Disc Structure

Fig. 1 shows the evolution of surface density (left pan el) and the final disc structure (right panel). Averaging is done by using

$$<f(\vec{r})> = \sum_{j=1}^N \frac{m_j}{\rho(\vec{r}_j)} W(\vec{r}-\vec{r}_j, h),$$

where $W(r,h)$ is the kernel given by

$$W(r,h) = \frac{1}{\pi h^3} \left\{ \begin{array}{ll} 1-\f... ...}{h} < 2,\\ &\\ 0 & {\rm otherwise}. \end{array} \right.$$

Figure 1: (Left) Surface density evolution from $t =$0 to 30 in units of $P_{\rm orb}$. The interval of time between adjacent contours is 5 ($t =$ 0, 5, $\ldots$ from bottom). (Right) Disc structure at $t = 30$. The black, the blue, and the red lines are for the surface density, the radial Mach number, and the angular velocity normalized by the stellar break-up velocity, respectively. The magenta line is for $\alpha_{\rm SS}$ and the green line is for the smoothing length normalized by the disc scale-height.