Optimization of Saturn paraboloid magnetospheric field model parameters using Cassini equatorial magnetic field data

The paraboloid model of Saturn's magnetosphere describes the magnetic field as being due to the sum of contributions from the internal field of the planet, the ring current, and the tail current, all contained by surface currents inside a magnetopause boundary which is taken to be a paraboloid of revolution about the planet-Sun line. The parameters of the model have previously been determined by comparison with data from a few passes through Saturn's magnetosphere in compressed and expanded states, depending on the prevailing dynamic pressure of the solar wind. Here we significantly expand such comparisons through examination of Cassini magnetic field data from 18 near-equatorial passes that span wide ranges of local time, focusing on modelling the co-latitudinal field component that defines the magnetic flux passing through the equatorial plane. For 12 of these passes, spanning pre-dawn, via noon, to post-midnight, the spacecraft crossed the magnetopause during the pass, thus allowing an estimate of the concurrent subsolar radial distance of the magnetopause R1 to be made, considered to be the primary parameter defining the scale size of the system. The best-fit model parameters from these passes are then employed to determine how the parameters vary with R1, using least-squares linear fits, thus providing predictive model parameters for any value of R1 within the range. We show that the fits obtained using the linear approximation parameters are of the same order as those for the individually selected parameters. We also show that the magnetic flux mapping to the tail lobes in these models is generally in good accord with observations of the location of the open-closed field line boundary in Saturn's ionosphere, and the related position of the auroral oval. We then investigate the field data on six passes through the nightside magnetosphere, for which the spacecraft did not cross the magnetopause, such that in this case we compare the observations with three linear approximation models representative of compressed, intermediate, and expanded states. Reasonable agreement is found in these cases for models representing intermediate or expanded states.