Truncation Radius

To determine the location of the truncation radius, a non-linear least square fitting method for the radial distribution of the surface density $\Sigma$ is applied. The fitting function adopted is

$$\Sigma \propto \frac{\left( \frac{r}{r_{\rm d}} \right)^{-p}}{1+\left( \frac{r}{r_{\rm d}} \right)^{q}},$$

where $p$ and $q$ are constants and $r_{\rm d}$ is the truncation radius.

Fig. 2 shows (a) the evolution of the disc radius over $0 \le t \le 30.02$ and (b) the dependence of the disc radius on the orbital phase over $25 \le t \le 30$, where the unit of time is $P_{\rm orb}$. The mean value of $r_{\rm d}$ averaged over $25 \le t \le 30$ is $r_{\rm d}/a = 0.385$.

Figure 2: (a) Evolution of the radius of the truncated disc, $r_{\rm d}$. The blue dot denotes $r_{\rm d}$ at each instance. The horizontal lines denote the 2:1, the 3:1, the 4:1, $\ldots$, and the 15:1 resonance radii from top to bottom. The red line denotes the orbit of the neutron star. The periastron passage of the neutron star is denoted by vertical dashed lines. (b) Orbital-phase dependence of the trncation radius. Averaging is done over $25 \le t \le 30$ in units of $P_{\rm orb}$. The periastron passage of the neutron star occurs at pahse 0. The mean value of $r_{\rm d}$ over this period is $r_{\rm d}/a = 0.385$.