Modulation of neutral interstellar He, Ne, O in the heliosphere. Survival probabilities and abundances at IBEX

Direct sampling of neutral interstellar (NIS) atoms by the Interstellar Boundary Explorer (IBEX) can potentially provide a complementary method for studying element abundances in the Local Interstellar Cloud and processes in the heliosphere interface.}{We set the stage for abundance-aimed in-depth analysis of measurements of NIS He, Ne, and O by IBEX and determine systematic differences between abundances derived from various calculation methods and their uncertainties.}{Using a model of ionization rates of the NIS species in the heliosphere, based on independent measurements of the solar wind and solar EUV radiation, we develop a time-dependent method of calculating the survival probabilities of NIS atoms from the termination shock (TS) of the solar wind to IBEX. With them, we calculate densities of these species along the Earth's orbit and simulate the fluxes of NIS species as observed by IBEX. We study pairwise ratios of survival probabilities, densities and fluxes of NIS species at IBEX to calculate correction factors for inferring the abundances at TS.}{The analytic method to calculate the survival probabilities gives acceptable results only for He and Ne during low solar activity. For the remaining portions of the solar cycle, and at all times for O, a fully time dependent model should be used. Electron impact ionization is surprisingly important for NIS O. Interpreting the IBEX observations using the time dependent model yields the LIC Ne/O abundance of $0.16\pm40%$. The uncertainty is mostly due to uncertainties in the ionization rates and in the NIS gas flow vector.}{The Ne/He, O/He and Ne/O ratios for survival probabilities, local densities, and fluxes scaled to TS systematically differ and thus an analysis based only on survival probabilities or densities is not recommended, except the Ne/O abundance for observations at low solar activity.