Cy. Zhang et S. Kwok, TRACE OF PLANETARY-NEBULA EVOLUTION BY DISTANCE-INDEPENDENT PARAMETERS, The Astrophysical journal. Supplement series, 88(1), 1993, pp. 137-167
Using existing infrared and radio data on a sample of 432 planetary ne
bulae, we have derived a number of distance-independent parameters for
comparison with evolutionary models of planetary nebulae. We find tha
t many of the observed properties of planetary nebulae can be explaine
d by current central star evolutionary models, even if the time scales
are subject to significant change by a factor of up to an order of ma
gnitude. Specifically, we find that the evolutionary tracks are well s
eparated in the radio surface brightness-central star temperature plan
e, therefore allowing us to determine the core mass of individual plan
etary nebulae. We also obtain the luminosity and gravity of the centra
l stars of individual nebulae, from their temperature and core mass, w
ithout relying on the distance assumptions. We find our results of the
core mass are in good agreement with those of Mendez, Kudritzki, & He
rrero and Tylenda et al. A systematic, large discrepancy is found betw
een the luminosity found in this work and that found by Gathier & Pott
asch.