Non-monochromatic whistler waves detected by Kaguya on the dayside surface of the moon
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011
Received: 9 August 2009
Accepted: 19 January 2010
Published: 21 February 2011
Non-monochromatic fluctuations of the magnetic field over the frequency range of 0.03–10 Hz were detected by Kaguya at an altitude of 100 km above the lunar surface. The fluctuations were almost always observed on the solar side of the moon, irrespective of the local lunar crustal field. They were also detected just nightside of the terminator (SZA < 123°), but were absent around the center of the wake. The level of the fluctuation enhanced over the wide range from 0.03 to 10 Hz, with no clear peak frequency. The fluctuations had the compressional component, and the polarization was not clear. The fluctuations were supposed to be whistler waves generated by the protons reflected by the lunar surface. The reflected protons are scattered in various directions, resulting a wide range of distribution of the velocity component parallel to the magnetic field. It may account for the wide range of frequency as observed, through cyclotron resonance of the wave with the reflected ions, in which the resonant frequency depends on the velocity component parallel to the magnetic field. However, there is also the possibility that the waves were generated by some nonresonant process.
Since the moon does not have a global magnetic field system, the solar wind particles can access the lunar surface directly. This results in the solar wind interaction with the moon being quite different from that with the Earth.
Absorption of the solar wind particles by the lunar surface leads to the formation of the lunar wake, a plasma cavity in the solar wind left on the anti-solar side of the moon (Colburn et al., 1967; Lyon et al., 1967; Ness et al., 1968; Schubert and Lichtenstein, 1974; Ogilvie et al., 1996; Owen et al., 1996; Bosqued et al., 1996). It has recently been determined that not all the solar wind particles are absorbed, but that 0.1–1% of the solar wind protons are reflected by the lunar surface (Saito et al., 2008). Some of the reflected protons can also access the center of the near wake due to their large Larmour radius (Nishino et al., 2009).
The solar wind interaction with the moon generates wave activities around the moon. WIND and Geotail spacecraft detected monochromatic whistler waves in the solar wind when the spacecraft were magnetically connected with the lunar wake (Farrell et al., 1996; Nakagawa et al., 2003). Monochromatic whistler waves were also detected by Lunar Prospector in association with the lunar external magnetic enhancements (LEME) or the lunar crustal magnetic field (Halekas et al., 2006a). These were circularly polarized waves propagating along the magnetic field against the solar wind flow. Their generation has been related to fieldaligned beams of ions or electrons.
The aim of this paper is to present the properties of the non-monochromatic waves observed mainly on the dayside surface of the moon, and to discuss their generation mechanism.
The bottom panel of Fig. 3 is an example of the dynamic spectrum of the B y component. The level of fluctuations enhanced during the period from 4:10 to 5:30. The frequency extended up to 5 Hz for the period 4:10–5:10, and then up to 10 Hz for 5:10–5:27. Although the fluctuations were most intense in the weak-field region around 5:20–5:27, just behind a LEME observed at 5:10–5:20, for most of the time (4:10–5:10), the magnetic fluctuations were observed far from LEME and seem to have nothing to do with them. Red (blue) bars at the bottom of the spectrum indicate that the spacecraft was magnetically connected with the dayside (nightside) surface of the moon. It should be noted that the spacecraft was not necessarily connected with the lunar surface when the magnetic fluctuations were observed, suggesting that the wave propagation was not exactly parallel to the magnetic field.
The 0.03- to 10-Hz fluctuations appeared repeatedly when the spacecraft was in the solar wind (on the dayside of the moon or near the wake boundary), and they disappeared as the spacecraft went into the center of the wake. It is recognized in Fig. 1 that an alternating pattern of presence and absence of the 0.03- to 5-Hz fluctuations was repeated at 2-h intervals. It is also recognized that the 0.03- to 5-Hz fluctuations are independent of intense low frequency fluctuations of 10−2 Hz. The orbit of Kaguya was nearly along the terminator on this day. The magnetic fluctuations were observed on the dawnside of the moon, where the solar wind particles can hit the lunar surface directly due to the 4° aberration angle of the solar wind flow caused by the motion of the moon in the solar system.
3. Summary of Observations
The properties of the magnetic fluctuations are summarized as follows:
Non-monochromatic fluctuations of the magnetic field over the frequency range of 0.03–10 Hz were detected by Kaguya at the altitude of 100 km above the lunar surface.
The fluctuations were almost always observed when the spacecraft was in the solar wind, irrespective of the local lunar crustal field. They were mainly observed on the solar side of the moon and also detected just nightside of the terminator (SZA < 123°), but they were absent around the center of the wake.
