Authors: Erick Powell (Boston University), Merav Opher (Boston University), Marc Kornbleuth (Boston University)

Neutral hydrogen in the hydrogen wall (beyond the heliopause) and heliosheath absorb wavelengths of light near Ly α from nearby stars. Heliospheric models are essential to understand these observations since the observations are an indirect method of probing the heliosphere. Opher et al. (2015) suggested that the solar magnetic field can collimate the solar wind plasma, resulting in a heliosphere with a split tail with two separated lobes. In the Moscow model confinement is seen due to the solar magnetic field but the two lobes are embedded within a long tail (Izmodenov & Alexashov 2015, 2020). The two models are similar in the nose region in both neutral hydrogen and plasma.   Here I will present the current state of Lyα heliospheric modeling and future work that will be done to investigate any potential observable differences between heliosphere models. While Wood et al. (2014) and others similar projects have previously modeled Ly α absorption from the kinetic-MHD Moscow models, no study has yet been conducted with respect to the BU model which will be essential for a direct observational comparison between these models. The standard approach to modeling Ly α with kinetic-MHD heliosphere models has been using the moments of the neutral distribution functions, assuming a locally Maxwellian hydrogen distribution, to approximate the column density of neutral hydrogen. It has been shown that due to the large mean free path of hydrogen, the distribution of hydrogen is not Maxwellian which is the motivation for the kinetic treatment of neutrals (Izmodenov et al. 2000, Izmodenov et al. 2001). Here I will describe the kinetic approach to modeling the column density I will be implementing for the BU model in the future.