THE ANALYTICAL STRUCTURE OF THE PRIMARY INTERSTELLAR HELIUM DISTRIBUTION FUNCTION IN THE HELIOSPHERE

A new analytical model based on the previous work of Lee et al. is presented for the distribution of interstellar helium in the heliosphere. The model is tailored for comparison with the IBEX-Lo observations in order to determine the bulk velocity and temperature of helium in the local interstellar cloud. The model includes solar gravity, spherically symmetric stationary ionization rates, transformation to the Earth/IBEX frame of reference, the IBEX viewing geometry with small spin-axis tilt, and integration of the atom differential intensity over energy and the instrument collimator solid angle. The analysis employs an expansion of the count rate about the peak of the velocity distribution to second order in the magnitudes of several small quantities: the ratio of the helium thermal speed to its bulk speed, the angle between the bulk velocity and the ecliptic, the two angles describing the tilt of the IBEX spin-axis away from Sun-pointing, the collimator angular width, and the angular difference between the observing longitude and the longitude where the projection of the bulk velocity onto the ecliptic is tangential to Earth's orbit. The model reveals the evolving ellipsoidal shape of the helium distribution as it moves along its average hyperbolic orbit. For specified interstellar parameters, the model predicts the latitudinal and longitudinal structure of the helium distribution. The model is in reasonable agreement with IBEX observations and the predictions of the other available models