Diagnostics for the rarefied plasmas in gaseous nebulae are reviewed, beginning with the pioneering papers of V. A. Ambartsumian. These papers, as well as the diagnostic techniques which have been developed on the basis of ideas contained in them, are discussed. Diagnostic techniques for homogeneous, as well as inhomogeneous, plasmas are described.Keywords: planetary nebulae: interstellar medium; plasma diagnostics nuclei of planetary nebulae. At present, the number of observed planetary nebulae in our galaxy is approaching two thousand. Many planetary nebulae have also been found in other galaxies, including spiral (M31, M33, etc.) as well as irregular and elliptical galaxies.The spectra of gaseous nebulae differ significantly from those of stars. They consist of a weak continuum spectrum and a large number of intense emission lines, of which the lines of hydrogen and ionized and neutral helium dominate in the visible range. However, the brightest lines in the spectra of nebulae, with wavelengths λ5007 Å and λ4959 Å were not identified for a long time, since they did not show up in the spectra of elements studied in earthbound laboratories. For this reason they were assumed to belong to an unknown element, nebulium. They were thus denoted by N 1 and N 2 (the nebulium 1 and nebulium 2 lines).The nature of the nebular emission in these lines was understood only after the development of quantum mechanics. In 1928 the American astrophysicist Bowen showed [1] that the N 1 and N 2 lines are forbidden lines of the O 2+ ion and are transitions from metastable levels of this ion. He also showed that the bright 3729 3726 + λ Å doublet in the spectra of nebulae is associated with forbidden transitions of singly ionized oxygen O + . This discovery was an indication of the low density of both matter and radiation in nebulae.
V. A. Ambartsumian's papers on gaseous nebulaeAmbartsumian's papers on the spectra of planetary and diffuse nebulae (all are collected in Volume 1 of his Scientific Papers [4]) were published in the 1930's. This was a time when theoretical astrophysics was being founded and research on gaseous nebulae was at its frontier.His first paper in this area [5] is devoted to determining the temperature of the nuclei of planetary nebulae.He proposed an original method for determining the temperature based on comparing the energy β H E emitted by the nebula in the Hβ line to the energy 4686 λ E emitted in the HeII λ4686 line. Here it is assumed that all the UV photons emitted by the central star of the nebula, and capable of ionizing hydrogen atoms and helium ions, are absorbed in the nebula. This method, known as Ambartsumian's method, yielded realistic estimates of the temperatures of the central stars that are close to their modern values.