Bootstrapping dielectronic recombination from second-row elements and
  the Orion Nebula
  Dielectronic recombination (DR) is the dominant recombination process for
most heavy elements in photoionized clouds. Accurate DR rates for a species can
be predicted when the positions of autoionizing states are known. Unfortunately
such data are not available for most third and higher-row elements. This
introduces an uncertainty that is especially acute for photoionized clouds,
where the low temperatures mean that DR occurs energetically through very
low-lying autoionizing states. This paper discusses S$^{2+} \rightarrow$ S$^+$
DR, the process that is largely responsible for establishing the [S~III]/[S~II]
ratio in nebulae. We derive an empirical rate coefficient using a novel method
for second-row ions, which do have accurate data. Photoionization models are
used to reproduce the [O~III] / [O~II] / [O~I] / [Ne~III] intensity ratios in
central regions of the Orion Nebula. O and Ne have accurate atomic data and can
be used to derive an empirical S$^{2+} \rightarrow$ S$^+$ DR rate coefficient
at $\sim 10^{4}$~K. We present new calculations of the DR rate coefficient for
S$^{2+} \rightarrow$ S$^+$ and quantify how uncertainties in the autoionizing
level positions affect it. The empirical and theoretical results are combined
and we derive a simple fit to the resulting rate coefficient at all
temperatures for incorporation into spectral synthesis codes. This method can
be used to derive empirical DR rates for other ions, provided that good
observations of several stages of ionization of O and Ne are available.
