Determination of interstellar helium parameters from the ULYSSES-NEUTRALGAS experiment: Method of data analysis

The GAS instrument on board the ULYSSES spacecraft has, for the first time, measured directly the interstellar flux of helium atoms in the inner solar system. From the locally measured angular distribution of the flux, the task is to derive the five parameters of the Maxwellian distribution function: density, bulk velocity vector, and temperature describing the state of the interstellar helium outside of the heliosphere, ''at infinity''. To accomplish this, a new method for the data analysis has been developed that employs Tarantola's approach. In the inverse problem considered a solution is found by optimizing (minimizing) the sum of squared residuals between the measured counts and the count numbers derived from a computer simulation. The mathematical formulation of this method is described in detail. The method proved to be reliable and robust in that it always finds a solution. In two extreme, but still typical cases of actual measurements the power but also the Limitations of the method are demonstrated. The solution obtained can either be unique, e.g. for measurements taken in the helium cone at 1.5 AU, or belongs, in cases of larger heliocentric distances and outside of the cone, to a one-dimensional family of equally acceptable helium parameters. To obtain a unique solution in the latter, ill-determined problem, further information is required, which can be achieved by combining measurements that are taken during sufficiently different conditions, e.g. downwind or crosswind with respect to the helium flow (comparable to the tomography problem). Three different approaches to this problem have been investigated. The confidence factor of a solution is estimated by a standard X(2) test and the error bars are determined from the covariance matrix. Also, the dependence of the solutions on systematic errors in a number of input parameters, such as background level, ionization rate, spacecraft attitude and efficiency function of the detector is studied.