Analysis of Stellar Occultation Data. Ii. Inversion, with Application to Pluto and Triton

We present a method for obtaining atmospheric temperature, pressure, and number density profiles for small bodies through inversion of light curves recorded during stellar occultations. This method avoids the assumption that the atmospheric scale height is small compared with the radius of the body, and it includes the variation of gravitational acceleration with radius. First we derive the integral equations for temperature, scale height, pressure, number density, refractivity, and radius in terms of the light-curve flux. These are then cast into summation form suitable for numerical evaluation. Equations for the errors in these quantities caused by Gaussian noise in the occultation light curve are also derived. The method allows for an arbitrary atmospheric boundary condition above the inversion region, and one particular boundary condition is implemented through least-squares fitting. When the inversion equations are applied to noiseless test data for a simulated isothermal atmosphere, numerical errors in the calculated temperature profile are less than 5 parts in 104. Nonisothermal test cases are also presented. We explore the effects of (1) the boundary condition, (2) data averaging (in the time, observer-plane, and body-plane domains), (3) systematic errors in the zero stellar flux level, and (4) light-curve noise on the accuracy of the inversion results. A criterion is presented for deciding whether inversion would be an appropriate analysis for a given stellar occultation light curve, and limitations to the radial resolution of the inversion results are discussed. The inversion method is then employed on the light curves for the 1988 June 9 occultation by Pluto observed with the Kuiper Airborne Observatory and the 1997 November 4 occultation by Triton observed with the Hubble Space Telescope. Under the (possibly incorrect) assumption that no extinction effects are present in the occultation light curve, the Pluto inversion yields a 110 K isothermal profile down to approximately 1215 km radius, at which point a strong thermal gradient, 3.9 0.6 K km 1, abruptly appears, reaching 93 K at the end of the inversion. The Triton inversion yields a differently shaped profile, which has an upper level thermal gradient, 0.4 K km 1, followed by a 51 K isothermal profile at lower altitudes. The Triton inversion shows wavelike temperature variations in the lower atmosphere, with amplitudes of 1 K and wavelengths of 20 km, that could be caused by horizontal or vertical atmospheric waves.