There was no clear peak frequency.
The fluctuations had the compressional component. They were not propagating along the background magnetic field lines.
They showed no preferred polarity.
4.1 Mode of the wave
If we assume the waves are generated at upstream of Kaguya, the observed frequency would depend on the direction of propagation. Waves propagating upstream would be convected down if the group velocity is smaller than the solar wind flow. They would then be detected at lower frequencies. On the other hand, if the waves were propagating down the solar wind flow, they would be observed at higher frequencies due to the Doppler shift. One might expect that some low-frequency waves, such as magnetohydrodymanic (MHD) waves, might have been detected by Kaguya at a higher frequency, however, these can not account for the frequency range up to 10 Hz as observed. Substituting k = ω/Vph into Eq. (1), where the phase speed Vph of a MHD wave is of the order of Alfvén speed or sound speed, Vph ∼ 0.1 Vsw, we obtain ωobs of the order of 10 ω.As the frequency of a MHD wave is smaller than the ion cyclotron frequency Ω i ∼ 0.03 Hz for this period, the frequency ωobs to be detected by Kaguya cannot exceed 0.3 Hz. Therefore, we conclude that a MHD wave is not an appropriate candidate for the non-monochromatic waves of 0.03–10 Hz as detected by Kaguya. Rather, it is the low-frequency waves at around 0.01 Hz that are explained by the Doppler shift of the MHD waves.
Given the observed frequency range up to 10 Hz, the wave detected by Kaguya is supposed to be a whistler mode wave. One may think it inconsistent that the nonmonochromatic waves were not propagating parallel to the magnetic field while the monochromatic whistlers reported in earlier publications were propagating parallel to the magnetic field (Farrell et al., 1996; Nakagawa et al., 2003). However, Halekas et al. (2006b) reported that the monochromatic whistler waves in the close vicinity of the moon propagated at all angles to the magnetic field with the largest percentage near ∼40°. Furthermore, the propagation direction of a whistler wave tends to be more and more parallel to the magnetic field as it propagates, because the group velocity is more parallel to the magnetic field than the phase velocity. It might then be detected as propagating parallel to the magnetic field at a long distance from the generation site.
4.2 Possible generation mechanism
It would be natural to think that the waves were associated with the plasma particles reflected by the lunar surface, as the waves were mainly observed on the solar side surface of the moon.
In the following sections, we discuss the generation mechanism of the whistler wave.
4.3 Cyclotron resonance
Cycrotron resonance with reflected particles.
Detection by s/c
Resonance condition (fundamental)
Downstream of s/c
Accessible if V g cos θ ks > Vsw
ω − ;∣k(Ve‖ − Vsw‖) cos θ kB ∣ = Ω e
Impossible as ω< Ω e
ω − ∣k(Vi‖ − Vsw‖) cos θ kB ∣ = −Ω i
Inaccessible to s/c
(Accessible only on the limb)
Upstream of s/c
Accessible if Vg cos θ ks < Vsw (convected down)
ω − ∣k(Ve‖ − Vsw‖) cos θ kB ∣ = Ω e
Impossible as ω < Ω e
ω − ∣k(Vi‖ − Vsw‖) cos θ kB ∣ = −Ω i
ω+∣k(Ve‖ − Vsw‖)cos θ kB ∣ = Ω e
Not likely as ω obs ≪ Ω e
ω+∣k(Vi‖ − Vsw‖)cos θ kB ∣ = −Ω i
Impossible as ω obs > 0
Accordingly, we conclude that the resonant particles must be protons if we assume cyclotron resonance as a generation mechanism of the whistler wave. A famous example of whistler waves generated through the cyclotron resonance with ions is the upstream waves at the Earth’s bow shock (Fairfield, 1974). There are two major frequency ranges of the waves upstream from the Earth’s bow shock, 0.01–0.05 Hz and 0.5–4 Hz. The former is thought to be MHD waves generated by the ions that are reflected by the bow shock to reach far upstream of the observer because of the large Larmour radius and then convected down by the solar wind flow (see Fairfield, 1969; Russell, 1994a, b). The latter is the whistler waves generated at the bow shock by the reflected ions, which propagate against the solar wind. The two frequency ranges seem to be analogous to those observed near the moon. The Earth’s bow shock is a huge obstacle as seen from the perspective of the solar wind ions. We need to examine whether the moon reflects a significant number of solar wind ions.
