Refining the orbits of the planets in HD 207832

Abstract: The star, HD 207832, has two Jupiter-like planets on orbits with poorly constrained eccentricities. The eccentricities are 0.27 [sup]+0.22[/sup] [sub]-0.10[/sub] and 0.13$^{+0.18}_{-0.05}$ respectively. Notably, the two sigma error allows eccentricities up to 0.71 for one of the planets. Due to the large error bars, one aim of this project is to refine them. This is done by simulating the system for different initial eccentricities within the two sigma error bars for both of the planets. If a simulated system is shown to be unstable, the initial eccentricities used in the simulation, can not describe the observed system, HD 207832. In this project, it has been shown that the outer planet, in HD 207832, can not exceed an initial eccentricity of 0.6 in order for the system to remain stable. Furthermore, The level of chaos of the two planets, in each simulated system, is investigated with the use of Fourier analysis. A code is written which calculates the Fourier transform of the eccentricities. The code then counts the number of peaks in the spectrum which determines the level of chaos in the system. In this project, the use of Fourier analysis, to determine the level of chaos, is shown to be useful when comparing the chaos between simulations that have similar integration times. It is also shown that the outcome in each simulation is very sensitive to the fixed timestep used. It is highlighted that small changes in the timestep can change the outcome of the simulation in the sense of making a stable system, unstable. HD 207832, further, has a habitable zone, where a planet can support liquid water on its surface, that is located between the two Jupiter-like planets. Radial velocity measurements have yet not been able to detect any planet within this zone. In this project, stable orbits for a small planet, within the habitable zone, are thus searched for. This is done for the nominal system of HD 207832, and for the case when one sigma has been subtracted from the eccentricities of the two Jupiter-like planets. In this project, by the use of test particles, a few orbits are shown to be stable over at least 250 Myr in both of the simulated systems. It is thus possible that HD 207832 has a habitable planet that has not yet been detected.