7 Inter-system matter model

Figure 12: Radial velocity of the extra-absorption (dots) and emission (open circles) in the barycentric rest frame. The dotted line is the RV curve of the K2 II-III star; the RV curve of the A2 star is also drawn (dash-dot line). The full line represents the RV curve of the extended region near the Roche-lobe limit of the K2 star (see Fig. 13).

In Fig. 12 we plot the radial velocity of the components and of the broad absorption and emission features in the center of mass (CM) frame, as function of orbital phase. Although not strictly sinusoidal, the excess emission/absorption follows the orbital motion of the K2 II-III star with a small phase shift and a larger amplitude, about 45-50 km$\,$s^-1. This does support our hypothesis that the emission/absorption features originate in a gas cloud placed somewhere within the system. If we assume that the system is fully synchronized, the location of such a cloud relative to the stars can be found from simple arguments.

Since the radial velocity of the supposed cloud is almost in phase with the K star, it should be located on the same side of that star with respect to the CM. Then the projected distance of the cloud is $a_{\rm cloud}=a_{\rm c}(K_{\rm cloud}/K_{\rm c})$, where $a_{\rm c} = a/(1+q)$, with q mass ratio and a the system separation, is the distance of the primary K star from the CM. $K_{\rm cloud}$ and $K_{\rm c}$ are the velocity semi-amplitudes of the cloud and of the cool star, respectively. Since the orbital solution gives $K_{\rm c} = 23.71$ and $(K_{\rm cloud}/K_{\rm c}) \sim 2$, then $a_{\rm cloud} \sim 7 \times 10^{7}~$km. From the radial velocity curves in Fig. 12 we can estimate a phase difference of $\sim$0 $.\!\!^{\scriptscriptstyle\rm p}$1 with respect to the K2 II-III star, which means that the cloud should lie outside the line joining the centers of two stars in the direction of advancing phases. Since we see absorption effects on the cool star spectrum only for a limited phase interval (0 $\hbox{$.\!\!^{\scriptscriptstyle\rm p}$ }$2-0 $\hbox{$.\!\!^{\scriptscriptstyle\rm p}$ }$4), the material should have a limited extent and some thickness perpendicularly to the orbital plane, because the system inclination is smaller than 90 $\hbox{$^\circ$ }$. According to the above estimate of the $a_{\rm cloud}$ distance and phase lag, the material seems to be located inside the Roche lobe of the cool star on the trailing hemisphere side.

The approximate location of the cloud is sketched as a shaded area in Fig. 13, where a scale model of HR 7428 is presented. Along the outer circle in Fig. 13, which indicates the position of the observer as a function of phase, the length of the arrows is proportional to the radial velocity of the broad emission/absorption feature in the CM rest frame.

Figure 13: Schematic model showing the Roche limit and the two components of the system in the orbital plane, as resulting from our solution. The cross indicates the center of mass of the system. The phase ranges of extra-absorption and broad emission features are stressed by thick grey lines. The possible location of the circumstellar region, responsible for the observed behaviour, is also showed as a shaded elliptical area.