An Estimation of Electrical Conductivity of the Moon Using Kaguya Magnetometer Data

The electrical conductivity structure of the moon can be determined by electromagnetic responses. From the simultaneous Apollo 12 and Explorer 35 magnetometer observations, the electrical conductivity structure of the lunar interior has been estimated (e.g. Sonett et al. 1972, Wiskerchen and Sonett 1977, Hood et al.1982). However, it so far contains significant ambiguity in orders of magnitude for the shallow part. The ambiguity principally comes from low sampling rate of Explorer 35, which is 6.14 sec. In order to restrict the ambiguity, we try to use the Kaguya Lunar MAGnetometer (LMAG) data, which has 32Hz sampling rate (Tsunakawa et al. 2010). Because we use only the magnetic field observation of Kaguya as the output of the response, we suppose that the external input is randomly oriented uniform field. If the moon responds, the magnetic field variation or noise is smaller in the radial component comparing to the horizontal component. The randomness is tested if the variations of north and east components are equal or not. The data used are from the nominal observation (about 100km in altitude) and above the Mare Imbrium (15~45N, 0~45W) where crustal field is minimal on the lunar surface. As the satellite takes about 1000sec passing this area, 1024 of one second averaged data is submitted to Fourier transformation to obtain power spectrum. The results when (1) the moon is in earth's tail lobe and (2) the moon is in the solar wind but Kaguya is in the lunar wake are used for analyses, since otherwise there exists plasma above the lunar surface. The power of radial, north and east component (Pr, Pn and Pe, respectively) are divided by total power (P=Pr+Pn+Pe) are plotted against the frequency. The randomness of input is examined whether Pn/P and Pe/P are equal or not. They are equal only for the frequency of 0.2Hz and lower of lunar wake data. The Pr/P data passed those criteria are compared with those calculated in uniform conductivity model, thus the effective conductivity is calculated. The lowest frequency (0.006Hz) data gave 2E-4 S/m, and the estimated effective conductivity slightly decreases with frequency toward 0.02Hz to 1E-4S/m and then decreases more steeply to 3E-6 S/m at about 0.2Hz. Taking the lowest frequency value, the skin depth is about 400km. It is thus consistent with Hood et al. (1982). To the surface, the present result constrains the upper limit of the conductivity two orders of magnitude lower than the previous estimate.