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Fig. 3

image

Correction factors Fshell and Frim, defined according to Eq. (8), as function of the respective (line-of-sight) Doppler expansions: the shell’s post-shock velocity Vpost (top panel) and the rim’s bulk expansion velocity Vrim (bottom panel). The crosses indicate the empirically determined F values for individual objects, where their error bars are derived from the sums of the relative error squares of the trigonometric and expansion distances. The thick dotted lines are the theoretical expectations from hydrodynamical models, namely a constant value of 1.25 for the shell and an average from the model curves in Fig. 5 of SBJ for the rim. The weakly dotted horizontal lines highlight unity. Evolution is always from low to high velocities (see text for details). The correction factor of NGC 3132 is not plotted here because this particular nebula is the most evolved of the whole sample and is in its recombination or reionisation phase, which is not covered by the hydrodynamical models employed for the determination of the correction factors.

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