The statistical relation between Zanstra temperatures and emission-line ratios

Abstract

A knowledge of the H I and He II Zanstra temperatures T Z (He II) and T Z (H I), and the Zanstra temperature ratio TR = T Z (He II)/T Z (H I) is of interest in evaluating the properties of planetary nebula (PNe) shells and their central stars. These parameters are only known for a small proportion of PNe however, and are very difficult to assess for more distant sources. It would therefore be of use if T Z (He II) and TR could be assessed using line ratios alone. It has been suggested that Stoy temperatures T STOY are related to the line ratios [O III]λ5007/Hβ and [Ne III]λ3868/Hβ, whilst Zanstra temperatures depend upon the level of nebular excitation. It has also been noted that TR may be correlated with [O II]λ3727/Hβ, He IIλ4686/Hβ and [N II]λ6548/Hα. It is therefore possible that line ratios may help to determine T Z (He II) and TR where normal procedures are inapplicable, albeit with lower levels of precision than is normally the case. We have, in the following, undertaken an investigation of the statistical relation between Zanstra temperatures and line ratios. This is used to evaluate the levels of precision to which TR and T Z (He II) can be determined using emission-line ratios alone. We find that the expected correlation between [O III]/Hβ and T Z (He II) is not borne out in the present analysis. It is also found that neither [N II]/Hα nor [O II]/Hδ is of use in defining the Zanstra temperature ratio TR. On the other hand, it is found that T Z (He II) can be determined using He IIλ4686/Hβ and a variety of other more complex line ratios, providing that log[T Z (He II)] < 5.2. The level of precision is of order σ{log[T Z (He II)]} ≅ 0.074 → 0.1. Similarly, ratios He IIλ4686/Hβ and He IIλ4686/He Iλ4471 can be used to determine TR to an accuracy of ∼0.25, providing that T Z (He II) < 8 × 10 4 K. It is noted that this latter parameter may permit estimates of shell Lyman continuum optical depth τ LyC , although the relation between TR and τ LyC is more complicated than has previously been supposed. All of these relations apply for metallicities similar to those encountered in the Galactic disc. They may not, however, be applicable where metallicities vary strongly from this, such as is the case in certain other extragalactic systems.