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Astron. Astrophys. 317, 793-814 (1997)

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1. Introduction

The simplicity of the classic Bondi-Hoyle-Lyttleton (BHL) accretion model makes its use attractive in order to roughly estimate accretion rates and drag forces in many different astrophysical contexts, ranging from wind-fed X-ray binaries (e.g. Anzer & Börner 1995), over supernovae (e.g. Chevalier 1996), and galaxies moving through intracluster gas in a cluster of galaxies (Balsara et al. (1994), to the black hole believed to be at the center of our Galaxy (Ruffert & Melia 1994; Mirabel et al. 1991). In the BHL scenario a totally absorbing sphere of mass M moves with velocity [FORMULA] relative to a surrounding homogeneous medium of density [FORMULA] and sound speed [FORMULA]. It has been investigated numerically by many workers (e.g. Ruffert 1994 and 1995, and references therein). Usually, the accretion rates of various quantities, like mass, angular momentum, etc., including drag forces are of interest as well as the properties of the flow, (e.g. distribution of matter and velocity, stability, etc.). All results pertaining to total accretion rates are in qualitative agreement (to within factors of two, ignoring the instablitites of the flow) with the original calculations of Bondi, Hoyle and Lyttleton (e.g. Ruffert & Arnett 1994).

The BHL recipe for accretion in the axisymmetric case for pressureless matter is the following. A ring of material with radius b (which is identical to the impact parameter) far upstream from the accretor and thickness db will be focussed gravitationally to a point along the radial accretion line downstream of the accretor. At this point the linear momentum perpendicular to the radial direction is assumed to be cancelled. Then, if the remaining energy of the matter at this point is not sufficient for escape from the potential, this material is assumed to be accreted. The largest radius b from which matter is still accreted by this procedure turns out to be the so-called Hoyle-Lyttleton accretion radius (Hoyle & Lyttleton 1939, 1940a, 1940b, 1940c; Bondi & Hoyle 1944)

[EQUATION]

where G is the gravitational constant. The mass accretion rate follows to be

[EQUATION]

I will refer to the volume upstream of the accretor from which matter is accreted as accretion cylinder.

However, if the assumption of homogeneity of the surrounding medium is dropped, e.g. by assuming some constant gradient in the density or the velocity distribution, the consequences on the accretion flow remain very unclear. Using the same conceptual procedures, one can 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 perpendicular to the mean velocity direction. Then, assuming that the angular momentum will be accreted together with the mass, it is only a small step to conclude that the amount of angular momentum accreted is equal to (or at least is a large fraction of) the angular momentum present in the accretion cylinder. Note, that if the velocity is a function of position, then by virtue of Eq. (1) also the accretion radius varies in space. Thus the cross section of the accretion cylinder (perpendicular to the axis) is not circular.

However, the reasoning of BHL calls for a cancelling of linear momentum perpendicular to the radial accretion line before matter is accreted. Together with this linear momentum also angular momentum is cancelled and so the matter accreted has zero angular momentum by construction! This point was first discussed by Davies & Pringle (1980), who were able to construct two-dimensional flows with small non-vanishing gradients for which the accreted angular momentum was exactly zero, by placing the accretion line appropriately. Thus, following these analytic investigations two opposing views are voiced about how much angular momentum can be accreted: either a large or a very small fraction of what is present in the accretion cylinder. Numerical simulations thus are called for to help solve the problem.

In this paper I would like to compare the accretion rates of several quantities (especially angular momentum) of numerically modeled accretion flows with gradients to the previous results of accretion without gradients (e.g. Ruffert 1994). One has to change some of the parameters of the flow (Mach number, size of the accretor) in order to get a good overview of which features are generic and which specific to that combination of parameters. Although several investigations of two -dimensional flows with velocity gradients exist (Anzer et al. 1987; Fryxell & Taam 1988; Taam & Fryxell 1989; Ho et al. 1989), three -dimensional simulations are scarse 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. Also in the models of Ishii et al. (1993) was the accretor only coarsly 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 is appropriate only for stationary flows). A simulation that was numerically better resolved was performed later by Ruffert & Anzer (1995), but since only one model was presented, the results cannot be taken as conclusive either. I intend to remedy these shortcomings in the present paper.

In Sect.  2 I give only a short summary of the numerical procedure used. Sects.  4 to  6 present the results, which I analyze and interpret in Sect.  8. Sect.  9 summarizes the implications of this work.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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