All Figures

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{9953f01.eps} \end{figure}$ Figure 1: The grid structure used in the computations. The radial domain is $[r_{\rm min}, r_{\rm max}] = [0.05, 0.70]$ and the $\varphi$ domain is the whole annulus $[0, 2\pi ].$ For our standard case this is covered with $N_{\rm r} \times N_\varphi = 200\times 200$ grid cells that are equally spaced in each direction. The Roche lobe of the primary, for our standard mass ratio q = M₂/M₁ = 0.1, is defined by the additional solid (red) line. The primary and secondary star are located at ( $x=x_{\rm p}=0, y=y_{\rm p}=0$ ) and ( $x=x_{\rm s}=-1,y =y_{\rm s}=0$ ) respectively. Note that in this figure, for illustrative purposes, we display a low-resolution $50 \times 50$ grid.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9953f02.eps} \end{figure}$ Figure 2: Greyscale plot of the surface density of the disk for the standard model after 1 binary orbit. The solid (red) curve indicates the Roche lobe of the primary star (central red dot).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f03.eps} \end{figure}$ Figure 3: Greyscale plot of the surface density of the disk for the standard model at 100, 150, 175 and 200 orbital periods. The solid (red) curve indicates the Roche lobe of the primary star (central red dot).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f04.eps} \end{figure}$ Figure 4: Radial distribution of the azimuthally averaged surface density $\Sigma (r)$ at different times. The solid black curve indicates the tapered initial profile.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f05a.eps}\hspace*{4mm} \... ....eps}\hspace*{4mm} \includegraphics[width=3.8cm,clip]{9953f05d.eps} \end{figure}$ Figure 5: Evolution of various global disk properties of the standard model as functions of time. The total mass in the computational domain, or equivalently the disk mass, is shown in the upper left panel. The disk radius, defined as the radius containing $99\%$ of the mass, is shown in the upper right panel. The disk eccentricity is shown in the lower left panel and the m=1 and m=2 Fourier amplitudes are shown in the lower right panel.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f06.eps} \end{figure}$ Figure 6: Time-evolution of the longitude of pericentre (periastron) of the disk. The solid darker (red) curve is the mass-weighted mean pericentre over the whole disk, calculated as described in the text. The lighter dashed (green) curve corresponds to a phase of the m=1 Fourier mode at the single radius r=0.37. Note that the phases are calculated in the inertial frame.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f07a.eps}\hspace*{4mm} \includegraphics[width=4cm,clip]{9953f07b.eps} \end{figure}$ Figure 7: Radial variation of the eccentricity and longitude of pericentre of the disk at various times (quoted in binary orbits).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{9953f08.eps} \end{figure}$ Figure 8: Time-evolution of the mean eccentricity of the disk (natural logarithm) for different kinematic viscosities (in dimensionless units).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f09a.eps}\hspace*{4mm} \... ...9c.eps}\hspace*{4mm} \includegraphics[width=4cm,clip]{9953f09d.eps} \end{figure}$ Figure 9: Dependence of various global disk parameters on the magnitude of the viscosity. upper left panel: growth rate of the eccentricity of the disk; upper right panel: the radius, $r_{\rm d},$ within which 99% of the mass of the disk is contained; lower left panel: the mass-weighted mean eccentricity of the disk $e_{\rm d}$ ; lower right panel: precession rate of the disk $\dot\varpi_{\rm d},$ negative values indicating retrograde precession. The values for $r_{\rm d}$ , $e_{\rm d}$ and $\dot\varpi_{\rm d}$ are determined at a time at which the system reaches its final quasi-steady state.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{9953f10.eps} \end{figure}$ Figure 10: Four snapshots of the disk surface density contours during one orbital period as viewed in the non-rotating frame. Time increases from top to bottom and left to right The solid (red) curve indicates the Roche lobe of the primary star. The viscosity is 10^-4, the mass ratio is 0.1 and H/r =0.05. As the companion has a close approach to the disk outer edge a tidal tail is pulled out ( top right). This subsequently rejoins the disk ( bottom left) which remains relatively unperturbed until the next close approach.