetic field strength of 33 nT, roughly corresponding to the maximum of magnetic field strength in the spacecraft orbits. The upper limit of the frequency range is the same with the previous study [Nakagawa et al., 2011]. The minimum value of the integrated power of the waves is selected to be enough large in detecting the broadband waves from the noise level.

[10] Applying this criterion, we selected 13,282 events (one event represents a 16 second time interval), which correspond to 1.1% of the analyzed period. Using the data set of the selected events, we have conducted the following statistical study of the broadband whistler-mode waves.

3.2. Distributions of the Waves

[11] The occurrence rate of the waves averaged within a 10° × 10° bin in the selenographical (ME) coordinates and Selenocentric Solar Ecliptic (SSE) coordinates are shown in Figures 2a and 2b, respectively. The black contours superposed in Figure 2a indicate 20 nT of the surface intensities of the lunar crustal magnetic field. The color contours superposed in Figure 2b indicate Solar Zenith Angle (SZA) of every 20°. These are the same manner with the occurrence distributions of the narrowband waves [Tsugawa et al., 2011].

Figure 2.

Spatial distributions of occurrence rate of the broadband waves (a) in the selenographical (Mean Earth/polar axis, ME) coordinates with 20 nT of surface magnetic field strength contour and (b) in the Selenocentric Solar Ecliptic (SSE) coordinates with SZA contours shown for every 20° (in the same manner with Figure 1f and 1g, respectively). The occurrence rates of Figures 2a and 2b are obtained by dividing the number of events by the number of 16 s interval data points for all orbits in each 10° × 10° bin. (c) The wave occurrence rate with respect to the B-surface angle which is obtained by dividing the number of the events by the number of 16 s intervals in each bin of 6°.

[12] Figure 2a shows that regions of high occurrence rates are clearly associated with the locations of magnetized crusts. The regions where the occurrence rate is higher than 3% are mainly located within the contours of 20 nT surface field. Meanwhile, Figure 2b shows that the occurrence rate is high in the region of SZA lower than 70° as well as on the south and dawn side. Most of the waves are observed on the dayside, not in the lunar wake. These results suggest that the waves are generated through the solar wind interaction with the lunar crustal magnetic field. The high occurrence distribution in the southern region can be explained by the localization of the magnetized crusts in Southern Hemisphere. Compared to these distributions of the occurrence, the distributions of the averaged integrated power of the waves have no significant spatial dependences (not shown here).

[13] It should be noted that the occurrence rate is not always high above the magnetized crusts (see Figure 2a). The waves were not frequently observed above some magnetized crusts; a typical example is the Crisium antipode region (∼20°S, ∼240°E) where the most strongly magnetized crust exists [e.g., Tsunakawa et al., 2010]. We also note that the selected events rarely contain pulse-like waves or magnetically perturbed structures, which result in broadband signs in the frequency spectra with strong intensities unexpectedly satisfying the selection criterion used in the present study. These pulse-like features in the waveform are observed when the spacecraft is above strongly magnetized crusts, suggesting that they are also associated with mini-magnetosphere or shock-like structure which would be generated near the magnetized crusts in the solar wind [Halekas et al., 2006b].

3.3. Ambient Magnetic Field Direction

[14] In addition to the location of the magnetized crusts, we show that the ambient magnetic field direction at the point of the spacecraft is another condition to observe the broadband waves. We have counted the number of events of the broadband waves with respect to the B-surface angle and have derived the wave occurrence rate in each angle as shown inFigure 2cby dividing the number of the events by the number of 16 s interval data points for all orbits. The occurrence rate is higher at greater angles. The percentage of events for the B-surface angle >19° (minimum angle for the magnetic connection to the lunar surface) represented by the shaded bars inFigure 2cis 82%. This result means that the waves are more observable when the ambient magnetic field is connected to the lunar surface. Since the group velocity vector of whistler-mode waves under the quasi-longitudinal approximation [e.g.,Gurnett, 1995] is confined within 19° with respect to the magnetic field vector, the waves are suggested to be originated from the Moon, particularly from the crustal magnetic filed as shown in Figure 2a.

