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Abstract. Terrestrial ecliptic dayside observations of the exospheric Lyman-α column intensity between 3–15 Earth radii (RE) by UVIS/HDAC (UVIS – ultraviolet imaging spectrograph; HDAC – hydrogen-deuterium absorptioncell) Lyman-α photometer at CASSINI have been analyzed to derive the neutral exospheric H-density profile at the Earth's ecliptic dayside in this radial range. The data were measured during CASSINI's swing-by maneuver at the Earth on 18 August 1999 and are published by Werner et al. (2004). In this study the dayside HDAC Lyman-α observations published by Werner et al. (2004) are compared to calculated Lyman-α intensities based on the 3D H-density model derived from TWINS (Two Wide-angle Imaging Neutral-atom Spectrometers) Lyman-α observations between 2008–2010 (Zoennchen et al., 2015). It was found that both Lyman-α profiles show a very similar radial dependence in particular between 3–8 RE. Between 3.0–5.5 RE impact distance Lyman-α observations of both TWINS and UVIS/HDAC exist at the ecliptic dayside. In this overlapping region the cross-calibration of the HDAC profile against the calculated TWINS profile was done, assuming that the exosphere there was similar for both due to comparable space weather conditions. As a result of the cross-calibration the conversion factor between counts per second and rayleigh, fc=3.285 counts s−1 R−1, is determined for these HDAC observations. Using this factor the radial H-density profile for the Earth's ecliptic dayside was derived from the UVIS/HDAC observations, which constrained the neutral H density there at 10 RE to a value of 35 cm−3. Furthermore, a faster radial H-density decrease was found at distances above 8 RE (≈r-3) compared to the lower distances of 3–7 RE (≈r-2.37). This increased loss of neutral H above 8 RE might indicate a higher rate of H ionization in the vicinity of the magnetopause at 9–11 RE (near subsolar point) and beyond, because of increasing charge exchange interactions of exospheric H atoms with solar wind ions outside the magnetosphere. 

Abstract Interstellar neutrals (ISNs), pick-up ions (PUIs), and energetic neutral atoms (ENAs) are fundamental constituents of the heliosphere and its interaction with the neighboring interstellar medium. Here, we focus on selected aspects of present-day theory and modeling of these particles. In the last decades, progress in the understanding of the role of PUIs and ENAs for the global heliosphere and its interaction with very local interstellar medium is impressive and still growing. The increasing number of measurements allows for verification and continuing development of the theories and model attempts. We present an overview of various model descriptions of the heliosphere and the processes throughout it including the kinetic, fluid, and hybrid solutions. We also discuss topics in which interplay between theory, models, and interpretation of measurements reveals the complexity of the heliosphere and its understanding. They include model-based interpretation of the ISN, PUI, and ENA measurements conducted from the Earth’s vicinity. In addition, we describe selected processes beyond the Earth’s orbit up to the heliosphere boundary regions, where PUIs significantly contribute to the complex system of the global heliosphere and its interaction with the VLISM.