These measurements do not place strong constraints on the conductivity of the lunar core. We would detect the observed effects as long as the core conductivity was greater than about 10 mho/m. If the outer cool layers of the moon, that are at temperatures below the effective Curie point, contain little or no free iron then these measurements are consistent with the presence of a conducting core whose radius is slightly larger than 400 km. If these outer layers of the moon contain significant amounts of free iron and hence exhibit the paramagnetism expected in such a situation the core size could be even greater.
The most controversial outstanding question of lunar structure is whether the moon possesses an iron or iron sulfide core. The moon's polar moment of inertia factor, C/MR2, 0.3905 + 0.0023 (Ferrari et al., 1980) permits the presence of a 364 km core of density 8 gm/cm3 If the core were as small as 300 km the core density consistent with this polar moment of inertia would be 12 gm/cm3 While some authors feel the gravity data demand a core (cf. Levin, 1979), we emphasize the lack of unanimity on this point. The seismic data are consistent with a core of radius up to about 360 km (Latham et al., 1978). However, the records from the one farside event are ambiguous and thus Goins et al. (1979) conclude there is little seismic evidence for or against a core. Despite the fact that generally accepted thermal models do not produce a moon molten to its center at any time during its history, its outer layers must have been molten (Brett, 1977). Stevenson (1980) has pointed out that differentiation in this molten ocean would lead to a shell of iron at the base of the magma ocean which would be gravitationally unstable to a displacement of the still solid interior of the moon. Eventually the iron would sink to the center and form a core without melting the entire moon. During this latter period a dynamo might be active leading to possible explanation of lunar paleomagnetic data. Stevenson and Yoder (1981) have continued to study this core formation mechanism and suggest further that the outer core is still liquid. In short, even though the existence of a core cannot be proven by the existing data, neither do they rule it out.
It should be possible to detect a metallic lunar core by electromagnetic sounding methods. Several different techniques have been proposed. The oldest and most popular technique is the use of an orbiting and a surface magnetometer to measure respectively the input to the moon and the sum of the input and the response. This technique has been applied in the solar wind, in the magnetosheath and in the magnetotail (Wiskerchen and Sonett, 1977; Dyal et al., 1976). A technique involving the use of two surface magnetometers to probe the deep interior has been outlined by Herbert (1980), but has not yet been applied to the Apollo 15 and 16 data sets which appear suited to this analysis. These two-instrument studies depend crucially on the accurate intercalibration of the magnetometers. The size of the effect expected is small, less than 1%, and no evidence has been presented that differences in inter-instrument calibration of this magnitude do not exist. In fact, during the first four months of Apollo 12 ALSEP operation the two Explorer 35 magnetometers differed in gain from 1.2 to 60.5% (Daily and Dyal, 1979).
Fortunately, there exists a means of probing the deep interior of the moon using a single magnetometer. This technique involves the use of the low-altitude, orbiting Apollo subsatellite magnetometers to measure the induced dipole moment of the moon in the geomagnetic tail lobes (Goldstein et al., 1976a,b). An induced dipole moment develops because the tail field cannot diffuse completely into the core during the relatively short interval required for the moon to traverse the geomagnetic tail. Thus the tail field lines are diverted as they pass around the core. This effect is small, less than 1% for a 400 km core, but the subsatellite magnetometers can be used to detect such a small distortion if measurements are obtained over many orbits. We note that as with the two instrument lunar sounding technique involving solar wind data, we need long swaths of data during which transients in the mantle can decay (cf. Wiskerchen and Sonnett, 1978).
The results obtained in this manner are in apparent contradiction to the results of the two instrument studies which infer either no evidence of a core with an upper limit of about 360 km (Hood et al., 1981) or a paramagnetic moon (Parkin et al., 1973). Since this controversy still exists, we have reexamined the Apollo 15 and 16 subsatellite magnetometer records in an attempt to obtain a more accurate result using the single satellite method.