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f11a.eps}\hspace*{4mm}\includegraphics[width=4cm,clip]{9953f11b.eps} \end{figure}$ Figure 11: Mean disk eccentricity $e_{\rm d}$ and disk radius $r_{\rm d}$ as functions of time for the standard model (red curve), the same case but with an added explicit bulk viscosity $\nu _{\rm bulk}=2\nu$ (green curve) and a case with standard parameters, but for which the initial disk radius is taken to be $r_{\rm d}(0) = 0.3$ (blue curve).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f12.eps} \end{figure}$ Figure 12: Time-evolution of the mean eccentricity of the disk for different disk aspect ratios $h \equiv H/r.$
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=3.9cm,clip]{9953f13a.eps}\hspace*{4mm} \includegraphics[width=4cm,clip]{9953f13b.eps} \end{figure}$ Figure 13: Left: dependence of the growth time ( $\sigma _{\rm d}^{-1}$ ) of disk eccentricity on h=H/r. Quoted is the time (in orbital periods) to increase the eccentricity by a factor of e; Right: the equilibrium surface density profile of the disk normalized to the central value for different h.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f14.eps} \end{figure}$ Figure 14: Dependence of the equilibrium disk precession rate $\dot\varpi_{\rm d}$ on disk temperature. The two separate lines with the triangles refer to two different grid resolutions, the upper to the standard case and the lower to $300\times 300$ . The additional curves with the small open and solid diamonds are approximate parabolic fits to the data points. Values obtained by solving the linear eigenvalue problem using the azimuthally averaged surface density profiles are also indicated by the filled circles. The open triangles are obtained from models where the disk is impacted by a mass-transfer stream (see Sect. 9 below).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f15.eps} \end{figure}$ Figure 15: Time-evolution of the pericentre (in the inertial frame) of the disk, $\varpi _{\rm d}(t)$ , for a model with an intermediate H/r=0.03.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f16.eps} \end{figure}$ Figure 16: Time-evolution of the mean eccentricity of the disk for different inner boundary conditions for a kinematic viscosity of $\nu = 10^{-4}$ (ten times the standard value).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9953f17.eps} \end{figure}$ Figure 17: Two-dimensional surface density structure for the model with the open outflow inner boundary condition after 250 orbital periods.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f18.eps} \end{figure}$ Figure 18: Time-evolution of the mean eccentricity of the disk (logarithmic) for different mass ratios q=M₂/M₁ of the binary for a kinematic viscosity of $\nu = 10^{-4}$ (ten times the standard value). The thinner black dashed lines indicate approximate linear fits.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f19a.eps}\hspace*{4mm} \includegraphics[width=3.9cm,clip]{9953f19b.eps} \end{figure}$ Figure 19: Left: dependence of the growth rate ( $\sigma _{\rm d}$ ) of the disk eccentricity on the mass ratio q. Right: the disk radius $r_{\rm d}$ as a function of time for different q. The curves are smoothed.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f20a.eps}\hspace*{4mm} \includegraphics[width=3.9cm,clip]{9953f20b.eps} \end{figure}$ Figure 20: Left: dependence of the growth rate ( $\sigma _{\rm d}$ ) of the disk eccentricity on the numerical resolution. The two-dimensional grid always has an equal number of grid points in each direction. Thus in the standard case 200 corresponds to $200\times 200.$ Right: the precession rate of the disk as a function of resolution.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9953f21.eps}\end{figure}$ Figure 21: Time-evolution of the mode amplitudes S_k,l (see Eq. (13)) for q=0.1 with a kinematic viscosity $\nu = 10^{-4}$ plotted on a logarithmic scale. The upper panel gives results for the case when only the component of the tidal potential with m=3 is retained. The lower panel gives results corresponding to the case when the full tidal potential is used. In both cases the mode with k=2 and l=3 grows at the same rate as the mode with k=1 and l=0, the latter mode being responsible for the disk eccentricity. The growth is slower when the full potential is used.