# Alpha Centauri: Disc Dynamics, Planet Stability, Detectability
## 2 Protoplanetary Disc Dynamics in Alpha Centauri
### Circumstellar Discs in Alpha Centauri  
The aim of this new hydrodynamical simulation was to quantify the process of disc truncation in order to assess the mass retention and exchange after repeated stellar interactions. We note that a similar numerical setup was recently proposed for the disc around B in Alpha Cen (2017) using slightly different values for the binary orbit. Here, the main difference is that we model both discs simultaneously and consider a revised value of the binary semimajor axis: \(a_{\rm b}=23.3\) au ([PERSON] _et al._, 2017) instead of 23.75 au. Given the previous exploration of a broad range of disc parameters (2017), we limit ourselves to a single case. We consider this scenario as an illustrative example of the formation scenario in Alpha Centauri. Figure 1 shows the evolution of the circumstellar discs in Alpha Centauri. The system is shown as it would appear in the sky. We see that the discs experienced a strong gravitational perturbation when the stars were close to the periastron (see second and forth panels in the top row). Tidal spirals formed and material was exchanged as the stars got closer to each other. This happens because the outer disc radii are larger than the tidal truncation radii caused by the stars. After a few orbits, this effect disappeared as the discs quickly reached their steady size set by tidal truncation. For instance, after three orbital periods, the discs only experienced mild perturbations as the stars orbited around each other. For the rest of the simulation, we did not see any noticeable morphological differences from one orbit to another--besides a very mild disc eccentricity excitation (2017). The long-term stability of the discs is guaranteed by the gas, as it efficiently damps the eccentricity excitations within the discs (that would otherwise be triggered in pure N-body integrations). We expected the gaseous disc to start dissipating on time scales of the order of several Myr (20,217). However, this effect did not affect the results presented in this work regarding disc dynamics. Figure 2 exhibits the surface density profiles as a function of the distance to the central star for the circumstellar discs around A (left panel) and B (right panel). We see that  
Figure 1: Gas column density of the Phantom hydrodynamical simulation of the circumstellar discs in the binary Alpha Centauri. The stars start at apoastron: A is in the top left corner, and B is in the bottom right corner. From left to right and top to bottom, we show the system at different evolutionary stages: 0, 0.5, 1, 1.5, 2.0, 2.5, 3, and 5 \(P_{\rm b}\), where \(P_{\rm b}\) is a binary orbital period. The red dots represent the stars of Alpha Centauri. the discs were initially extended up to 10 au following the density profile described in Section 2.2. After only three binary orbital periods, both discs sizes remained practically unchanged. The disc profiles around A and B were very similar and were marked by a drastic break at around 3 au from the host star. Material beyond that distance was less dense. In other words, the bulk of the disc was mainly contained below 3 au. We also note that, due to the difference in stellar mass, the circumstellar disc around the secondary star B converged faster towards the tidal truncation radius compared to the disc around primary star A. The initial values used in this study to initialise the disc masses, although in agreement with typical values [17], were admittedly arbitrary and practically unconstrained from observations. We can, however, interpret our results in the broader context of circumstellar discs in binaries. Integrating the profiles in Figure 2 radially after five binary orbits, we find that the gaseous disc masses around A and B were equal to 3266 \(M_{\oplus}\) and 2167 \(M_{\oplus}\), respectively. Assuming a dust-to-gas ratio of 1%, this means that there were about 33 \(M_{\oplus}\) and 22 \(M_{\oplus}\) of dust available to form rocky planets around A and B, respectively.