  The boundary conditions of the heliosphere are set by the ionization, density
and composition of inflowing interstellar matter. Constraining the properties
of the Local Interstellar Cloud (LIC) at the heliosphere requires radiative
transfer ionization models. We model the background interstellar radiation
field using observed stellar FUV and EUV emission and the diffuse soft X-ray
background. We also model the emission from the boundary between the LIC and
the hot Local Bubble (LB) plasma, assuming that the cloud is evaporating
because of thermal conduction. We create a grid of models covering a plausible
range of LIC and LB properties, and use the modeled radiation field as input to
radiative transfer/thermal equilibrium calculations using the Cloudy code. Data
from in situ observations of He^O, pickup ions and anomalous cosmic rays in the
heliosphere, and absorption line measurements towards epsilon CMa were used to
constrain the input parameters. A restricted range of assumed LIC HI column
densities and LB plasma temperatures produce models that match all the
observational constraints. The relative weakness of the constraints on N(HI)
and T_h contrast with the narrow limits predicted for the H^O and electron
density in the LIC at the Sun, n(H^0) = 0.19 - 0.20 cm^-3, and n(e) = 0.07 +/-
0.01 cm^-3. Derived abundances are mostly typical for low density gas, with
sub-solar Mg, Si and Fe, possibly subsolar O and N, and S about solar; however
C is supersolar. The interstellar gas at the Sun is warm, low density, and
partially ionized, with n(H) = 0.23 - 0.27 cm^-3, T = 6300 K, X(H^+) ~ 0.2, and
X(He^+) ~ 0.4. These results appear to be robust since acceptable models are
found for substantially different input radiation fields. Our results favor low
values for the reference solar abundances for the LIC composition.

Astrophysics