Realistic Models for Filling and Abundance Discrepancy Factors in
  Photoionised Nebulae
  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.
