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Astron. Astrophys. 358, 1058-1068 (2000)

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1. Introduction

The expansion velocity of a planetary nebula (PN) is the single most important parameter determining its evolution. Surprisingly, it is only known for about 300 PNe, mostly bright objects in the Galactic disk. The nebular expansion after the PN ejection occurs in conjunction with the increase in stellar temperature. While the nebular radius and its expansion velocity define the nebular dynamical age, the position of the central star in the HR diagram defines a post-mass-loss stellar age. If correctly determined, both ages should be equal. However, the two time scales correlate very poorly: the dynamical ages are on average much shorter than the stellar ages (e.g. Pottasch 1984 p.234). Possible reasons are that the distances are poorly known, leaving both the radius and luminosity uncertain, and that the expansion velocity may vary both with position in the nebula and with time.

Expansion velocities are known to vary. The [NII ] expansion velocity is almost always larger than that in [OIII ] (Wilson 1950), indicating internal velocity fields for which a single velocity may be a poor representation (Gesicki et al. 1996, 1998; resp. Paper I and II). Marten & Schönberner (1991), and recently Schönberner & Steffen (1999, 2000) present hydrodynamical calculations for an evolving PN. Their models always show velocity increasing with radius. This acceleration must be taken into account when deriving dynamical ages.

In this paper we will present the first expansion velocities for PNe in the Bulge, for which the distance is approximately known. Photo-ionization models are used to derive internal velocity fields, showing how the expansion velocity varies with radius. We calculate the original pre-PN outflow velocity, to estimate the effects of the acceleration over time. In this way, more robust dynamical ages can be derived.

Stellar time scales are very sensitive to the core mass (and therefore luminosity) of the star, with lower-mass stars evolving much slower. Even for objects at reasonably known distance, the PN luminosity cannot be determined to the required accuracy. The white dwarf mass distribution is quite narrow (e.g. Weidemann 1987), and as a result the full range of stellar luminosities is only about a factor of two. The uncertainties are of the same order, because of the need to convert from a nebular emission line flux to a stellar radiation field. We will show that the problem can be inverted: by requiring the new dynamical ages and stellar ages to be the same, the position in the HR diagram can be derived without using the uncertain luminosity. This will allow us to determine core masses for the central stars. Recently the masses of central stars of PNe were discussed by Gorny et al. (1997) and Stasinska et al. (1997) and we will compare their results with ours.

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© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000