Earth and Planetary Science Letters 304 (2011) 22–28 Contents lists available at ScienceDirect Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl Saturn's very axisymmetric magnetic field: No detectable secular variation or tilt Hao Cao a,⁎, Christopher T. Russell a, Ulrich R. Christensen b, Michele K. Dougherty c, Marcia E. Burton d a UCLA Institute of Geophysics and Planetary Physics, Los Angeles, CA 90095, USA b Max Planck Institute for Solar System Research, Max-Planck-Strasse 2, 37191 Katlenburg-Lindau, Germany c Blackett Laboratory, Imperial College London, SW72AZ, UK d Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA article info abstract Article history: Saturn is the only planet in the solar system whose observed magnetic field is highly axisymmetric. At least a Accepted 20 February 2011 small deviation from perfect symmetry is required for a dynamo-generated magnetic field. Analyzing more Available online 5 March 2011 than six years of magnetometer data obtained by Cassini close to the planet, we show that Saturn's observed field is much more axisymmetric than previously thought. We invert the magnetometer observations that Editor by: T. Spohn were obtained in the “current-free” inner magnetosphere for an internal model, varying the assumed unknown rotation rate of Saturn's deep interior. No unambiguous non-axially symmetric magnetic moment is Keywords: Saturn detected, with a new upper bound on the dipole tilt of 0.06°. An axisymmetric internal model with Schmidt- magnetic dynamo normalized spherical harmonic coefficients g10=21,191±24 nT, g20=1586±7 nT. g30=2374 ±47 nT is interior structure derived from these measurements, the upper bounds on the axial degree 4 and 5 terms are 720 nT and 3200 nT respectively. The secular variation for the last 30 years is within the probable error of each term from degree 1 to 3, and the upper bounds are an order of magnitude smaller than in similar terrestrial terms for degrees 1 and 2. Differentially rotating conducting stable layers above Saturn's dynamo region have been proposed to symmetrize the magnetic field (Stevenson, 1982). The new upper bound on the dipole tilt implies that this stable layer must have a thickness LN=4000 km, and this thickness is consistent with our weak secular variation observations. © 2011 Elsevier B.V. All rights reserved. 1. Introduction gravitational and atmospheric data (Anderson and Schubert, 2007; Read et al., 2009). Secular variation of the terrestrial magnetic field The tilt of the magnetic dipole with respect to the rotation axis for has been widely studied (Bloxham and Gubbins, 1985; Jackson et al., solar system planets other than Saturn varies from values of five 2000) as a useful tool to investigate the fluid motion in the Earth's degrees or less at Mercury (Anderson et al., 2010), to roughly ten outer core. One of the most well defined features is the dipole moment degrees at Earth and Jupiter, and to up to 60° at Uranus (Russell and currently changing about 5% per 100 years (Barton, 1989). At the Dougherty, 2010). A tilted dipole magnetic field enables a very outer planets, constraints have been placed on the Jovian magnetic sensitive measurement of the rotation rate of the dynamo region deep field (Connerney and Acuna, 1982; Yu et al., 2010). For Saturn, direct in the interior of a planet. At Earth, the variation in the rotation rate of measurements of the magnetic field were made by Pioneer 11 in 1979, the dipole at a period of 60 years has detected the torsional oscillation Voyager 1 and 2 in 1980 and 1981 respectively. Several axisymmetric of the core and its correlation with the length of the day (Roberts et al., magnetic field models were proposed from these observations 2007). At Jupiter it has been used to make measurements to (Connerney et al., 1982; Davis and Smith, 1990). In this paper we millisecond accuracy of the System III rotation rate (Yu and Russell, show that there is no unambiguous non-axisymmetric intrinsic 2009). In contrast, at Saturn the signal that was originally thought to magnetic moment which would allow us to determine the rotation be due to a rotating internal field was found to be changing (Galopeau rate of Saturn's interior. The dipole tilt must be less than 0.06°. No and Lecacheux, 2000), and hence due to exterior, not interior sources. secular variation in the quarter century from the Pioneer 11 to the This so-called SKR period is hence analogous to the Jupiter System IV Cassini observations is detected exceeding the probable errors in the period (Sandel and Dessler, 