Relative o II Intensities in Gaseous Nebulae.

The intensity ratio r = I(3729)/I(3726) tends to a value r(∞) at high densities determined by radiative transition probabilities and a value r(0) at low densities determined by collision strengths, proportional to collision cross-sections. This ratio has been measured in nebulae for which these two limiting values should be approached. The transition probability calculations are discussed; the best-calculated value of r(∞) obtained is 0.43. From observations of IC 4997 it is concluded that the correct value is 0 35 + 0.04. For future applications, values of the transition probabilities are adopted consistent with r(∞) = 0.35. Results of improved collision-strength calculations are presented, including those for transitions between all individual J-levels. The quantities required in these calculations are used to calculate quantum defects in various O I spectral series. Comparison with observed quantum defects shows that the collision strengths should be correct to within per cent. The calculations give r(0) to be 1.50 at low temperatures and 1.42 at high temperatures. Electron-density estimates of 18 and 10 are obtained from the surface brightnesses of two nebulae, NGC 281 and NGC 7000, for which the low- density limit should be approached Assuming T0 = 104° K, these densities would be consistent with r = 1.47-1.48. The observed ratios are 1.37 and 1.38, respectively, suggesting densities of the order of 100cm-3. The discrepancy is probably real and due to an inhomogeneous density distribution, together with selection effects. The ratio r' = I(7320)/I(7330), calculated to be between 1.24 and 1.31 for all values of Te and Ne, is in satisfactory agreement with available measurements Expressions are obtained for the intensity ratios r and r" = I(3729) + I(3726)/I(7320) + I(7330) as functions of T0 and N0. For IC 418 the measured value of r, 0.37 ± 0.03 is consistent with the density Ne = 2.5 x 104 cm-3 obtained from the surface brightness, interpreted assuming the hydrogen emission to be concentrated in a hollow spherical shell. For NGC 7027, r = 0.47, measured by Aller and Minkowski, gives N0 = 0.85 x 104 cm-3 , which is considerably smaller than values previously obtained from other forbidden-line ratios. The latter values are confirmed by using r" = 1.38, measured by Aller, Bowen, and Minkowski, which gives Ne = 3 x 104 cm-3. It is considered that the discrepancy, which is too large to be attributed to errors in observations or in atomic parameters, is due to the occurrence of local density fluctuations. The measured values of r and r" are consistent with a model having a background density of the order of 5 x 102 cm-3 and in which dense clouds or filaments, with densities of the order of 7 x 104 cm-3, occupy 1 or 2 per cent of the total volume. There is similar evidence for density fluctuations in a number of other bright planetaries In many cases direct photographs reveal the presence of filamentary structure It is pointed out that for IC 418 there is evidence of large-scale density and possibly temperature variations, but the spectrophotometric evidence does not suggest the existence of local density fluctuations This is consistent with the particularly uniform appearance of this object.