The simplicity of the classic Bondi-Hoyle-Lyttleton (BHL) accretion model makes its use attractive in order to estimate roughly accretion rates and drag forces applicable in many different astrophysical contexts. Various aspects of the BHL flow have repeatedly been investigated in the past by many authors. In the BHL scenario a totally absorbing sphere of mass M moves with velocity relative to a surrounding homogeneous medium of density and sound speed . In this second instalment, I extend the investigations started in Ruffert (1997, henceforth R1) to include density gradients of the surrounding medium. Usually, the accretion rates of various quantities, like mass, angular momentum, etc., including drag forces, are of interest as well as the bulk properties of the flow, (e.g. distribution of matter and velocity, stability, etc.). The results pertaining to total accretion rates tend to agree well qualitatively (to within factors of two, and ignoring the instabilities of the flow) with the original calculations of Bondi, Hoyle and Lyttleton (Hoyle & Lyttleton 1939, 1940a, 1940b, 1940c; Bondi & Hoyle 1944). However, the question of whether and how much angular momentum is accreted together with mass from an inhomogeneous medium has remained largely unanswered, although R1 has attempted a first answer. It has already been summarised in the introduction of R1, that the strict application of the BHL recipe to inhomogeneous media, including some small constant gradient in the density or the velocity distribution, yields that the accreted matter has zero angular momentum by construction (Davies & Pringle, 1980).
where G is the gravitational constant. The mass accretion rate follows to be
I will refer to the volume upstream of the accretor from which matter is accreted as accretion cylinder. One can additionally calculate (Dodd & McCrea 1952; Illarionov & Sunyaev 1975; Shapiro & Lightman 1976; Wang 1981) how much angular momentum is present in the accretion cylinder for a non-axisymmetric flow which has a gradient in its density or velocity distribution perpendicular to the mean velocity direction. Then, assuming no redistribution of angular momentum, the amount accreted is equal to (or at least is a large fraction of) the angular momentum present in the accretion cylinder.
The uncertainty about how much angular momentum can actually be accreted in a BHL flow stems from these two opposing views involving either a large or a very small fraction of what is present in the accretion cylinder. In the first paper R1, I showed that the answer is not clear cut, but depends on the initial and boundary conditions. Roughly 7% to 70% of the total angular momentum available in the accretion cylinder is accreted.
In this second paper I would like to compare the accretion rates of the angular momentum of numerically modeled accretion flows with density gradients to the previous results of accretion with velocity gradients (R1). Although several investigations of two -dimensional flows with gradients exist (Anzer et al. 1987; Fryxell & Taam 1988; Taam & Fryxell 1989; Ho et al. 1989; Benensohn et al 1997, Shima et al, 1998), three -dimensional simulations are scarce due to their inherently high computational load. Livio et al. (1986) first attempted a three-dimensional model including gradients, but due to their low numerical resolution the results were only tentative. In the models of Ishii et al. (1993) the accretor was only coarsely resolved, while the results of Boffin (1991) and Sawada et al. (1989) are only indicative, because due to the numerical procedure the flows remained stable (too few SPH particles in Boffin 1991 and local time stepping in Sawada et al. 1989 which was described to be appropriate only for stationary flows). Also Sawada et al. (1989) only investigated velocity gradients.
In order to be able to compare the new results to previous models of R1, I will use the same values for the gradients as in R1. However, as will be mentioned in connection with Eq. 6 (which had already been presented in R1), the expected angular momentum accretion is reduced by a factor of six, when changing from velocity to density gradients. Thus the clear separation between angular momentum from the bulk flow one from the unstable, fluctuating flow blurs. On the other hand arbitrarily large specific angular momenta cannot be accreted because of the ang. mom. barrier felt by matter spiralling into the accretor. A simulation with a very large density gradient was done, too, mainly to be able to compare to a previous 2D model (Fryxell & Taam, 1988).
In Sect. 2 I give an only short summary of the numerical procedure used. Sects. 3 and 4 present the results, which I summarise in Sect. 5.
© European Southern Observatory (ESO) 1999
Online publication: June 17, 1999