# Alpha Centauri: Disc Dynamics, Planet Stability, Detectability
## 4 Detectability of Planets in Alpha Centauri
### Radial Velocity  
If we assume that hypothetical planets around A and B are coplanar with the binary orbital plane, then the inclination of the binary orbital plane (of about 79 deg with respect to the sky) significantly lowers the probability of planetary transits. Here, we are mainly interested in exoplanets in the binary Alpha Cen AB. Therefore, in this section, we assess the detectability of inner Solar System analogues around A and B (see Section 3.3) through radial velocity methods. Our goal is to compare our synthetic RV curves against the capabilities of current detectors such as HARPS2, NEID3, and ESPRESSO4.  
Footnote 1: [[https://www.esa.org/en/lat/](https://www.esa.org/en/lat/)]([https://www.esa.org/en/lat/](https://www.esa.org/en/lat/))  
Figure 10 summarises the results obtained from simulating the triple system with REBOUND over two periods of the inner binary, where each star has the four planets of the inner Solar System on S-type orbits. In the upper panels of the figure, we show the projection of each system on the plane of the sky. These projections were made using the same angles as in Section 2.1. In the lower panels, we plot the radial component of the velocity for each star (from left to right: A, B, and C). At first glance, there appear to be no significant deviations in the radial velocity signals due to the presence of planets.  
Figure 9: Maps of dynamical stability assessed using MEGNO values for the semimajor axis (\(a_{p}\)) and planetary mass (\(m_{p}\)) space over a period of 100,000 years. Regions indicating dynamical stability are highlighted in yellow.  
We therefore conducted an additional simulation, which was similar to the previous integration but without including any planets. This allowed us to subtract one signal to the other, for each star, in order to reveal the planetary features. Figure 11 presents the outcome of these simulations, where the bottom row shows the residual signal in the radial velocity curves. In addition, we plotted the lower limits in resolution corresponding to NEID and ESPRESSO spectrometers. The corresponding value for HARPS is not shown, as its value of 1 m/s is outside the scale presented in these graphs. From this analysis, we infer that S-type configurations analogous to the inner Solar System could in principle be detected (around A, B, and C) using NEID and ESPRESSO. We note however that the radial velocity signals are remarkably weak, with their semiamplitudes being mostly below 1 m/s, which renders their detection feasible but extremely challenging.  
Figure 11: Temporal evolution of the radial velocity for each star in the Alpha Cen triple stellar system: A (**left**), B (**centre**), and C (**right**). The upper panels display the system’s evolution with orbiting planets. The middle panel presents the star’s radial velocity in the absence of planets, while the lower panel shows the result of subtracting the two aforementioned signals. The lowermost panels also illustrate the minimum radial velocity resolutions achievable by the HARPS, NEID, and ESPRESSO spectrometers.  
Figure 10: Each column depicts the evolution of the system with its planets over two periods of the binary, projected onto the plane of the sky (**upper panels**), and the estimated radial velocity of the system’s three stars (**lower panels**) In the upper panels, the planets are represented by coloured dots and Alpha Cen A and B by star symbols.