[15] This feature provides the reason of the high occurrence distribution on the dawn side in SSE coordinates (Figure 2b). Since the interplanetary magnetic field tends to follow the Parker spiral, the azimuth angle of the magnetic field is approximately −45° in GSE coordinates at 1 AU from the Sun. This condition causes easier magnetic connection to the dawn side than the dusk side on the dayside of the Moon. The requirement of the magnetic connection to observe the waves would make the occurrence high on the dawn side.

4. Broadband and Narrowband Waves

[16] The high occurrence rate regions of broadband whistler-mode waves (Figures 2a and 2b) are located nearby those of narrowband whistler-mode waves [Tsugawa et al., 2011]. Both occurrences are high near the magnetized crusts in ME coordinates and on the south and dawn side in SSE coordinates. The broadband waves are observed closer to the locations of the magnetized crusts and spread smaller SZA region, where the occurrence rates of the narrowband waves tend to decrease as shown in Tsugawa et al. [2011, Figure 2]. Since in selecting narrowband waves in Tsugawa et al. [2011] we used strict criteria of the peak intensity with the drop level larger than 20 dB, there is a possibility that the narrowband waves could not be identified just above the magnetized crusts and small SZA region because of the presence of the broadband waves. To clarify the association of the two types of waves, we compare their properties in detail.

[17] We show a typical event of the narrowband waves observed in the vicinity of the broadband waves in Figure 3a. Compared with the orbit shown in Figure 1, Kaguya passed in the same region in ME coordinates and 40° westward in SSE coordinates during this event. The broadband waves are observed from 1:40 to 2:05 UT above the SPA region and after that the narrowband waves from 2:05 to 2:20 UT. The waves in the frequency of 1–2 Hz are left-hand polarized from 1:55 to 2:20 UT as shown inFigure 3b. The electron energization is observed with the broadband and narrowband waves during 1:40–2:20 UT (Figure 3d). The ion reflection is observed with the broadband waves during 1:40–2:05 UT (Figure 3e). It is consistent with the statistical properties shown in the previous section and the study of Tsugawa et al. [2011] that the broadband waves are observed just above the magnetized crusts and smaller SZA and that the narrowband waves are observed near the magnetized crusts and SZA region of 40°–90°. The narrowband waves are present simultaneously with the broadband waves from 1:55 to 2:05 UT, whereas we cannot recognize the narrowband waves if we used the criteria of the sharp peak intensity. Figure 3cshows time series of the angle between the wave vector (k) and sunward (x) as a function of the wave frequency. We derived the angle by adopting the MVA to three-dimensional waveforms reproduced by the inverse FFT from each frequency component of wave spectra. We note that the cosine of the k-x angle corresponds to the significance of the Doppler-shift effect on the waves in the solar wind medium measured in the spacecraft frame. When the angle is 0°, the Doppler-shift term has the largest negative value. When the angle is 90°, on the other hand, the Doppler-shift effect is absent, resulting in the measurement without the modification of the frequency spectra of waves propagating in the solar wind frame of reference. The k-x angles of the narrowband waves concentrate in 15°–35°, while those of the broadband waves vary widely. The left-hand polarization of the narrowband waves (Figure 3b) is caused by a specific sunward wave vector direction and the large negative Doppler-shift [e.g.,Halekas et al., 2006a; Tsugawa et al., 2011]. On the other hand, the various polarizations of the broadband waves (Figure 3b) are possibly caused by various wave vector directions and a variety of the Doppler-shift effect due to the wide range of k-x angles.

Figure 3.

The broadband and narrowband waves detected by Kaguya on May 4, 2008. (a) The fast Fourier transform (FFT) spectrum, (b) ellipticity spectrum, (c) angle of the wave vector (k) to the sunward direction (x), and differential energy fluxes of (d) electrons and (e) ions. The superposed white and blue lines in Figure 3a correspond to the absolute values of the lower hybrid frequency (flh) and proton cyclotron frequency (fcp), respectively. (f) Doppler-shifted dispersion relations of whistler-mode blanch in cold plasma using the addressed parameters. Positive and negative frequencies represent right- and left-hand polarizations, respectively.

