  We use newly developed 3D kinetic MHD models of the heliosphere to predict
heliospheric H I Lyman-alpha absorption for various lines of sight. These
predictions are compared with actual Lyman-alpha spectra from the Hubble Space
Telescope, many of which have yielded previous detections of heliospheric
absorption. We find that the absorption predicted by the models is weakly
affected by both the magnitude and orientation of the assumed ISM magnetic
field. Models with B=1.25-2.5 micro-Gauss and an angle of alpha=15-45 deg with
respect to the upwind direction of the ISM flow generally provide the best fits
to the data, but the sensitivity of the Lyman-alpha absorption to many model
input parameters makes it difficult to fully characterize the region of
parameter space allowed by the data. We also use the models to assess the
degree to which heliospheric asymmetries induced by the ISM field should be
apparent in Lyman-alpha absorption. An ISM field that is skewed with respect to
the ISM flow vector results in substantial azimuthal asymmetries in both the
hydrogen wall and heliosheath, but only the heliosheath asymmetries yield
potentially detectable asymmetries in Lyman-alpha absorption; and then only in
downwind directions, where comparison with the data is complicated by few
actual absorption detections and an insufficient model grid extent.
