A planetary nebula is a shell of ionized gas around a hot central star, formed as an average-mass star sheds its outer atmosphere and dies. Planetary nebulae have a relatively short life span of about 20,000 years a fraction of a stars life time. Surrounding gases are exposed to the core of the star causing them to glow and reach temperatures of 100,000° C. Eventually the star becomes a ‘white dwarf’ then shrinks and fades. Planetary nebulae both expand and fade as they grow older. Planetary nebulae have shapes such as spherical, elliptical and bi-polar forms. The spectrum of planetary nebulae consists mostly of the emission line of hydrogen, helium, oxygen, nitrogen and neon. Planetary nebulae are valuable tools to astronomers. Astronomers are able to learn how the nuclear processes in older stars produce elements like carbon and nitrogen. They help astronomers better understand how chemical elements are recycled back into the galaxy to produce the gas and dust that form new stars. By observation astronomers can understand these processes but in order to do this they need to find a way to accurately measure their distances.
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The problem with accurately measuring planetary nebulae distance’s to Earth is that they are remote and a census cannot be generated without accurate measurements of the distances. Planetary nebulae vary greatly in both luminosity and distance. Techniques such as trigonometric parallax are not accurate because planetary nebulae including those in our Milky Way are too far away. Planetary nebulae do decrease in surface brightness (flux per unit area) as they expand (radius increase). (Frew, Parker and Bojicic, 8). Typical statistical distance scales have very large uncertainties especially for large planetary nebulae.
Planetary nebulae are important for measuring distance of cosmic bodies because they are found in all Hubble types. They are useful for a distance range comparable to Cepheid. Planetary nebulae use simple and accurate photometric methods so background noise can be removed. They can be observed at only one epoch and relatively immune to metallicity variations. They are derived from a population insensitive to internal reddening. Some of the limitations to use planetary nebulae as distance indicators are that “for late type galaxies there is potentially serious confusion with compact HII regions, and background noise from large scale diffused emission can not be suppressed using the narrow-band filter technique. Also, planetary nebulae are secondary indicators requiring an extragalactic zero point calibration. (Jacoby and Clardullo, 54) Some of the statistical scales used to measure the distance of planetary nebulae have included the luminosity function or PNFL, the extinction method and the radial expansion method.
The method of distance determination based on planetary nebulae luminosity function (PNLF) is almost 20 years old and has become established as one of the most reliable ways of getting distances to elliptical galaxies out to about 20 Mpc. Planetary nebulae can be identified by comparing two CCD images: one taken through a narrow “on band” filter centered at the red shifted wavelength of the λ5007 nebular emission line, and another taken through an “off band” filter at a nearby wave length. The planetary nebulae which are unresolved point sources at typical extragalactic distance are detected by blinking the on-band vs. the off-band images. The limiting distance for this method may be 50 MPc for an 8-m telescope. The distance obtained from the planetary nebulae luminosity function (PNFL) is compared with the distances from surface brightness fluctuation (SBF) method and with Cepheid distances. Both PNFL and SBF distances agree with Cepheid distance much better than they agree with each other. Looking only at comparisons with Cepheid it would seem the PNFL distances are good to only about ± 0.3 mag, (Mendez, 101)
Another method used is determining a planetary nebulae distance is the extinction method. This method investigates the ultra violet spectrum of the central star. Interstellar extinction causes a characteristic absorption near 200Å. From the strength of the absorption the extinction can be found. The extinction can also be measured from a comparison of the observed ratio of strength of certain nebular emission lines with the theoretically expected ratio. The relationship between interstellar extinction and distance in the direction combined with the observed magnitude, this leads to the distance of the star. Because the interstellar material is distributed vary irregularly throughout the galaxy extinction distance relation can differ strongly for different direction. In order to determine a reliable relation it is therefore necessary to use stars that are as close as possible to the line of sight of the planetary nebulae. This means that mainly planetary nebula plane can be studied. Distance relations for directions outside the galactic plane can only be determined for the first few hundred parsecs. (Gathue, Kapteyn, 21)
The radial expansion method uses the relationship between the mass and radius of the planetary nebula. The whole process suggests that ionized mass increases proportionally to the radius of the planetary nebula. The derived electron densities from forbidden line intensity ratios for a number of galactic planetary nebulae measurements are used to establish an empirical mass-radius relation that can be used to determine distances. This relation is justified by comparing its results with a simple theoretical model of the central stars. Unfortunately the MA values do not fit except for small distances and there are some discrepancies for a given planetary nebula but the general trend seems to work, but in some case the ionized luminosity stars are unrealistically large unless the ionized radius is very small. Although the mass-radius relation is assumed to valid within a relatively large size interval the distance to the largest object are probably less reliable. (Maciel and Pottasch 1-5)
While these three methods seem useful to measure planetary nebulae distances, the newest method developed by three astronomers from the University of Hong Kong, Dr. David Frew, Professor Quentin Parker and Dr. Ivan Bojicic developed a method for measuring more accurate distances between “planetary nebulae” and Earth. Their solution based on the Hɑ S-r relation is both simple and elegant. It is only necessary to use three parameters to be measured for each planetary nebula, the size of the object taken from the latest high resolution surveys; an accurate measurement of how bright the object is in the red hydrogen-alpha emission line and the amount of dimming toward the nebula by making an estimate of interstellar reddening. From these values the Hɑ surface brightness can be calculated from which the true radius of the nebula can be estimated. Combining this number with the angular size of the nebula allows its distance to be determined by trigonometry. The method is briefly explained in the abstract by one of the creators “The SHɑ-r technique is simple in its application, requiring only an angular size, an integrated Hɑ flux, and the reddening of the PN. From these quantities, an intrinsic radius is calculated, which when combined with the angular size, yield the distance directly. Further we have found the optical thick PNe tend to populate the upper bound of the trend, while optically thin PNe fall along the lower boundary in the SHɑ-r plane. This enables sub-trends to be developed which offer even better precision in the determination of distances, as good as 18 per cent in the case of optical thin, high-excitation PNe. This is significantly better than any previous statistical indicator” (Frew, Parker, Bojicic, 1)
This is not the first statistical distance scale developed, but it is the first to measure brightness in the hydrogen-alpha (Hɑ) emission. This method uses the best quality input data obtained to date. Unlike radio methods that fluxes for the very largest and faintest planetary nebulae, using hydrogen-alpha can be measured since very large planetary nebula are the most common, measuring distances is then critical. This method has been heavily calibrated; nearly 300 galactic planetary nebulae have distance based on more than one primary method. For these planetary nebulae, a weighted average distance has been calculated based on the quoted uncertainties of each individual distance determination. For consistency, individual distances were combined with each method first. These were combined with distances from other primary methods weighted by inverse variance to determine the final weighted distance.
