Astron. Astrophys. 354, 1014-1020 (2000)

5. Accretion models

Early analytical accretion models by Hoyle & Lyttleton (1939) and Bondi & Hoyle (1944) dealt with homogeneous, uniform flows interacting with an accreting sphere. In recent years numerical simulations by various authors have basically confirmed these analytical results (e.g. Ruffert 1996 and references therein). These studies can be directly applied to situations, where the Bondi-Hoyle accretion radius,

is small compared to distances over which density and velocity gradients in the stellar wind are significant (M is the mass of the accretor, G the gravitational constant, and the relative velocity of the medium far away from the accretor). For evolved low mass binary systems, like s-type symbiotics or  Aurigae systems, this condition is not fulfilled, as for these systems . Several hydrodynamical simulations for  Aur and symbiotic binary systems have been performed, e.g. Theuns & Jorissen (1993), Bisikalo et al. (1995), Theuns et al. (1996), Walder (1997), and Mastrodemos & Morris (1998). These simulations found that the accretion rate is significantly lower than predicted by the Bondi-Hoyle-Lyttleton formula, and that the accretion wake is spiral-shaped. In the following we model the occultation seen in RW Hya around in terms of wind accretion.

5.1. Model assumptions

The velocity and density distribution of the unperturbed M-giant wind inside the accretion radius of the white dwarf determines the orientation of the accretion wake. The M-giant wind law of SY Mus (Dumm et al. 1999) suggests that the M-giant wind expands at negligible velocities until it reaches a stellar distance of M-giant radii. At the wind is then strongly accelerated. The accretion geometry is thus strongly influenced by the M-giant wind acceleration. At present the mechanism of wind formation in non-pulsating M-giants is very poorly known. Radiation pressure on dust grains is important, but it will only act beyond several stellar radii from the M-giant, where dust formation starts (Danchi et al. 1994). The mechanism which brings the wind material to the condensation distance is not known.

For our hydrodynamical simulation we therefore represent the M-giant wind in the following simplified way: Similarly to Theuns & Jorissen (1993) we assume that at any point non-thermal wind driving forces are balanced by gravitation of the M-giant. The forces acting on the M-giant wind are thus gravitation due to the white dwarf, and forces due to gas pressure gradients. Around the accretor the unperturbed wind velocity, , then behaves like

Our wind velocity law is slightly steeper than the one of Mastrodemos & Morris (1998) who performed 3D SPH accretion simulations of detached binary systems containing a mass losing AGB star.

All the parameters entering the numerical simulation are listed in Table 2. In our calculation the M-giant wind is allowed to accelerate from a sphere with radius (Schild et al. 1996). The isothermal wind starts with an initial velocity perpendicular to this sphere. The mass-loss rate, , is taken from Kenyon & Fernandez-Castro (1987), the stellar masses and orbital period are from Schild et al. (1996). The constant gas temperature, , was set to a value typical for the electron temperature in the ionized nebula of symbiotic binaries. For the average mass per nucleus, µ, we assume solar composition, where hydrogen is fully ionized.

Table 2. Our model parameters. The subscript r refers to the M-giant, h to the accreting whitedwarf. The radii correspond to numerical and not physical surfaces.

5.2. Hydrodynamic code

We solve the adiabatic 3D Euler equations employing, which corresponds to the isothermal case. For this we use the AMRCART code, described in Walder & Folini (2000) ¹. For our simulation we work in a fixed frame of reference. AMRCART combines the adaptive mesh refinement algorithm of Berger (1985) with the high-resolution finite volume integrator of Colella (1990). The numerical method is therefore very similar to that of Ruffert (1996). It is, however, different from the SPH-method used by Theuns & Jorissen (1993) and Mastrodemos & Morris (1998). A comparison made by Walder (1997) confirms that the two different methods give similar results. Even with the adaptive mesh it is beyond present computer resources to resolve the white dwarf with the numerical grid. We have chosen a sphere of radius , into which the material is accreted. Along the accreting sphere fully absorbing boundary conditions were applied. These are the same boundary conditions as used by Ruffert (1996). They implicitly assume that the flow between the sphere and the surface of the white dwarf has no influence on the flow outside of the sphere and through the sphere.

5.3. Results of the model calculation

The resulting density and velocity distribution in the orbital plane is shown in Figs. 4 and 5.

Fig. 4. Hydrodynamical simulation for the RW Hya system. Density (logarithmic) and projected velocity distribution in the orbital plane. Densities are given by contour lines, velocities by arrows. In the upper panel arrows of correspond to a velocity of . The system rotates anti-clockwise. The center of mass is marked with a cross, The accretor is marked with a small circle.

Fig. 5. Enlargement of Fig. 4, showing both high density ridges in the neighbourhood of the accretor. The circle corresponds to the numerical boundary of the accretor.

The most striking feature in Fig. 4 is the accretion wake, an elongated region of highly increased density. The accretion wake is limited by an inner and an outer shock front, behind which the density steeply rises, leading to an inner and an outer high density ridge. Due to geometrical rarefaction and wind acceleration, the inner ridge is much denser than the outer ridge. In addition, the inner high density ridge close to the accretor extends along an almost straight line (Fig. 5). This geometry, together with the high densities along the inner ridge, leads to the strongly enhanced column density at in Fig. 6, with peak column density . About of this maximum column density arises from matter closer than to the accretor. Contrary to the inner high density ridge, the outer ridge is strongly curved. Because of this, and due to smaller densities, the outer ridge does not lead to high column densities in Fig. 6. In Fig. 6 we show the column density towards the accretor as a function of orbital phase. There, the width at half of the maximum column density due to the inner high density ridge is . There the ionizing photons from the white dwarf radiation field can no longer compensate for the much increased recombination of ionized hydrogen, and a neutral region can form, with peak column densities of neutral hydrogen of the order of , which is of the order of the observed column density of neutral hydrogen at . It is this neutral region along the inner high density ridge which we associate with the observed high column density close to quadrature.

Fig. 6. Column densities on the line of sight to the accretor, in units of . The densities are calculated from our numerical simulation. The gap around is due to the M-giant's photospheric eclipse.

We find that the position of both ridges is stable. From our simulation we get a stable accretion rate of . Thus of the M-giant wind is captured by the accretor. This value is comparable to what has been found by Mastrodemos & Morris (1998) for their Model 3. The accretion efficiency is thus much smaller than, for Bondi-Hoyle accretion.

Between the numerical boundary of the accretor at and , in the plane of the orbit, we find an almost circular flow around the accretor. We cannot decide whether an accretion disk would form around the accretor if a smaller calculation boundary were chosen. We expect that the formation of an accretion disk would not significantly influence the shape of the accretion wake.

© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000
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