Temperature and Density Fluctuations in Planetary Nebulae

Abstract

The determination of the chemical composition of gaseous nebulae depends on whether they contain fluctuations in density and/or temperature beyond those predicted by photoionization models or pressure balance. These fluctuations are strongly suggested by the unexpectedly large observed strengths of O II and C II recombination lines. If there are dense clumps, the derived abundances can be wrong by a factor of 2 or more. This paper does not address the physics of producing fluctuations but rather examines the spectroscopic consequences if the fluctuations exist. There are 10 planetary nebulae (PNs) or portions of spatially resolved PNs in which the recombination line O II λ4649 has been measured along with collisionally excited O III] λ1664, [O III] λ4363, λ5007, C III] λ1908, and the recombination line C II λ4267. The C+2/O+2 obtained from λ1908/λ1664 is the same as that from the recombination lines, λ4267/λ4649. This result, which is little affected by reddening, positioning of the ultraviolet observations relative to the optical, or any temperature or density fluctuations, strongly suggests that the standard physics of the recombination lines is correct. We define T4363 as the temperature that would produce the observed dereddened [O III] λ4363/λ5007 ratio at low densities (ne < 104 cm-3, so that the collisional de-excitation of the 1D level of O+2 is negligible.) Similarly, T1664 describes (O III] λ1664)/λ5007, T4649 describes (O II λ4649)/λ5007, and T1908 describes (C II λ1908)/(C III] λ4267). We have extensively investigated the case where two separate zones along the line of sight have arbitrary densities and temperatures. We show by models and physical reasoning that the inequalities T1664 ≥ T4363 ≥ T1908 ≥ T4649 must hold with a general distribution of temperatures within the nebulae for low densities. For high densities, T4363 ≥ T1664 is possible but the other inequalities must hold. Plots of various temperature ratios are given showing permitted and forbidden regions with and without density fluctuations. We analyze the line strengths in the PNs for which there are measurements of C II λ4267 as well as ultraviolet and optical lines of [O III] and [O II]. Only 12 of the 47 lines of sight have understandable line ratios if no fluctuations are present, even if errors in line ratios of ~30% in the line-strength ratios are allowed. The most discrepant objects require an increase in the observed carbon line ratio λ1908/λ4267 by an order of magnitude to bring the C+2 abundances into agreement unless there are severe fluctuations. Spatially resolved photometry is needed to determine whether it is very local variations of temperature and/or density that produce anomalous line strengths with present-day spatial resolution.