Basics of abundance determinations in ionized nebulae

These are methods in which no check is made for the consistency of the derived abundances with the observed properties of the nebulae. They can be schematically subdivided into direct methods and statistical methods. 

Stasiriska Abundances In H II Regions And Planetary Nebulae 3.1.1. Direct methods 

The abundance ratio of two ions is obtained from the observed intensity ratio of lines emitted by these ions. For example, O 1 1 /111 can be derived from 

Te can be derived using the ratio of the two lines [O III] A4363 and [O III] A5007, which have very different excitation potentials. Other line ratios can also be used as temperature indicators in nebulae, such as [N ii] A5755/6584 and [S III] A6312/9532. The Balmer and Paschen jumps, the radio continuum and radio recombination lines also allow to estimate the electron temperature, but the measurements are more difficult. 

Plasma diagnostic diagrams combining all the information from temperature- and density-sensitive line ratios can also be constructed for a given nebula (e.g. Aller Czyzak 1983), plotting for each pair of diagnostic lines the curve in the (Te,n) plane that corresponds to the observed value. The curves usually do not intersect in one point, due to measurement errors and to the fact that the nebula is not homogeneous (and also to possible uncertainties in the atomic data) and provide a visual estimate of the uncertainty in the adopted values of Te and n. 

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