Plasma Analysis of the Spectrum of an Emission Nebula
Joachim Köppen Kiel/Strasbourg/Illkirch March 98
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Interstellar gas is most conspicous when ionized by a hot star in the neighbourhood, such as in a H II region, planetary nebulae, the nuclei of active galaxies, and quasars. This plasma - at temperatures around 10000 K - produces a spectrum with strong emission lines of recombination lines of hydrogen and helium, and lines of heavy elements (C, N, O, Ne, S, Ar, Cl, ...) excited by collisions with the electrons. The nebula is optically thin in almost all these lines, the processes of line excitation are well known and the atomic data is quite accurate. Therefore, one can reliably analyse the spectra and derive the chemical composition in the gas.
A simple, but rather good method if one has a rich and high quality spectrum is the technique of Plasma Diagnostics. One assumes that the whole emitting region can be treated as a isothermal and homogeneous volume of gas having the same degree ionization everywhere. In the Plasma Applet we perform such kind of analysis. It proceeds in the following steps:
First, one determines the extinction due to the intervening interstaller gas and dust by comparing the observed Balmer decrement - in our case the intensity ratio of Halfa and Hbeta lines - with the theoretical value which is almost independent of the physical state of the gas. Then, all intensities are corrected using the standard interstellar extinction law.
The intensity ratios of certain collisionally excited lines, such as [O III] 5007 and 4363 Å and [N II] 6584 and 5755 Å , are strongly dependent on the temperature of the gas, and therefore useful to measure this temperature. Since [N II] comes from a lower ionization zone as [O III], the two values need not be the same in a real nebula. As all collisionally excited lines are quite sensitive to the temperature - of the colliding electrons - taking into account this difference in the analysis improves the results. In the applet the [N II] temperature (if available) is used for the ions O II, N II, S II, S III, the [O III] temperature is taken for all other (higher) ions.
The intensity ratios of other collisionally excited lines, [S II] 6731 and 6717 Å are sensitive to the density of the electrons, but only in the range 100 to 100000 particles per cubic cm, and somewhat to the temperature. If the line ratio is too low or too high, the density is taken as the limiting value in the useful range. However, results near these limits must be taken with great caution, especially the high density limit, because the intensity of e.g. the [N II] lines decreases strongly with increasing density, and the derived abundances would be rather uncertain.
Both density and temperature diagnostics are done by comparing the observed line ratios with those computed with ionic models having 5 and 6 energy level. Since there is some mutual influence between the outcome of all four steps, the whole diagnostics is repeated 5 times which is well enough to obtain all parameters within less than 1 percent.
If no values could be derived, the applets adopts "reasonable" guesses of c=0 for extinction, 10000 K for temperature, and 1000 particles per cubic cm for density.
With the derived temperatures and density, the intensities of all observed lines - normalized to Hbeta - are evaluated to get the abundances of the ions relative to the protons (viz. hydrogen). Since not all ions of all elements are observable in the spectrum, one has to correct for the unseen stages of ionization. This is done with ionization correction factors which are based on the fact that ions with similar ionization potential are found with the same fraction. In the applet, the standard ICFs (e.g. L.H.Aller's Astrophysics of Thermal Nebulae) are used. We make these assumptions:
Note that these recipes are not accurate formulae and may not be valid for all levels of excitation of the nebula....
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