The evolution of planetary nebulae. VIII. True expansion rates and visibility times

TL;DR

This study uses radiation-hydrodynamics modeling to determine the true expansion velocities of planetary nebulae, revealing they expand nearly twice as fast as previously thought, which impacts estimates of their visibility times and death rates.

Contribution

It provides the first direct estimate of true PN expansion velocities using modeling, leading to revised visibility times and death-rate densities.

Findings

Mean true expansion velocity is 42 km/s.

Visibility time to reach 0.9 pc is about 21,000 years.

Higher expansion rate affects population and death rate estimates.

Abstract

The visibility time of planetary nebulae (PNe) in stellar systems is an essential quantity for estimating the size of a PN population in the context of general population studies. For instance, it enters directly into the PN death rate determination. The basic ingredient for determining visibility times is the typical nebular expansion velocity, as a suited average over all PN sizes of a PN population within a certain volume or stellar system. The true expansion speed of the outer nebular edge of a PN is, however, not accessible by spectroscopy -- a difficulty that we surmount by radiation-hydrodynamics modelling. We find a mean true expansion velocity of 42 km/s, i.e. nearly twice as high as the commonly adopted value to date. Accordingly, the time for a PN to expand to a radius of, say 0.9 pc, is only 21000 +/- 5000 years. This visibility time of a PN holds for all central star masses since a nebula does not become extinct as the central star fades. There is, however, a dependence on metallicity in the sense that the visibility time becomes shorter for lower nebular metal content. With the higher expansion rate of PNe derived here we determined their local death-rate density as (1.4 +/- 0.5) x E-12 PN pc^{-3} yr^{-1}, using the local PN density advocated by Frew (2008).