Models for magnetospheric mass density and average ion mass including radial dependence

Analytical models for magnetospheric mass density, ρ m, and average ion mass, M, were created from a database of ρ m and electron density, n e, values from six spacecraft missions by making use of the Eureqa nonlinear genetic regression algorithm. All values of ρ m were determined from Alfvén frequencies, and the values of n e were determined from plasma wave or spacecraft potential data. Models of varying complexity are listed. The most complex models appearing in this paper are capable of modeling ρ m within a factor of 1.81, and M within a factor of 1.34 if n e is used as an input parameter, or within a factor of 1.45 if n e is not used. The most important parameters for modeling ρ m are L, the solar EUV index F10.7, magnetic local time, MLT, the geomagnetic activity index Kp, and the solar wind dynamic pressure, Pdyn. The very simplest model for M depends on Kp. In more complex models for M including n e, the most important parameters are n e with L, F10.7, and Pdyn or Kp. In more complex models for M not including n e, the most important parameters are Kp, MLT, F10.7, L, and the auroral electrojet index, AE. Explanations for most of the dependencies are given. We also demonstrate the danger of calculating spatial dependence without taking account of different conditions sampled in different regions. Here we avoid that problem by using multivariant models.