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9953f22.eps} \end{figure}$ Figure 22: As in Fig. 21 but for q=0.2.Note that there is a very close correspondence between S_2,3 and S_1,0when only the m=3 component of the tidal potential is used.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9953f23.eps} \end{figure}$ Figure 23: Time-evolution of the mode amplitudes S_k,l, plotted on a logarithmic scale, for q=0.1 ( upper panel) and q=0.2 ( lower panel). For these cases, the tidal potential with the m=3 component removed is used and the kinematic viscosity $\nu = 10^{-4}.$ When q=0.1 little growth of the disk eccentricity or S_1,0 is seen. When q=0.2 some growth occurs but at a significantly slower rate than when the full potential is used (see Fig. 22).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f24a.eps}\hspace*{4mm} \includegraphics[width=4cm,clip]{9953f24b.eps} \end{figure}$ Figure 24: Mean disk eccentricity $e_{\rm d}$ and disk radius $r_{\rm d}$ as functions of time for models that include mass inflow through the L₁ point and different inner boundary conditions and viscosities. For the first two plots (green and red curves) the standard viscosity 10^-5 has been used, while the third plot (blue curve) is for a model that has been continued from the first at time $t\approx 230$ but with $\nu = 3\times 10^{-5}.$
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=3.8cm,clip]{9953f25a.eps}\hspace*{4mm}... ...9cm}\includegraphics[width=4cm,clip]{9953f25c.eps}\hspace*{1.9cm}} \end{figure}$ Figure 25: Disk mass $m_{\rm d}$ , radius $r_{\rm d}$ and eccentricity $e_{\rm d}$ as functions of time for models including mass inflow through the L₁ point with different initial conditions. The first (red) curve corresponds to an initially empty Roche lobe of the primary, while in the second (green) a standard initialized disk is used. The ``viscous outflow'' condition and a viscosity $\nu = 10^{-4}$ (ten times standard) are used.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f26.eps}\end{figure}$ Figure 26: Greyscale plot of the surface density of the disk for the model with stream inflow that started with an initial disk at 210, 220, 230 and 240 orbital periods. The solid (red) curve indicates the Roche lobe of the primary star (central red dot). The ``viscous outflow'' condition is used at the inner boundary.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{9953f27.eps} \end{figure}$ Figure 27: Longitude of the disk pericentre (in the inertial frame) as a function of time. The solid (red) curve corresponds to a disk in a quasi-steady state with stream inflow (as displayed in the previous Fig. 26). The light dashed (green) line corresponds to a model where the stream is switched off at t=240and the simulation is continued.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9953f02.eps} \end{figure}$	Figure 2: Greyscale plot of the surface density of the disk for the standard model after 1 binary orbit. The solid (red) curve indicates the Roche lobe of the primary star (central red dot).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f03.eps} \end{figure}$	Figure 3: Greyscale plot of the surface density of the disk for the standard model at 100, 150, 175 and 200 orbital periods. The solid (red) curve indicates the Roche lobe of the primary star (central red dot).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f04.eps} \end{figure}$	Figure 4: Radial distribution of the azimuthally averaged surface density $\Sigma (r)$ at different times. The solid black curve indicates the tapered initial profile.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f06.eps} \end{figure}$	Figure 6: Time-evolution of the longitude of pericentre (periastron) of the disk. The solid darker (red) curve is the mass-weighted mean pericentre over the whole disk, calculated as described in the text. The lighter dashed (green) curve corresponds to a phase of the m=1 Fourier mode at the single radius r=0.37. Note that the phases are calculated in the inertial frame.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f07a.eps}\hspace*{4mm} \includegraphics[width=4cm,clip]{9953f07b.eps} \end{figure}$	Figure 7: Radial variation of the eccentricity and longitude of pericentre of the disk at various times (quoted in binary orbits).