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**Session 63 - Stars and A Radio Source.**

*Oral session, Tuesday, January 14*

*Harbour C, *

## [63.01] Luminosity Functions of Planetary Nebulae

*S. Kwok, M. Tremblay (University of Calgary)*
New planetary nebulae luminosity functions (PNLF) have been constructed
with improved core mass and age grids.
Four Schoenberner tracks with central star masses of 0.565, 0.6, 0.644 and
0.835 M_ødot are used to generate normalized curves of luminosity versus
time and effective temperature versus time.
The normalized functions are found to be remarkably similar, giving us
confidence that more evolutionary tracks can be derived by interpolation.
Seven tracks
were generated using this method for the following core masses: 0.6, 0.62,
0.63, 0.64, 0.65, 0.66 and 0.68 M_ødot.

The nebular expansion is modeled by the momentum conserving equation of the
interacting stellar winds model. The OIII luminosity is calculated at
each time interval using the
CLOUDY photoionization code. The resulting time evolution of the OIII flux,
for each central star mass, is used to generate the PNLF. The OIII flux is
given at 100 points between 0 and 40,000 years, and is monitored at shorter
intervals near the peak. The flux between successive data points is
determined by linear interpolation.

To generate the luminosity function, 100,000 nebulae are selected randomly in
age from 0 to 40,000 years, with a core mass chosen according to one of the
following distributions:

a. Gaussian core mass distribution:
PNLF were generated using gaussian distributions with mean masses of 0.60,
0.61, 0.62, and 0.63 M_ødot and a standard deviation of 0.02 M_ødot.

b. Initial-Final mass distribution:
Points are selected randomly in initial mass from 1.25 to 9 M_ødot,
subject to the initial mass function. The final
mass is calculated using the initial-final mass relationship of Bryan et
al. (1990, ApJ, 365, 301).

The PNLFs generated are compared with the observed
M31 data. While the PNLFs
based on the gaussian core mass distribution are similar
to those obtained by Jacoby (1989, ApJ, 339, 39), those generated with
realistic initial mass--final mass relationship predict
an excess of bright PNe unless there is an upper core
mass cutoff of 0.7 M_ødot. The possible relationship between the upper
core mass limit
and the Hubble type and metallicity of the galaxy remains to be investigated.

**Program
listing for Tuesday**