1 Introduction

The interplanetary Lyman $\alpha$ glow was first observed in the late 1960s and identified as an interplanetary emission in the early 1970s (Thomas & Krassa 1971; Bertaux & Blamont 1971). The study of the spatial distribution of the hydrogen atoms which are the source of this UV glow in the interplanetary medium has led to various interesting results. The early studies on the interplanetary glow are reviewed by Ajello et al. (1987).

In 2002, there are at least five UV photometers or spectrometers in the interplanetary medium that can study the interplanetary Lyman $\alpha$ glow. The oldest is UVS on Voyager 1 launched in 1977 (Broadfoot et al. 1977). At its present position, more than 80 AU from the Sun, UVS/Voyager 1 gives an unprecedented view of the interplantary glow in the outer heliosphere. SWAN on SOHO was designed to study the interplanetary glow and its variations with solar cycle. Its was launched in December 1995 (Bertaux et al. 1995). Other spectrometers were designed to study planetary atmospheres but are also able to study the interplanetary UV emissions. UVS on Galileo was launched in the early 1990s and is still operating (Hord et al. 1992). UVS on NOZOMI (Fukunishi et al. 1999) has also studied the interplanetary glow. Finally, high resolution line profile measurements of the interplanetary Lyman $\alpha$ emission have been performed by GHRS on HST (Clarke et al. 1998).

Costa et al. (1999), using the SWAN/SOHO hydrogen cell data, have found that the temperature of the interplanetary hydrogen at large distances from the sun (say 50 AU) is significantly larger than the value estimated for the gas in the Local Interstellar Medium. Moreover, the bulk velocity inferred from their study is around 20 or 21 km s^-1 at 50 AU, which is lower than the 26 km s^-1 relative velocity between the Sun and the Local Interstellar Gas. It has been suggested that these results prove that the interstellar hydrogen atoms are heated and decelerated when crossing the region that constitutes the boundary, or interface, between the expanding solar wind and the ionized component of the interstellar gas. Because of coupling processes through charge exchange between protons and hydrogen atoms, the hydrogen atom velocity distribution is actually modified when crossing the region of the heliospheric interface.

Modeling this interface is a very difficult task. It is even more complex when effects of proton-neutral hydrogen coupling are taken into account. Baranov & Malama (1993) first published hydrogen distributions deduced from a self-consistent computation of the plasma-neutral atoms coupling at the heliospheric interface. These authors showed that the hydrogen distribution is significantly different from the simple results of the hot model (Thomas 1978; Lallement et al. 1985) which assumes a simple Gaussian distribution of the gas in the outer heliosphere. More recently, Izmodenov et al. (1999) have studied in detail the results of interstellar hydrogen filtration at the heliospheric interface in the frame work of the two-shock model developed by Baranov & Malama (1993).

The hydrogen distribution in the inner heliosphere is mainly influenced by ionization processes from the Sun. However, effects of the interface imprinted on the distribution at large distances from the Sun will remain because of the very large mean free path of the hydrogen atoms in the interplanetary medium.

Studying the interplanetary glow data requires one to model the scattering process of the Lyman $\alpha$ photons in the interplanetary medium. The scattering of a single photon can be accurately described by the Angle Dependent Partial Frequency Redistribution (ADPFR) function which relates the energy of the incoming and outgoing photons with the velocity of the scatterer and the scattering angle. A model based on a Monte Carlo scheme to represent this function for large numbers of photons was developed by Quémerais (2000) and applied to hydrogen velocity distributions derived from hot model calculations, i.e. without heliospheric interface effects. These calculations allowed then to derive line shifts and line widths of the interplanetary glow which is impossible in the case of the simpler hypothesis of Complete Frequency Redistribution (CFR).

In this paper, we present the results of ADPFR radiative transfer computations including hydrogen velocity distributions derived from the two-shock heliospheric interface model.

After reviewing the most significant aspects of the modeling, we present the results obtained for an observer at 1 AU from the Sun. An obvious application concerns the data of the Lyman $\alpha$photometer on-board SOHO (Bertaux et al. 1995).

The aim of this work is to characterize the differences between Hot Model and Heliospheric Interface model results and their possible application to existing data sets.

In future works, the results presented here will be tested on actual spectral measurements of the interplanetary background obtained by the STIS/HST instrument. Hydrogen cell measurements of the SWAN/SOHO instrument (Quémerais et al. 1999) will also be used.