1988) and the rotation period of the inversions. interior of Saturn remains unknown, except for estimates based on 2. Cassini observation and data selection Since the Saturn orbit insertion of Cassini on 30 June 2004 ⁎ Corresponding author at: 595 Charles E. Young Dr. East 6862 Slichter Hall Los Angeles, CA 90095, USA. Tel.: +1 310 825 4321; fax: +1 310 206 8042. (Dougherty et al., 2005), the magnetometer onboard made continu- E-mail address: [email protected] (H. Cao). ous measurements of Saturn's magnetic field over a wide range of 0012-821X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2011.02.035 H. Cao et al. / Earth and Planetary Science Letters 304 (2011) 22–28 23 1000 0 [nT] r -1000 B -2000 1000 [nT] θ 0 10 [nT] B 0 φ B -10 0 2000 4000 6000 8000 Pseudo Time Fig. 1. Cassini's magnetometer measurements of three magnetic field components inside L=3.8 Rs from Rev 003 to Rev 126. The azimuthal component is clearly almost two orders of magnitude smaller than the radial and meridional components. “Pseudo Time” here is the sequential count of the measurements used in the analysis, a small fraction of the total data obtained by the magnetometer. latitude and planetocentric distance. In particular, revolutions 6, 28, 3. Inversion technique and an axisymmetric model 46, 53, 68–78, 116, 125, 126 achieved both high inclinations and low periapsis altitudes. These passes together with the lower inclination To deal with outliers in the data, a robust fitting procedure using passes provide an excellent data set in order to examine both the tilt iteratively reweighted least squares linear regression (Holland and of the dipole (or any non-axially symmetric magnetic moment) and Welsch, 1977) is applied to all inversions in this analysis. The weights the rotation rate of the planet. Fig. 1 shows the three magnetic field at each iteration are calculated by applying a Cauchy weighting components from Cassini's magnetometer measurements inside fi dipole L-shell=3.8 Rs (dipole L-shell here is the magnetic eld lines Table 1 of a spin-axisymmetric dipole field which intersect the equatorial Trajectory information of the 37 Cassini orbits adopted in this analysis, the first column plane at distance L, 1 Rs=60,268 km as the IAU standard definition of shows the revolution number of each orbit, the second and third columns show the the Saturn equatorial radius) from Rev 3 (February 2005) to Rev 126 start time and end time of each orbit, the fourth column shows the periapsis distance. (February 2010) in KRTP, spherical polar Saturn centered coordinates Rev Start time End time Periapsis distance with K signifying Kronian, and R, T and P signifying the radial, (UT) (UT) (Rs) meridional and azimuthal directions. The measurements adopted in 003 2005-Feb-01 04:00:00 2005-Feb-27 06:54:59 3.50 this study are regarded to be current-free since they avoid the current 004 2005-Feb-27 06:55:00 2005-Mar-19 16:54:59 3.50 generated by the Enceladus interaction with the rotating magneto- 005 2005-Mar-19 16:55:00 2005-Apr-06 23:29:59 3.51 006 2005-Apr-06 23:30:00 2005-Apr-23 23:59:59 2.60 spheric plasma near the dipole L-shell=3.95 Rs (Jia et al., 2010). The 007 2005-Apr-24 00:00:00 2005-May-12 05:23:59 3.59 azimuthal component is almost two orders of magnitude smaller than 008 2005-May-12 05:24:00 2005-May-30 08:15:59 3.60 the radial and meridional components, as one would expect if the field 009 2005-May-30 08:16:00 2005-Jun-17 13:09:59 3.59 were nearly axisymmetric. Table 1 shows the start time, end time, and 012 2005-Jul-24 07:24:00 2005-Aug-11 08:51:59 3.61 periapsis distance for each orbit used in this analysis ordered by 013 2005-Aug-11 08:52:00 2005-Aug-28 11:53:59 3.59 014 2005-Aug-28 11:54:00 2005-Sep-14 16:45:59 2.88 revolution number. Fig. 2 shows the spatial coverage of these orbits 015 2005-Sep-14 16:46:00 2005-Oct-02 23:59:59 3.00 inside L-shell=3.8 Rs. The upper panel shows the latitude versus 016 2005-Oct-03 00:00:00 2005-Oct-21 00:00:00 3.00 radial distance, which is unaffected by any uncertainty in our 028 2006-Aug-28 19:14:01 2006-Sep-17 17:19:00 2.96 knowledge of the rotation rate of the planet. The lower panel shows 045 2007-May-19 05:19:01 2007-Jun-04 06:04:00 3.24 046 2007-Jun-04 06:04:01 2007-Jun-20 06:20:00 2.75 the latitude versus longitude. The longitude is calculated by assuming 047 2007-Jun-20 06:20:01 2007-Jul-09 08:59:00 2.46 the rotation period is 10h33m00s, which lies between two values 053 2007-Nov-25 11:25:01 2007-Dec-11 12:11:00 2.54 suggested by Anderson and Schubert (2007) and Read et al.