An analytical model of interstellar gas in the heliosphere tailored to interstellar boundary explorer observations

The stationary distribution of interstellar neutral gas in the heliosphere subject to solar gravity, solar radiation pressure, photoionization, and charge exchange is investigated analytically assuming ionization rates and radiation pressure that are proportional to R ^-2, where R is the heliocentric radius. The collisionless hyperbolic trajectories of the individual atoms including ionization losses are combined with Liouville's Theorem to construct the heliospheric phase-space distribution function of an interstellar gas species in the solar reference frame under the assumption that the distribution is a drifting Maxwellian at large distances from the Sun. The distribution is transformed to the Earth (essentially Interstellar Boundary Explorer (IBEX)) frame as a function of solar longitude. The expression is then tailored to the latitudinal scan of IBEX as a function of longitude using the fact that IBEX detects each atom close to perihelion in its hyperbolic orbit. The distribution is further adapted to IBEX by integrating the differential intensity over the entrance aperture solid angle of the IBEX-Lo collimator, and over energy to predict the IBEX count rate of helium. The major features of the predicted count rate are described, including a peak in longitude, a peak in latitude at each longitude, and the widths of the major peak in both latitude and longitude. Analytical formulae for these features are derived for comparison with IBEX observations in order to determine the temperature and bulk velocity of the gas in interstellar space. Based in part on these formulae, the results for helium are presented in the companion paper by Möbius et al.