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Fig. A.1


Top: correction factors and vs. peak-separation velocities as derived from our 1D radiation-hydrodynamics nebular model sequences with 0.605 (left) and 0.625 M (right) central stars. Evolution is from lower to higher velocities and back. The correction factor F (left) is a continuation beyond maximum stellar temperature of that shown in Fig. 5 for the 0.605 M sequence. We present the F evolution for two different treatments of the radiation transport: “on the spot” (orange, o.t.s.) and “outward only” (red, o.o.). The circles indicate the phases in which the recombination front is located well inside the outer region of the rim. The right panel shows a different correction factor, , not used before, which is spanning the evolutionary period of the 0.625 M sequence immediately prior to maximum temperature (see text for more details). The arrows in both panels indicate the models used in the surface-brightness columns below, and the horizontal dashed lines highlighten the factor range 1.4 ± 0.3. Note the different ordinates of both panels. Bottom: columns of normalized surface brightness distributions of [O iii], [N ii], and Hα (symbols) along the minor axes for NGC 3132, NGC 6565, and NGC 6886 compared to those predicted from selected models taken from our hyrodynamics simulations at the positions M1, ..., M4 from the top panels. The models’ surface brightnesses are scaled to the individual angular sizes of the nebulae. The models at M1 and M2 are about 11 000 yers old, have a stellar luminosity of about 230 L and are well within the reionisation stage after the end of recombination. The two models M3 and M4 used for NGC 6886 are 330 years apart: temperature and luminosity change within this time span from about 168 000 K and 4300 L to about 179 000 K and 2400 L. The dashed parts of the [N ii] intensity profile seen in the younger (M4) model depict the contribution of the innermost halo region upstream the outer nebular shock where still some N+ has survived. In [O iii], we see the contributions of shell (outer peaks) and rim (inner peaks), in [N ii] only the (recombining) shell. In the older model, the shell is nearly absent in [O iii] but not in [N ii] nor in Hα (outer shoulders only).

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