As soon as a substantial data base was available for Fourier analysis the Apollo subsatellite magnetometer data were examined for signs of an induced magnetic dipole moment. An induced magnetic moment was observed, of magnitude -6.3 + 2.4 x 1022 Gauss-cm3 per Gauss of applied field. However, dual instrument studies with one instrument on the surface gave a positive induced moment consistent with a paramagnetic moon (cf. Parkin et al., 1973). If the subsatellite measurements were affected by local plasma diamagnetism then the observed moment would have been too positive. A possible answer assuming both sets of measurements were correct was that the moon had an ionosphere up to heights below the altitude of the subsatellite (Russell et al., 1974a,b). However, signature of this induced field had day-night symmetry whereas a day-night asymmetry would be expected for a lunar ionosphere (Goldstein and Russell, 1975). Hence, the data were reinterpreted as evidence in favor of a lunar core, despite the apparent two magnetometer evidence to the contrary (Goldstein et al., 1976a, b). In this latter work it was shown also that there is little evidence for temporal decay of the signal on time scales of up to 30 hours. Since this time work on the intercalibration of the Explorer 35 magnetometers and the possible effects of these calibration differences and gain changes on the two instrument sounding technique have been addressed (King and Ness, 1977; Daily and Dyal, 1979). These studies indicated that there were problems with the earlier inferences of a paramagnetic moon, and this resolved the apparent contradiction between the two methods. Further, since that period of time more data have become available with which to assess possible plasma diamagnetic and tail dynamic events. Thus, we deemed it important at this time to re-examine the subsatellite data in an attempt to determine the best possible estimate of the induced magnetic moment. We do this not expecting the moment to change from earlier estimates. Rather, we would hope that only the accuracy of the estimate would improve.
Figure 1 shows the magnetic field strength measured with the Apollo 16 subsatellite on a pass through the tail in April, 1972. This figure reveals one difficulty of the technique. The tail field is seldom steady. Temporal variations induce currents in the outer layers of the moon and can mimic the variations of interest if they contain power at half the orbital period. We have minimized this effect by using the surface magnetometers to detect temporal changes, and if they are small, to remove them from the subsatellite records. Although this process adds some noise to the subsatellite data due to near surface induction effects, it is a second order effect and very small at the frequency of interest.
|Fig. 1. The solid line in the upper panel shows the orbital average magnetic field strength observed by the Apollo 16 subsatellite while the moon traversed the geomagnetic tail in late April, 1972. The dashed line shows the predicted field strength based on the correlation of field strength and solar wind dynamic pressure observed during an interval when the dynamic pressure of the solar wind varied significantly while the moon remained in the tail lobe. The upper row of arrows shows the tail sounding intervals of Parkin et al. (1973). The lower row of arrows indicates the crossings by the moon of the current sheet in the center of the tail. The lower panel shows the induced dipole moment estimated from the subsatellite data. Negative moments are attributed to the presence of a lunar core. Positive moments are attributed to a paramagnetic moon or to the presence of energetic plasma around the moon.|
The moon also frequently crosses the current sheet in the center of the tail on this tail pass. These crossings are indicated by the upward arrows in the middle of the plot. Surrounding these current sheet crossings are depressions in the field magnitude caused by the plasma sheet which contains hot plasma with an energy density of several keV per cubic centimeter. We have used three procedures to determine when we are in the plasma sheet. First, we have used hourly averages of the dynamic pressure of the solar wind provided by the National Space Science Data Center to predict the field magnitude on the tail. In the distant tail our data showed that a linear correlation with dynamic pressure was a good predictor. This prediction is shown by the dashed line. We have examined the energetic particle data from the energetic particle experiment on the subsatellite and we have examined plasma regime identifications provided by J. W. Freeman from the SIDE instrument on the lunar surface. In the analysis, then, we have eliminated any interval of plasma sheet data. The lower panel shows the induced moments we calculate on this tail pass using the same Fourier analysis techniques employed in earlier studies (Russell et al., 1974a,b). A core should produce a negative moment. The diamagnetic plasma sheet will produce a positive moment. During this pass the moon is frequently in the plasma sheet and there are frequent intervals of positive moments correlated with these intervals.
