Table 2: Expansion time scales from proper-motion measurements. The data are either from Palen et al. (2002), optical measurements, or from the compilation of Terzian (1997), radio measurements. The angular radii, $\theta _{\rm rim}$ , and their expansion rate, $\dot{\theta}_{\rm rim}$ , refer to the semi-minor axes. The effective temperatures are spectroscopic values (Méndez 1992) or He II Zanstra temperatures (Gorny, priv. comm.)

Object $T_{\rm eff}$ $\theta _{\rm rim}$ $\dot{\theta}_{\rm rim}$ $\hspace{3mm}\theta_{\rm rim}/\dot{\theta}_{\rm rim}$ comment reference

[K] [mas] [mas yr^-1] [yr]

IC 2448 65 000 4500 $2.25\pm0.6$ $2000\pm\ \ 600$ optical Palen et al. (2002)

NGC 6578 67 000 3360 $1.60\pm0.4$ $2100\pm\ \ 600$ optical Palen et al. (2002)

NGC 6884 87 000 2280 $1.14\pm0.3$ $2000\pm\ \ 600$ optical Palen et al. (2002)

NGC 3242 75 000 8800 $13.2\pm4.7$ $700\pm\ \ 300$ radio Hajian et al. (1995)

NGC 7662 100 000 6200 $5.6\pm 5.0$ $1100\pm1000$ radio Hajian & Terzian (1996)

NGC 7027 200 000 4000 $4.7\pm1.0$ $900\pm\ \ 200$ radio Hajian et al. (1993), Masson (1989)

**Table 2:** Expansion time scales from proper-motion measurements. The data are either from Palen et al. (2002), optical measurements, or from the compilation of Terzian (1997), radio measurements. The angular radii, $\theta _{\rm rim}$ , and their expansion rate, $\dot{\theta}_{\rm rim}$ , refer to the semi-minor axes. The effective temperatures are spectroscopic values (Méndez 1992) or He II Zanstra temperatures (Gorny, priv. comm.)
Object	$T_{\rm eff}$	$\theta _{\rm rim}$	$\dot{\theta}_{\rm rim}$	$\hspace{3mm}\theta_{\rm rim}/\dot{\theta}_{\rm rim}$	comment	reference
	[K]	[mas]	[mas yr^-1]	[yr]
IC 2448	65 000	4500	$2.25\pm0.6$	$2000\pm\ \ 600$	optical	Palen et al. (2002)
NGC 6578	67 000	3360	$1.60\pm0.4$	$2100\pm\ \ 600$	optical	Palen et al. (2002)
NGC 6884	87 000	2280	$1.14\pm0.3$	$2000\pm\ \ 600$	optical	Palen et al. (2002)
NGC 3242	75 000	8800	$13.2\pm4.7$	$700\pm\ \ 300$	radio	Hajian et al. (1995)
NGC 7662	100 000	6200	$5.6\pm 5.0$	$1100\pm1000$	radio	Hajian & Terzian (1996)
NGC 7027	200 000	4000	$4.7\pm1.0$	$900\pm\ \ 200$	radio	Hajian et al. (1993), Masson (1989)

Source LaTeX | All tables | In the text

	1 Introduction
	2 The hydrodynamical model
	3 The models in comparison with observations
	4 The expansion parallaxes
	5 Summary and discussion
	References
	Online Material
	Appendix A:Hydrodynamical PNe sequence with a 0.696 M $_{\odot }$ central-star