The Bondi-Hoyle-Lyttleton scenario has been applied to a variety of problems in the years since its introduction. I will now discuss some examples of these. Each of these problems could be the subject of a review article by themselves (and often have been), so I am not able to discuss the issues involved in great depth. However, I hope that this will provide a reasonable sample of the wide range of areas where the Bondi-Hoyle-Lyttleton model has proven useful.
5.1. Binary Systems
The problem of accretion in a binary system seems to be the most popular application of the Bondi-Hoyle-Lyttleton analysis. As noted above, the inevitable drag force simply causes the orbit to change. The gas supply can either be from a stellar wind, or from common envelope (CE) evolution.
Wind accretion seems to be one of the most popular applications of the Bondi-Hoyle-Lyttleton geometry. However, there are a number of potential complications. For the Bondi-Hoyle-Lyttleton solution to be valid, accretion must be driven by a wind, rather than by Roche lobe overflow. The work of Petterson (1978) warns that the presence of Roche lobe overflow will substantially complicate matters, and that allowance must be made for the possibility when comparing theory with observations. The orbital motion of the binary can also cause problems - see Theuns and Jorissen (1993); Theuns et al. (1996) for a discussion. These papers studied accretion rate in a binary, where the wind speed was comparable to the orbital velocity. Consequently, the flow pattern was substantially different from that envisaged by Bondi, Hoyle and Lyttleton. Theuns et al. (1996) found that the accretion rate for a binary is decreased by a factor of about ten compared to the prediction of equation 32. They attribute this difference to the disrupting effect of the orbital motion. Moving to higher mass ratios, Struck et al. (2004) modelled wind accretion onto substellar companions of Mira variables. They found that the mean accretion rates were generally similar to those predicted by Bondi, Hoyle and Lyttleton. However, the flow was highly variable - both due to instabilities in the accretion flow and the intrinsic variability of the star. The ultimate `wind' is that produced by an explosion. In this case, the very high velocities involved tend to make BH comparable to the size of the accreting body. The work of Kley et al. (1995) has already been mentioned. However, the problem had been studied before - MacDonald (1980) estimated accretion rates using modified a Bondi-Hoyle-Lyttleton formula.
Jackson (1975) used the predictions of Bondi-Hoyle-Lyttleton theory to derive the system parameters of Cen X-3. Similar work was performed by Eadie et al. (1975), Pounds et al. (1975) and Lamers et al. (1976). By considering the accretion of a high velocity wind by neutron stars, Pfahl et al. (2002) concluded that most of the low luminosity, hard X-ray sources known in our Galaxy could be powered by such systems. Modified Bondi-Hoyle-Lyttleton accretion has also been used to study cases where a giant star's wind is being accreted by a main sequence star. Some examples are the work of Chapman (1981) and Che-Bohnenstengel and Reimers (1986). The Bondi-Hoyle-Lyttleton geometry is a useful first approximation to wind accretion in binary systems. However, unless the wind speed is much greater than the orbital velocity, the accretion rates can deviate significantly from the simple predictions.
At the extreme end of the mass ratio scale, Bondi-Hoyle-Lyttleton accretion has even been used to estimate accretion rates onto a planet embedded in a disc (Nelson and Benz, 2003). Although the situation simulated was not entirely appropriate to the original analysis, Nelson and Benz point out that it represents a maximum possible accretion rate. This rate turns out to be extremely high, showing the need for higher resolution simulations of planetary accretion flows.
Common Envelope evolution occurs when two stellar cores become embedded in a large gas envelope. Such an envelope is typically produced when one of the members of the binary system swells as it leaves the main sequence. For a more detailed discussion of Common Envelope evolution itself see, e.g. Iben and Livio (1993). In such cases, accretion rates are critical for determining the detailed evolution of the system. In computing accretion rates, modified Bondi-Hoyle-Lyttleton formulæ are often used e.g. Taam and Bodenheimer (1989) - see also the review by Taam and Sandquist (2000).
5.2. Protostellar Clusters
Bondi-Hoyle-Lyttleton flow is also likely to be applicable to regions of star formation. Although single stars will be stopped by the drag force, real stars are generally thought to form in clusters. Protostars and gas are trapped inside a gravitational well, and orbit within it. The drag will then simply cause a change in orbit - as is the case for X-ray binaries. Indeed, the approximation is likely to be better for protostars in a protocluster. This is because the orbital motion of the protostars is the `source' of the wind, rather than a wind from a companion. As a result, the geometry is simpler (since the orbital motion does not have to be added to the wind velocity). Furthermore, non-inertial forces (coriolis and centrifugal) are likely to be far less significant.
