  This paper explores the sensitivity of line profiles of H2D+, HCO+ and N2H+,
observed towards the center of L1544, to various kinematic and chemical
parameters. The total width of the H2D+ line can be matched by a static model
and by models invoking ambipolar diffusion and gravitational collapse. The
derived turbulent line width is b=0.15 km/s for the static case and <~ 0.05
km/s for the collapse case. However, line profiles of HC18O+ and N2H+ rule out
the static solution. The double-peaked H2D+ line shape requires either infall
speeds in the center that are much higher than predicted by ambipolar diffusion
models, or a shell-type distribution of H2D+, as is the case for HCO+ and N2H+.
At an offset of ~20 arcsec from the dust peak, the H2D+ abundance drops by a
factor of ~5.
