Planetary nebula luminosity function
Planetary nebula luminosity function (PNLF) is a secondary distance indicator used in astronomy. It makes use of the [O III] λ5007 forbidden line found in all planetary nebula which are members of the old stellar populations (Population II). It works well for both spiral and elliptical galaxies despite their completely different stellar populations and is part of the Extragalactic Distance Scale.
To estimate the distance to a galaxy using the PNLF one must first locate point sources within the galaxy that are visible at λ5007 but not when the entire spectrum is considered. These points are candidate PNe, however, there are three other types of objects that would also exhibit such an emission line that must be filtered out: HII regions, supernova remnants, and Lyα galaxies. After the PNe are determined, to estimate a distance one must measure their monochromatic [O III] λ5007 fluxes. With this one then has a statistical sample of PNe. One then fits the observed luminosity function to some standard law.
Finally, one must estimate the foreground interstellar extinction. There are two sources of this, from within the Milky Way and internal extinction of the target galaxy. The first is well known and can be taken from sources such as reddening maps computed from H I measurements and galaxy counts or from IRAS and DIRBE satellite experiments. The later, only occurs in target galaxies which are either late type spiral or irregular. However, this extinction is difficult to measure. In the Milky Way, the scale height of PNe is much bigger than that of the dust. Observational data and models support that this holds true for other galaxies, that the bright edge of the PNLF is primarily due to PNe in front of the dust layer. The data and models support a less than 0.05 magnitude internal extinction of a galaxy's PNe.
Physics behind process
The PNLF method is unbiased by metallicity. This is because oxygen is a primary nebular coolant; any drop in its concentration raises the plasma’s electron temperature and raises the amount of collisional excitations per ion. This compensates for having a smaller number of emitting ions in the PNe. Consequently, a reduction in oxygen density only lowers the emergent [O III] λ5007 emission line flux by approximately the square root of the difference in abundance. At the same time, the PNe’s core responds to metallicity the opposite way. In the case where the metallicity of the progenitor star is smaller, then the PNe’s central star will be a bit more massive and its emergent ultraviolet flux will be a bit larger. This added energy almost precisely accounts for the decreased emissions of the PNe. Consequently, the total [O III] λ5007 flux that is produced by a PNe is practically uncorrelated to metallicity. This beneficial negation is in agreement with more precise models of PNe evolution. Only in extremely metal-poor PNe does the brightness of the PNLF cutoff dim by more than a small percentage.
The relative independence of the PNLF cutoff with respect to population age is harder to understand. The [O III] 5007 flux of a PNe directly correlates to the brightness of its central star. Further, the brightness of its central star directly correlates to its mass. In a PNe, the central star's mass directly varies in relation to its progenitor's mass. However, by observation, it is demonstrated that reduced brightness does not happen.
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