Astron. Astrophys. 337, 311-320 (1998)

1. Introduction

Wind-fed accretion by a compact gravitating object is an important astrophysical phenomenon, which arises in many situations including massive X-ray binaries.

Wind accretion has been studied extensively both analytically and numerically. Hoyle & Lyttleton (1939) were the first to study an axisymmetric wind accretion onto a gravitating object immersed in a uniform flow. Assuming that the fluid particles collide at the axis and lose their tangential momentum, they obtained a mass accretion rate of,

where the accretion radius, , is given by

and , , G, M are the density, velocity of the gas at infinity upstream, the gravitational constant and the mass of the object, respectively. In this estimate the pressure is neglected which means that the Mach number of the gas is infinitely large.

Bondi & Hoyle (1944) have worked on the model in more detail and Bondi (1952) obtained a formula for the case of spherical accretion. The latter case means that the Mach number at infinity is zero. He also proposed an interpolation formula for flows with finite Mach number.

The numerical computation of axisymmetric wind accretion was first attempted by Hunt (1971, 1979) and general agreement between the accretion rates from analytical estimates and his numerical calculations was found. Shima et al. (1985) and Koide et al. (1991) calculated the same problem using a finer mesh, a modern algorithm and a supercomputer, and found accretion rates about a factor two larger than those obtained by Bondi.

If the flow at large distances is not uniform, angular momentum can be transferred to the compact object causing spin up or spin down. Ho et al. (1989) considered this problem based on non-axisymmetric simulations. Two-dimensional (planar) numerical computations of an inhomogeneous flow were carried out and non-steady 'flip-flop' motions were found by several authors (Matsuda et al. 1987, Taam & Fryxell 1988, Fryxell & Taam 1988)

Furthermore it was found that non-steady motion occurs even in a homogeneous medium (Matsuda et al. 1991). Livio et al. (1991) suggested a possible cause of the instability. Boffin & Anzer (1994) calculated two-dimensional wind accretion using a smoothed particle method (SPH) and confirmed the unsteadiness. Benensohn et al. (1997) calculated uniform wind accretion of an adiabatic gas with polytropic index and got 'flip-flop' nonsteady motions.

Three-dimensional simulations of wind accretion were performed and compared with two-dimensional cases by Sawada et al. (1989) and Matsuda et al. (1991, 1992). The three-dimensional calculations performed by Ishii et al. (1993), Ruffert (1994a, 1994b, 1995, 1996) and Ruffert & Arnett (1994) have sufficient spatial resolution to lead to non-steady oscillatory flows. Generally these oscillations have lower amplitudes than the corresponding two dimensional flows.

Since the real size of any astrophysical object is usually many orders of magnitude smaller than the accretion radius, it seems impossible to calculate the flow all the way to the surface. Thus the inner boundary of the computations is much larger than the real object. This is an artifact of the simulations.

But one finds that most of these calculations show non-steady behaviour of various degrees. The flows for which is close to unity tend to exhibit the largest fluctuations.

In this present investigation we want to focus on the special case of isothermal flows. Wind accretion with close to unity has been studied by Matsuda et al (1991), Boffin & Anzer (1994), and Ruffert (1996). As far as the instability of such flows with close to unity is concerned the situation is at present fairly unclear: Boffin & Anzer found in their 2 D calculations that low values of lead to more violent flows when compared to flows with higher values of ; whereas Ruffert obtained for his 3D flows with low systematically smaller amplitudes of and . In the 2 D calculations of Matsuda et al. showed smaller fluctuations and larger fluctuations as compared to the corresponding quantities for larger values of . Physically they can be thought of as approximations to configuration of low optical depth and efficient radiative losses resulting in a temperature distribution which is almost uniform.

In principle it would be desirable to include an energy equation which describes all gain and loss mechanisms of the flow. But this approach would complicate our calculations enormously. Therefore we shall use the approximation of isothermality.

The objective of this study is to calculate the wind accretion flows of an isothermal gas at various Mach numbers, , and to study the unsteadiness of the accretion column and the appearance of accretion disks around compact objects using a fine mesh and high resolution scheme.

Here we present the results for two dimensional wind accretion of an isothermal gas by a new high resolution numerical scheme with fine numerical meshes.

© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998
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