Electron Temperatures and Electron Densities in Planetary Nebulae

Abstract

Electron temperatures T_e and electron densities N_e are estimated from a study of the relative intensities of the forbidden lines in the following nebulae: NGC 7027, 2440, 7662, 6572, IC 418 and Orion. For certain ions (N II, O III, O II and S II) it is possible to measure the relative intensities of two multiplets originating from different metastable terms. Each intensity ratio gives a relation between T_e and N_e. A further relation may be obtained if it is assumed that N₁(O I)/N₁(N I)=N₁(O II)/N₁(N II), where N₁(X) is the number of ions X in the ground state per cm₃. Recently calculated electron excitation cross-sections enable these various relations to be obtained in numerical form. The observed relative intensities of the forbidden lines are corrected for absorption and systematic calibration errors by comparing observed and theoretical relative intensities in the hydrogen spectrum. Simultaneous solutions for T_e and N_e are then obtained from the forbidden line intensity ratios. The values of T_e range from $$1\cdot 3\times{10}^{4}\,\text{to}\,2\cdot 0\times{10}^{4}$$deg. K, and the values of N_e from $$8\times{10}^{3}\,\text{to}\,5\times{10}^{4}$$ per cm₃. The consistency of the various $${T}_{e},\,{N}_{e}$$ relations is particularly satisfactory for NGC 7027, NGC 2440 and IC 418; for the other objects considered the observed intensities tend to be either less reliable or less complete. With the exception of IC 418, the densities obtained from the forbidden lines are greater than those obtained from the surface brightness by a factor of order 3. These differences are probably a consequence of the densities being non-uniform. The surface brightness method gives essentially a r.m.s. density for the total geometrical volume, while the forbidden line methods give average densities for the active emitting regions (clouds and filaments). Such differences would not be expected for IC 488, which is particularly uniform. In a final section the abundance ratios N(O)/N(N) are estimated to be 1·6, 0·43 and 2·0 for NGC 7027, NGC 2440 and IC 418 respectively. It is concluded that the results reveal a real difference in composition between NGC 2440 and the other two objects.