Figure 7 shows that the fluctuations were weak during the period from 13:15 to 13:35, despite the fact that the reflected protons were continuously observed. A part of the period (13:22–13:35) might be related with the absence of the magnetic connection to the lunar surface, but the period of the disconnection was much shorter. It is not surprising that the periods of absence of the magnetic connection and weak fluctuations disagree because the propagation of the waves was not exactly parallel to the magnetic field. The reason for the depression of the fluctuation is not known, and any attempt to determine it would require a simulation study of the trajectories of the reflected particles and the mechanism of the excitation of the waves in which the configuration of the magnetic field would play a crucial role.
Here we have assumed that whistler waves with a variety of (ω, k) would be generated that would correspond to a range of resonant velocities of the reflected protons and that they co-exist in the solar wind flow near the moon. However, it would require further theoretical or numerical work to determine whether the whistler mode would become unstable over the wide range of frequency as observed here.
The highest resonant frequency is given by the steepest line in Fig. 8. According to Saito et al. (2008), the energy of the reflected protons are 70% of the incident solar wind, that is, ∣V i ∣ ∼ 0.84Vsw. Therefore, we can estimate the largest inclination of the order of 1.84 Vswcosθ kB .A solar wind speed of ∼350 km s−1 and a plasma density of ∼6 × 106 m−3 were estimated from the upstream observation by ACE. The estimated electron density agreed with the plasma frequency obtained from the plasma wave measurement made by LRS/WFC instrument onboard Kaguya (courtesy of Y. Kasahara). By substituting these parameters together with Ω e = 2π × 1.4 × 102 Hz, ω p = 2π × 2.2 × 104 Hz, and Ω i /Ω e = 0.54 × 10−3 into Eqs. (3) and (6), we obtain the highest resonance frequency ω/Ω e = 0.1 cos θ kB at ck/Ω e = 53, which corresponds to 14 cos θ kB Hz. The waves would be Doppler shifted and then observed by Kaguya. Using Eq. (1) we obtain the highest frequency to be observed as (14 cos θ kB − 8 cos θ kS ) Hz, where θ kS is the angle between the wave number vector and the solar wind flow. This result seems to be consistent with the upper frequency of ∼10 Hz of the observed waves, as the wave number vector k was not parallel to the magnetic field nor the solar wind flow.
This condition is satisfied at frequencies higher than 1.2/ cos θ kB cos θ kS Hz for the parameters of February 27, 2008. In other words, low-frequency components of the non-monochromatic waves whose frequency is less than 1.2 Hz can not come from downstream of the spacecraft. They must be generated upstream of the spacecraft and then convected down. Indeed, the altitude of Kaguya, 100 km above the lunar surface, seems to be too low with respect to the Larmour radius of the reflected ions, which is as large as 1000 km. The ions can not rotate even one cycle of gyration before they reach the altitude of the spacecraft. It may therefore be difficult for the waves to grow through the cyclotron resonance before reaching the spacecraft.
4.4 Some non-resonant instabilities
Another possibility is that the broadband emission was due to some non-resonant instabilities. Injection of the reflected protons into the solar wind plasma causes relative cross-field electron-ion streaming in which modified two-stream instability may be present (McBride et al, 1972; Wu et al, 1984; Matsukiyo and Scholer, 2003). The advantages of the modified two-stream instability is that it grows within a short period that is comparable to the lower-hybrid frequency and much shorter than the gyro period and that the fluctuations have a compressional component. The broadband emission may then be due to a cascade process (Matsukiyo and Scholer, 2003; Gary et al., 2008). It would require further work to determine the generation mechanism as well as the growth rate of the whistler waves and the direction of the wave number k to be chosen.
The non-monochromatic, 0.03- to 10-Hz fluctuations of the magnetic field were detected by Kaguya at an altitude of 100 km above the lunar surface when the spacecraft was in the solar wind. The magnetic fluctuations were the whistler mode wave generated by the protons reflected by the lunar surface. The waves were not propagating parallel to the magnetic field, and the fluctuations had a compressional component. There was no peak frequency nor prefered polarization. The observed frequency range can be explained by cyclotron resonance of the whistler waves with the protons reflected by the lunar surface; however, it is not known why they were not propagating parallel to the magnetic field. Another possibility that the cross field velocity difference between the reflected ions and incident solar wind particles may cause some nonresonant instability, such as modified two-stream instability. Further theoretical or numerical work are required to reveal the exact generation mechanism.
The authors are grateful to S. Machida, Y. Kasahara, K. Tsubouchi, M. Nishino, and S. Matsukiyo for valuable comments and discussion. The authors are thankful to Y. Saito for the E-t diagram in Fig. 7 and Y. Kasahara for the electron density measured by LRS/WFC. This work was supported by JSPS Grant-in-Aid for Scientific Research project 21540461.
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