Bonnell et al. (2001) performed a thorough study of accretion in a protocluster. They simulated the evolution of a gas cloud containing many small point masses (representing protostars). The point masses grew by accreting the gas. When the gas dominated the mass of the cluster, Bonnell et al. found that the accretion was best described by tidal lobe overflow (examining whether material was bound to the cluster or the star). However, as the mass in stars grew, Bondi-Hoyle-Lyttleton accretion became the more significant mechanism. The transition occurred first for the most massive stars which had sunk into the cluster core. However, massive stars are very luminous and Edgar and Clarke (2004) showed that radiative feedback can disrupt the Bondi-Hoyle-Lyttleton flow once stellar masses exceed 10 (this is obviously dependent on the prevailing conditions in the protocluster).
Unfortunately, direct observations of this process are not available. Protoclusters contain large quantities of dusty gas, which greatly obscure regions of interest. Furthermore, the expected luminosities are lower, and the emission wavelengths less distinctive than those of X-ray binaries.
5.3. Galaxy Clusters
Galaxies orbiting in a cluster are another candidate for Bondi-Hoyle-Lyttleton accretion. One immediate complication is the high temperature of the intergalactic medium (IGM). The IGM is typically hot enough to emit X-rays, and hence the galactic motions will usually be subsonic. Ruderman and Spiegel (1971) suggested that the IGM might be heated (at least in part) by the accretion shocks inherent to Bondi-Hoyle-Lyttleton accretion. Galaxies are also rather porous objects, and contain their own gas. In a study of M86, Rangarajan et al. (1995) concluded that the `plume' observed was probably the result of ram-pressure stripping of material from the galaxy itself. Stevens et al. (1999) simulated galaxies under such conditions, and concluded that "the ram-pressure stripped tail will usually be the most visible feature." This paper also contains a list of observed wakes.
De Young et al. (1980) observed M87, and found evidence for subsonic Bondi-Hoyle-Lyttleton flow. However, higher resolution observations by Owen et al. (2000) suggest that this simple picture is not sufficient. In particular, the active nucleus of M87 drives an outflow. A filament has been observed trailing Abell 1795 both in the optical (Cowie et al., 1983) and in X-rays (Fabian et al., 2001). It has been proposed (Sakelliou et al., 1996) that this filament is an accretion wake, but Fabian et al. (2001) note that the gas cooling times aren't quite right for this simple approximation to be completely valid. Sakelliou (2000) constructed a simple theoretical model of a Bondi-Hoyle-Lyttleton wake behind a galaxy. Wakes were expected to extend for up to 20. The wakes would form behind slow moving, massive galaxies in low temperature clusters.
5.4. Other Applications
The original application of Bondi-Hoyle-Lyttleton accretion was to the flow of the interstellar medium past the Sun. Sikivie and Wick (2002) apply a similar analysis to the flow of dark matter past the Sun. They suggest that annual variations in WIMP detections may be partially attributable to the focusing of the flow by the Sun.
Bondi-Hoyle-Lyttleton accretion was invoked by Kamp and Paunzen (2002) to explain the unusual chemical abundances of -Bootis type stars. These stars have metal abundances typical of the interstellar medium (that is, metal-poor). Kamp and Paunzen suggest that radiation pressure on dust grains (which contain most of the metals) prevents the accretion of the heavier elements, while gas accretes in a Bondi-Hoyle-Lyttleton fashion. Moving to higher energies, accretion onto neutron stars moving through gas clouds has been proposed as a mechanism for producing X-ray sources in the Galaxy (Ostriker et al., 1970) and in globular clusters (Pfahl and Rappaport, 2001). However with neutron stars, magnetic fields can cause significant complications - see, e.g. Toropina et al. (2001).
Maeda et al. (2002) studied the central portions of our Galaxy with Chandra. Finding evidence for recent activity, they suggest that this could have been powered by the central black hole accreting material from an expanding supernova shock. This would be a transient example of Bondi-Hoyle-Lyttleton accretion. The potential luminosity from this is rather high (comparable with the Eddington Limit). However, there is a complication due to the thermal pressure of the ambient gas, which could reduce the inferred luminosity substantially.