In their original analyses, Bondi, Hoyle and Lyttleton made many simplifications. Despite these, the broad picture they present seems to be correct. Numerical studies have been made of the purely hydrodynamic problem, and of cases where extra physical processes are relevant. Bondi-Hoyle-Lyttleton accretion has also been used to explain phenomena in a variety of astronomical contexts.
Of course, the original Bondi-Hoyle-Lyttleton results cannot be applied without some thought. Numerical studies have shown that the flow pattern is more complicated than that originally envisaged. Meanwhile, real systems are always more complicated than theoretical ones. Bondi-Hoyle-Lyttleton accretion should be regarded as a reference model - it is unlikely to explain any system in detail, but it can serve as a useful basis for classifying behaviours. It can be applied as a test model on systems of all scales - from binary stars up to galaxies in clusters.
There are many future avenues for research. As well as improving simulations of accretion in binaries, studies need to be made on Bondi-Hoyle-Lyttleton accretion for flows where the accretor is orders of magnitude smaller than the accretion radius. Previous numerical work has hinted at lurking instabilities, but sufficient computing resources have yet to be brought to bear. Extra physical processes are also candidates for inclusion, especially radiative feedback. Radiative feedback is likely to be relevant in the context of both X-ray binaries and star formation simulations, and could alter the flow pattern significantly. On the observational side, better observations of systems previously modelled with a simple Bondi-Hoyle-Lyttleton analysis will show deviations, which can then be used to enhance our understanding of them.
Time has not eroded the usefulness of the Bondi-Hoyle-Lyttleton accretion geometry. It provides a simple framework for examining and refining theory and observation.
I am indebted to my supervisor, Cathie Clarke, for her help and patience throughout my PhD. This work was completed while I was at Stockholm Observatory, funded by the EU-RTN Planets (HPRN-CT-2002-00308). Matthew Bate and Jim Pringle both gave useful pointers to references for this article. The derivation in section 2.3 is based on that given by Douglas Gough in his lectures on Fluid Dynamics. Gerry Gilmore read an early draft of this article, and made a number of helpful suggestions. Finally, I am also grateful to the referees, for drawing further issues and work in the area to my attention.