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.

History and background

Starting with the time of Edwin Hubble, the brightest stars have been employed as extragalactic distance indicators. However, it was not until the early 1960s that planetary nebula (PNe) were recognized as being some of the “brightest stars” and consequently useful as extragalactic distance indicators. During the early stages of their evolution, a planetary nebula's luminosity is on par with their asymptotic giant branch (AGB) ancestors. Even though most of their continuum emission emerges in the far-ultraviolet, rather than the optical or near infrared, their detectability is not hampered. In fact, since most of the central star's flux is emitted at energies below 13.6 eV, the photoionization physics ensures that their energy is transformed into a series of optical, infrared, and near-UV emission lines. Fortuitously, approximately 10% of the flux emitted by a young PNe is in the one emission line of doubly-ionized oxygen at 5007 °A. Therefore, for the purposes of cosmology, a PNe may be thought of a cosmic machine that turns continuum emission into monochromatic flux.

However, only in the late 1970s was the initial PNe derived distance estimate computed. The first study of the PNLF was conducted in 1989. Ironically, the technique was first applied to galaxies outside our Local Group before being applied to it. The reason for this odd order of adoption is due to the fact that any one PNe is not a standard candle and that distance estimates to individual PNe within our own galaxy are very inaccurate, an error factor of 2 being average. However, by way of sampling a large number of PNe, one may apply the PNLF to produce accurate distance estimates to galaxies. Because PNe are found in all galaxies, the PNLF is unique in that it may be utilized to estimate distances to all large galaxies within the Local Supercluster independent of their environment and Hubble type.

Procedure

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 Milkyway 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 Milkyway, 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.

References

• Ciardullo, Robin (January 2003), "Distances from Planetary Nebulae", eprint arXiv:astro-ph/0301279{{citation}}: CS1 maint: date and year (link)
• Ciardullo, Robin (July 2004), "The Planetary Nebula Luminosity Function", eprint arXiv:astro-ph/0407290{{citation}}: CS1 maint: date and year (link)
• Ferrarese, Laura; Ford, Holland C.; Huchra, John; Kennicutt, Robert C., Jr.; Mould, Jeremy R.; Sakai, Shoko; Freedman, Wendy L.; Stetson, Peter B.; Madore, Barry F.; Gibson, Brad K.; Graham, John A.; Hughes, Shaun M.; Illingworth, Garth D.; Kelson, Daniel D.; Macri, Lucas; Sebo, Kim; Silbermann, N. A. (2000), "A Database of Cepheid Distance Moduli and Tip of the Red Giant Branch, Globular Cluster Luminosity Function, Planetary Nebula Luminosity Function, and Surface Brightness Fluctuation Data Useful for Distance Determinations", The Astrophysical Journal Supplement Series, 128 (2): 431–459{{citation}}: CS1 maint: multiple names: authors list (link)
• Jacoby, George H. (April 1 1989), "Planetary nebulae as standard candles. I - Evolutionary models", Astrophysical Journal, Part 1 (ISSN 0004-637X), 339: 39–52 {{citation}}: Check date values in: |date= (help)CS1 maint: date and year (link)
• Schoenberner, D.; Jacob, R.; Steffen, M.; Sandin, C. (August 2007), "The evolution of planetary nebulae IV. On the physics of the luminosity function", eprint arXiv:0708.4292{{citation}}: CS1 maint: date and year (link)