Comment on “Rotation rate of Saturn's interior from magnetic field observations” by Giacomo Giampieri and Michele K. Dougherty

[1] Giampieri and Dougherty [2004] re-analyzed observations of Saturn’s magnetic field obtained by the Pioneer 11 (P11) spacecraft in 1979 and Voyagers 1 and 2 (V1, V2) in 1980 and 1981. They claim to ‘‘have obtained the first direct measurement of the rotation rate of the internal magnetic field’’. [2] We show that this claim is not valid; that their analysis of magnetic field data is flawed; and their conclusions regarding the nature of Saturn’s magnetic field are unsupported. [3] The P11, V1 and V2 flybys were separated by about 438 (P11 to V1) and 725 (P11 to V2) days. The uncertainty in Saturn’s rotation period (10 h 39 m 24 s ±7 s) deduced from radio emissions [Desch and Kaiser, 1981] translates into an uncertainty in the exact number of Saturn rotations between subsequent encounters of about ±0.2 rotations and ±0.3 rotations, respectively. However, more recent analysis of Saturn’s radio emissions [Galopeau and Lecacheux, 2000] yields a period that varies with time and often differs from the Voyager-era estimate by as much as 1% or >325 seconds. Uncertainties of this size result in differences of a complete rotation every 40 days, thus between the P11 and V1, V2 encounters, 10 or more rotations difference could be accrued. In light of this current uncertainty in Saturn’s rotation period, no analysis that considers only minor adjustments to the rotation period of ±7 seconds, the limited range considered by Giampieri and Dougherty [2004], can resolve the major discrepancy between periods determined from Saturn’s radio emissions. [4] Giampieri and Dougherty [2004] also performed an analysis of magnetic field observations obtained by the P11 Vector Helium magnetometer (VHM), V1, and V2, without regard to the significant differences in the accuracy of measurement afforded by these missions. The P11 VHM observations cannot be used to improve upon the Z3 magnetic field model deduced from the combined Voyager magnetometer observations [Connerney et al., 1982a] for two reasons. First, P11 was a spinning spacecraft and knowledge of the spacecraft attitude was rather poorly known at the time of the Saturn encounter. In fact, a rather large error (1.4 degrees) in the attitude of the P11 spacecraft was discovered and characterized by comparison of the P11 VHM observations with the field calculated using the Z3 magnetic field model [Connerney et al., 1984a]. This roll attitude error was subsequently independently confirmed by analysis of the imaging photopolarimeter observations (see notes added in proof to Connerney et al. [1984b] by L. Davis Jr. and L. R. Doose, Davis and Smith [1985], and Connerney et al. [1985]). One can hardly claim that the P11 VHM observations are independent measurements once they have been corrected by comparison to the Connerney et al. Z3 model magnetic field. It is not clear from Giampieri and Dougherty’s discussion which P11 magnetometer observations they used among the many possibilities: those corrected by direct comparison to the Z3 model, those adjusted by the subsequent use of corrected photopolarimeter limb observations, or those adjusted by allowing the roll attitude of P11 as a free parameter, minimized along with the magnetic field parameters. In any case the accuracy of these roll-corrected observations is unknown. [5] Second, after adjusting for the P11 roll attitude error, the remaining differences between the P11 VHM observations and the Z3 model are everywhere less than the stated instrument accuracy of 1% [Smith et al., 1980] and even less than the discontinuous step error (0.5%) associated with the instrument range changes [Connerney et al., 1984a]. Figure 4 of Connerney et al. [1984a] shows this very clearly. Therefore, these data cannot be used to improve our knowledge of Saturn’s magnetic field; the measurements are consistent with the Z3 model to well within the accuracy of measurement. By attempting to further reduce the RMS residuals of the P11 VHM observations, Giampieri and Dougherty [2004] merely fit the remaining instrument error and range changing artifacts to spherical harmonic expansions. [6] In order to identify the rotation phase of Saturn and hence obtain a rotation rate, Giampieri and Dougherty [2004] must demonstrate that they measure significant non-axisymmetric magnetic field components. However, their statistical analysis of the uncertainty associated with model parameters they derive is flawed. Their ‘‘formal error’’ appearing in their Table 2 is not an appropriate estimate of parameter uncertainty if the residuals are correlated. The model residuals are indeed highly correlated and dominated by either unmodeled external fields (in the case of V1 and V2) or instrument range changing and residual attitude errors (P11). The other, larger estimate of model parameter uncertainty (sigma) appearing in their Table 2 only shows how much each individual internal field parameter changes upon changing the assumed rotation period by 2.4 seconds. This ignores the co variability of model GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L02201, doi:10.1029/2004GL021398, 2005