Velocity profiles of ground state lines of H _ { 2 } D ^ { + } , HC ^ { 18 } O ^ { + } and N _ { 2 } H ^ { + } , 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 H _ { 2 } D ^ { + } line is double-peaked like that of the other ions , but previous models that fit the HC ^ { 18 } O ^ { + } and N _ { 2 } H ^ { + } profiles are found not to fit the H _ { 2 } D ^ { + } data .
Matching the H _ { 2 } D ^ { + } 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 C ^ { 18 } O emission indicates a chemical age of { { } _ { < } \atop { { } ^ { \sim } } } 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 H _ { 2 } D ^ { + } profile is affected by absorption in the outer layers of the core , if gas motions in these layers are sufficiently small .