[18] Figure 3fshows Doppler-shifted dispersion relations of whistler-mode waves under the solar wind parameters at 02:00 UT, when the broadband and narrowband waves are present simultaneously. The number density and bulk velocity of the solar wind are estimated by data set of ACE spacecraft. While the angle between k and magnetic field (B) varied in each frequency range, we assume 30° by referring the waves in the frequency range of 1–2 Hz at 02:00 UT. We draw dispersion curves every 30° of the k-x angle from 0° to 90°. Positive and negative frequencies represent right- and left-hand polarizations, respectively. The frequencies of the narrowband whistler-mode waves in the solar wind frame will be approximately 10–50 times higher than the local proton gyro-frequency. If the k-x angle ranges from 0° to 90°, the waves will be observed with various polarization and in the broadband frequency range up to 50 times of local proton gyro-frequency, which corresponds to ∼5 Hz under the assumed solar wind condition. This estimation indicates that the broadband and narrowband waves observed by Kaguya can be explained by the waves generated in the same wave source and propagated in the solar wind frame of reference. The observed narrowband waves could be a part of the broadband whistler-mode waves as a consequence of small k-x angle.

[19] We can explain the reason of high occurrence distribution of narrowband waves on the dawn side [see Tsugawa et al., 2011, Figure 2d] if they are a part of the broadband waves. The geometrical condition due to the Parker spiral which results in the frequent magnetic connection from the spacecraft to the lunar surface on the dawn side could cause high occurrence rate of the broadband waves and the narrowband waves as well. In addition to the magnetic field direction, the previous studies suggested that the properties of whistler-mode waves propagating in the solar wind frame should be also important for the formation of the narrowband waves [e.g.,Orlowski et al., 1995]. The precise conditions to detect the narrowband waves should be examined in the future study.

5. Conclusions

[20] We analyzed the broadband whistler-mode waves detected by Kaguya near the Moon. It was revealed that the waves were observed more frequently when the spacecraft was closer to the magnetized crusts in the solar wind, showing that the waves are generated by the solar wind interaction with the lunar crustal magnetic field.

[21] The broadband whistler-mode waves were statistically observed in the vicinity of the location where the narrowband whistler-mode wavers were observed. Statistical and typical event studies provided a possibility that the two types of waves are generated in the same wave source and are observed differently in the spacecraft frame. The properties of frequency and polarization of the waves can be explained by various wave vector directions of the broadband waves and specific wave vector directions of the narrowband waves.

[22] Since the broadband waves are clearly correlated with ions reflected by the crustal magnetic field (see Figures 1e and 3e), the ion beams are suggested to be a presumable energy source of the waves. This suggestion is basically consistent with the previous study [Nakagawa et al., 2011], which remarks that the ions reflected by the lunar surface would generate the waves. We also observed electron energization in association with the wave activities of not only the broadband waves but the narrowband waves (see Figures 1d and 3d). The energetic electrons are also a possible source of the waves as suggested by Halekas et al. [2008]. The energies required for gyroresonant interaction with the whistler-mode waves in the spacecraft frame for the period ofFigure 3f are roughly estimated to be 140 eV–1.2 keV for ions and 790 eV–2.3 keV for electrons, respectively. While the precise generation mechanism of the waves remains unsolved, investigations of particle reflections by the Moon and plasma structures around the magnetized crusts would provide thorough understanding of the wave generation process and are left in the future study.

Acknowledgments

[23] The authors wish to express their sincere thanks to all members of the Kaguya project team for processing and analyzing the data, J. S. Halekas for the LP data, and the ACE SWEPAM instrument team and the ACE Science Center for the ACE data. This work was supported by the Global COE program ‘Global Education and Research Center for Earth and Planetary Dynamics’ at Tohoku University.

[24] The Editor thanks two anonymous reviewers for assisting in the evaluation of this paper.

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