A modified Chapman function for the polar regions of oblate planet ionospheres

Abstract

The goal of this paper is to derive expressions for the modified Chapman function Che for the north and south polar regions of an oblate planet. Formulas for Che in an oblate planet atmosphere for high, middle and lower latitudes (including the equator) were derived in our previous investigation [Adv. Space Res. 27 (11) (2001) 1895]. For this purpose the classic ionosphere theory for a spherical planet was used as introduced by Chapman. The modified Chapman function for a rotational ellipsoid depends on the solar zenith angle χ, altitude h, latitude ϕ and the solar declination δ. Due to the complex geometry of an oblate planet, represented as an ellipsoid of revolution with the polar axis as the rotation axis, the polar latitudes ϕ=±90° appear as more specific cases. This paper presents the results of our work on the modified Chapman function Che for the poles of oblate planetary bodies. These results show the necessity of introducing Che in numerical analyses of the ionospheres of Jupiter, Saturn, Uranus and Neptune. For example, on Saturn (the most oblate planet), the vertical profile of the relative electron production rate clearly deviates from the “normal” profile calculated with the standard Chapman function Ch for spherical planet. At larger zenith angles ( χ=100°) this deviation reaches a factor of five in the ionization rate maxima and increases with solar zenith distance χ. These profiles pertain at the pole for h=2150 km above the level of the ammonia clouds, where one of the ionospheric peaks of Saturn has been observed from spacecraft radio occultation. A table for Che for the ionosphere of Saturn is presented. This table is calculated for different altitudes and solar zenith angles χ=45°, 60°, 75°, 80°, 83°, 85°, 87°, 90°, 93°, 95°, 97° and 100°. The function Che for the giant planets has a dependence on the scale height, unlike the standard Ch function. That is why Che tables must be calculated for each planet separately.