  Velocity profiles of ground state lines of H2D+, HC18O+ and N2H+, observed
previously with the CSO and IRAM 30m telescopes, are modeled with a Monte Carlo
radiative transfer program to study the temperature, density and velocity
structure of the pre-stellar core LDN 1544. The H2D+ line is double-peaked like
that of the other ions, but previous models that fit the HC18O+ and N2H+
profiles are found not to fit the H2D+ data. Matching the H2D+ observations
requires at least three modifications to the model at small radii: (1) the
density profile must continue to rise inward and not flatten off toward the
center; (2) the gas temperature must be nearly constant and not drop inwards
significantly; (3) the infall velocity must increase inward, in a fashion
intermediate between `quasi-static' (ambipolar diffusion) and `fully dynamic'
(Larson-Penston) collapse. The C18O emission indicates a chemical age of <~0.1
Myr. The effects of a flattened structure and rotation on the line profiles are
shown to be unimportant, at least on the scales probed by single-dish
telescopes. Alternatively, the H2D+ profile is affected by absorption in the
outer layers of the core, if gas motions in these layers are sufficiently
small.