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{9953f08.eps} \end{figure}$	Figure 8: Time-evolution of the mean eccentricity of the disk (natural logarithm) for different kinematic viscosities (in dimensionless units).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f11a.eps}\hspace*{4mm}\includegraphics[width=4cm,clip]{9953f11b.eps} \end{figure}$	Figure 11: Mean disk eccentricity $e_{\rm d}$ and disk radius $r_{\rm d}$ as functions of time for the standard model (red curve), the same case but with an added explicit bulk viscosity $\nu _{\rm bulk}=2\nu$ (green curve) and a case with standard parameters, but for which the initial disk radius is taken to be $r_{\rm d}(0) = 0.3$ (blue curve).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f12.eps} \end{figure}$	Figure 12: Time-evolution of the mean eccentricity of the disk for different disk aspect ratios $h \equiv H/r.$
Open with DEXTER

$\begin{figure} \par\includegraphics[width=3.9cm,clip]{9953f13a.eps}\hspace*{4mm} \includegraphics[width=4cm,clip]{9953f13b.eps} \end{figure}$	Figure 13: Left: dependence of the growth time ( $\sigma _{\rm d}^{-1}$ ) of disk eccentricity on h=H/r. Quoted is the time (in orbital periods) to increase the eccentricity by a factor of e; Right: the equilibrium surface density profile of the disk normalized to the central value for different h.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f15.eps} \end{figure}$	Figure 15: Time-evolution of the pericentre (in the inertial frame) of the disk, $\varpi _{\rm d}(t)$ , for a model with an intermediate H/r=0.03.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f16.eps} \end{figure}$	Figure 16: Time-evolution of the mean eccentricity of the disk for different inner boundary conditions for a kinematic viscosity of $\nu = 10^{-4}$ (ten times the standard value).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9953f17.eps} \end{figure}$	Figure 17: Two-dimensional surface density structure for the model with the open outflow inner boundary condition after 250 orbital periods.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f18.eps} \end{figure}$	Figure 18: Time-evolution of the mean eccentricity of the disk (logarithmic) for different mass ratios q=M₂/M₁ of the binary for a kinematic viscosity of $\nu = 10^{-4}$ (ten times the standard value). The thinner black dashed lines indicate approximate linear fits.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f19a.eps}\hspace*{4mm} \includegraphics[width=3.9cm,clip]{9953f19b.eps} \end{figure}$	Figure 19: Left: dependence of the growth rate ( $\sigma _{\rm d}$ ) of the disk eccentricity on the mass ratio q. Right: the disk radius $r_{\rm d}$ as a function of time for different q. The curves are smoothed.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=4cm,clip]{9953f20a.eps}\hspace*{4mm} \includegraphics[width=3.9cm,clip]{9953f20b.eps} \end{figure}$	Figure 20: Left: dependence of the growth rate ( $\sigma _{\rm d}$ ) of the disk eccentricity on the numerical resolution. The two-dimensional grid always has an equal number of grid points in each direction. Thus in the standard case 200 corresponds to $200\times 200.$ Right: the precession rate of the disk as a function of resolution.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9953f22.eps} \end{figure}$	Figure 22: As in Fig. 21 but for q=0.2.Note that there is a very close correspondence between S_2,3 and S_1,0when only the m=3 component of the tidal potential is used.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{9953f26.eps}\end{figure}$	Figure 26: Greyscale plot of the surface density of the disk for the model with stream inflow that started with an initial disk at 210, 220, 230 and 240 orbital periods. The solid (red) curve indicates the Roche lobe of the primary star (central red dot). The ``viscous outflow'' condition is used at the inner boundary.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{9953f27.eps} \end{figure}$	Figure 27: Longitude of the disk pericentre (in the inertial frame) as a function of time. The solid (red) curve corresponds to a disk in a quasi-steady state with stream inflow (as displayed in the previous Fig. 26). The light dashed (green) line corresponds to a model where the stream is switched off at t=240and the simulation is continued.
Open with DEXTER