|Fig. 2. The solid line in the upper panel shows the orbital average magnetic field strength observed with the Apollo 15 subsatellite during a tail passage in late January, 1972. The dashed line shows the predicted field strength. We have shaded the intervals in which we believe the moon is in or near the plasma sheet. This identification is based on the ratio of predicted to observed field strength and the presence of plasma sheet particles at the subsatellite or on the lunar surface. The lower panel shows the induced moment.|
Figure 2 shows a second pass through the tail obtained with the Apollo 15 subsatellite magnetometer. Here we have shaded the plasma sheet entries. Again the periods in which we are clearly in the tail lobes are the periods of negative moments.
Performing this exercise for the entire 7 months of Apollo 15 and 16 data we obtain only 21 orbits of useful tail lobe data. The center time of these periods and the derived moments are given in Table 1. These 21 orbits in turn give an induced moment of -4.23 + 0.64 x 1022 Gauss-cm3 per Gauss of external field. This is equivalent to a G-factor (Goldstein et al., 1976a,b) of - 0.0080 + 0.0011.
These results are consistent with our earlier analysis of the entire data set with less conservative rejection criteria. The previous analysis gave a G-factor ranging from -0.0062 + 0.0045 to - 0.0093 + 0.0023 depending on the data subset used. These values differed from zero by from 1.5 to 4 standard deviations of the mean while our present result differs from zero by 7 standard deviations. Our reanalysis has not changed the G-factor but it has apparently changed the accuracy of its determinations. We would not expect a G-factor of zero if the moon had no core because of the paramagnetism of the crust. In fact, reasonable coreless moon G-factors range up to 0.012 (Goldstein et al., 1976a,b). This positive value is significantly different from our negative moment. Thus, our measurements provide evidence that the moon has a significant induced magnetic dipole moment. This moment is most likely due to currents deep in the interior of the moon in a highly conducting mantle or on the surface of a lunar core. The size required for any such core depends on the permeability of the lunar crust which in turn depends on the iron content. The minimum core radius of 435 + 15 km would occur for a moon with no crustal free iron. If there is free iron in the lunar crust then radius of any core could be still larger.
The present limited data do not place constraints on the conductivity of any such core. We could satisfy the observations with conductivities as low as 10 mho/m while the conductivity of an iron core would be about 105 mho/m. A conductivity of 105 mho/m could be supplied by molten basalt (Khitarov et al., 1970). The gravity data while suggesting the presence of a dense core, do not prove it. Within the limits imposed by the polar moment of inertia a 300 km radius core would have a density of 12 gm-cm-3 and a 364 km core would have a density of 8 g cm-3. Thus the gravity data indicate that, if there is an iron or iron-sulphide core, it is of radius slightly smaller than we obtain. The seismic data of Latham et al. (1978) also are consistent with somewhat smaller (molten) core ( 360 km) but do not prove it. In short, all three deep lunar sounding techniques are consistent with some sort of small lunar core, but none can be interpreted as unambiguous proof of its existence. Magnetic sounding suggests a "core" of enhanced conductivity; gravity data are consistent with a core of enhanced density, and the seismic data are consistent with a molten core.
Perhaps further analytical refinements will make these numbers more precise. However, they have now the benefit of a decade's examination. What is needed is an independent data set. The magnetic sounding could be provided by a lunar polar orbiter at low altitudes; improved gravity measurements could come from a high altitude polar orbiter, such as the proposed Doppler relay satellite; and improved seismic data from a new and more extensive ground network.
The authors acknowledge useful discussions of this work with L. L. Hood. We are also grateful to K. Anderson and R. Lin for the use of their energetic particle data from the Apollo subsatellites and to J. Freeman for the use of the plasma data from his SIDE instrument. This research was supported by the National Aeronautics and Space Administration under grant NGR 05-007-351.
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