# Alpha Centauri: Disc Dynamics, Planet Stability, Detectability
## 3 Stability of Planets in Alpha Centauri  
We now supposed that planets have formed in Alpha Cen, and we employed numerical tools to evaluate the stability of these bodies within the triple stellar system. Such planets are subject to intricate perturbative interactions that can challenge their long-term stability. Although the process of planetary formation in this kind of system remains not fully understood, our preceding sections have demonstrated that substantial portions of  
Figure 4: Gas column density of the discs around A and B after 5 binary orbital periods. The disc contents are split into pristine (**left column**) and alien captured material (**right column**). Top left (**bottom left**) panel shows the material that was around A (B) initially. Top right (**bottom right**) panel shows the alien captured material by A (B) from B (A). The captured (alien) material is shown to be well distributed and mixed with the disc pristine material. The red dots represent the central stars.  
Figure 3: Disc surface density profiles of the alien material captured around A from the disc around B (**left**) and captured around B from the disc around A (**right**)—after 5 binary orbital periods.  
circumstellar disc material could be available for planetary formation, thus potentially favouring the emergence of low-mass planets. In this section, we shall delve into the dynamic stability of these systems by employing the Mean Exponential Growth of Nearby Orbits (MEGNO) stability parameter (see, e.g., [25]).  
The MEGNO parameter is a powerful numerical tool for assessing the stability of N-body gravitational systems. It quantifies the exponential growth of nearby orbits in phase space over a specified time span. In essence, MEGNO gauges the rate at which adjacent trajectories in phase space diverge over time, thereby offering a quantitative metric for orbital stability. The MEGNO algorithm integrates the equations of motion for a set of closely aligned initial conditions and computes their rate of divergence. A MEGNO value approaching two corresponds to a regular orbit and, hence, a stable system, whereas values substantially larger than two imply chaotic orbits and potentially unstable systems. In this work, we used the MEGNO implementation available in the REBOUND package [26; 27; 28].  
Our experimental approach was as follows: first, we placed massless test particles uniformly distributed in semimajor axis and eccentricity around each of the stars, and we evaluated the MEGNO parameter. This allowed us to identify the system's allowed and forbidden resonant regions. Then, we placed particles with one Earth mass to ascertain which regions remained viable for hosting Earth-like planets. Last, we introduced individual planets with masses which followed the observed rocky planet mass distribution in our Solar System. By doing so, we created planet analogues of the inner Solar System but within a triple star environment. It is worth mentioning that planets in triple star systems can have stable inclined orbits, e.g., [29]. In this work, however, we limited ourselves to the coplanar case (i.e., the planet is coplanar with the inner binary system). Incidentally, this configuration corresponds to more stable circumstellar orbits in double and triple systems.