Dw = ∑i=1nwiDi∑i=1nwi
Where D1D2, ….Dnare the individual distance estimates, with associated weights w1w2, ….wn determined from the inverse variances, wi = 1δi2. The uncertainty of the weighted mean distance was calculated as
δDw = V1V12-V2∑i=1nwiFi-Fw20.5
where V1=∑i=1nwi and V2=∑i=1nwi2
Finally for each calibrator the linear radius was determined from the angular distance. (Frew, Parker, Bojicic, 4.2) This approach, because it uses both the surface brightness and radius provides distance calculations with less uncertainty the previous statistical scales, “The overall impression of the hydrogen alpha relation is a well-behaved linear trend with a shallower gradient for small radii. “The resulting so-called ‘surface brightness- radius relation’ has been robustly calibrated using more than 300 planetary nebulae, whose accurate distances have been determined via independent and reliable means.” (Asian Science, 2)
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The weakness of the hydrogen alpha method like all statistical scales and astronomy in general are the large amounts of uncertainty due to all of the theoretical unknowns involved, results can only be based on what can be seen and what is already known. The strength of the Hɑ-Sr method is its simplicity. It uses only three parameters for each planetary nebula: the size of the object, an accurate measurement of how bright the object is in the red hydrogen-alpha emission line and an estimate of the objects interstellar reddening. This method has been robustly calibrated using more than 300 planetary nebulae whose accurate distances have been determined independently. The extensive calibration and use of the surface brightness-radius relation has made this statistical scale a method for finding planetary nebulae distances than those used previously.
As in any field of astronomy there are always new developments and theories being worked on all of the time. This is also true in the field of using planetary nebulae as distant indicators. While the Hɑ=Sr method has improved on discovering and cataloguing the distances of more then 300 planetary nebulae there are always new and exciting things in development. The Gaia telescope launched by the European Space Agency in 2003 is currently making direct distance measurements in the Milky Way including planetary nebulae. Not all planetary nebulae can be measured this way so the Hɑ-Sr technique will be used for many years to come. “This means SHɑ- r relation of F08 has been independently validated by Jacob et al. (2013), Ali et al. (2015) and Smith (2015) as the most reliable statistical distance scale given in literature to date.” (Frew, Parker, Bojicic, 8) In follow-up papers a further catalogue will include the distances for planetary nebulae that new data is currently being collected for, including objects discovered only recently.
- Asian Scientist Newsroom, and Wildtype Media Group. “Just How Far Away Are Planetary Nebulae?” Asian Scientist Magazine | Science, Technology and Medical News Updates from Asia, 22 Apr. 2016, www.asianscientist.com/2016/04/in-the-lab/estimate-distances-planetary-nebulae/.
- Frew, et al. “Hα Surface Brightness–Radius Relation: a Robust Statistical Distance Indicator for Planetary Nebulae.” OUP Academic, Oxford University Press, 17 Nov. 2015, academic.oup.com/mnras/article/455/2/1459/1100544.
- Gathier, R. “Distances to Planetary Nebulae.” Kapteyn Astronomical Institute, Gronongen, The Netherlands, 1983.
- Jacoby, Gerorge H, and Robin Ciardullo. “Planetary Nebulae as Distance Indicators.” The Extragalactic Distance Scale; Proceedings of the ASP 100th Anniversary Symposium, Victoria, Canada, June 29-July 1, 1988 (A90-14129 03-90). San Francisco, CA, Astronomical Society of the Pacific, 1988, p. 42-56; Discussion, p. 57, 58., 1988.
- Maciel, W J, and S R Pottasch. “Distance of Planetary Nebulae.” Kapteyn Astronomical Institute, Postbus 800, NL-9700 AV Groningen, The Netherlands, 1979.
- Mendez, Roberto H. “Distance From the Planetary Nebulae Luminosity Function.” Post-Hipparcos Cosmic Candles / Edited by A. Heck and F. Caputo. Dordrecht ; Boston : Kluwer Academic Publishers, 1999. (Astrophysics and Space Science Library ; v. 237), P.161.
- “New Method to Estimate More Accurate Distances between Planetary Nebulae and the Earth.” ScienceDaily, ScienceDaily, 11 Apr. 2016, www.sciencedaily.com/releases/2016/04/160411112240.htm.
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