Realistic Models for Filling and Abundance Discrepancy Factors in Photoionised Nebulae

Abstract

When comparing nebular electron densities derived from collisionally excited lines (CELs) to those estimated using the emission measure, significant discrepancies are common. The standard solution is to view nebulae as aggregates of dense regions of constant density in an otherwise empty void. This porosity is parametrized by a filling factor $f<1$. Similarly, abundance and temperature discrepancies between optical recombination lines (ORLs) and CELs are often explained by invoking a dual delta distribution of a dense, cool, metal-rich component immersed in a diffuse, warm, metal-poor plasma. In this paper, we examine the possibility that the observational diagnostics that lead to such discrepancies can be produced by a realistic distribution of density and temperature fluctuations, such as might arise in plasma turbulence. We produce simulated nebulae with density and temperature fluctuations described by various probability distribution functions (pdfs). Standard astronomical diagnostics are applied to these simulated observations to derive estimates of nebular densities, temperatures, and abundances. Our results show that for plausible density pdfs the simulated observations lead to filling factors in the observed range. None of our simulations satisfactorily reproduce the abundance discrepancy factors (ADFs) in planetary nebulae, although there is possible consistency with \ion{H}{ii} regions. Compared to the case of density-only and temperature-only fluctuations, a positive correlation between density and temperature reduces the filling factor and ADF (from optical CELs), whereas a negative correlation increases both, eventually causing the filling factor to exceed unity. This result suggests that real observations can provide constraints on the thermodynamics of small scale fluctuations.

13 pages, 12 figures

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