Have Radial Velocity Surveys Missed Any Planets?

Sammanfattning: The project was aimed at numerically assessing exoplanetary systems to distinguish their capabilities of hosting additional planets. The shortcomings of the radial velocity method sometimes causes hindrance in the detection of terrestrial planets. Although modern spectrometers have evolved and improved drastically, the process of distinguishing signals from smaller planets is still difficult and cumbersome. Besides the technical difficulties, the geometry of the system is also of paramount importance in the detection process. For these reasons, we resort to other means to evaluate the potential for the existence of additional planets, especially in systems with large gaps between their known planets. Computer simulations allow us to study such systems in great detail. We input parameters of a hypothetical planet (Earth-mass in our case) for a given range of orbits and eccentricities where we expect to find our planet, along with the other known bodies, in the simulation program, based on the orbital dynamics, the program returns an easy-to-read stability map of the system. We restrict ourselves to the habitable zones of the systems for the range of orbits. The simulations were run using the $N$-body integration software package REBOUND. The WHFast integrator combined with the chaos indicator, the mean exponential growth factor of nearby orbits (MEGNO), ran the simulations over a specified time period and returned the MEGNO values which were used to plot the so-called stability maps. We looked at a total of 15 systems out of which two were found to be almost completely stable for the given initial conditions while four were found to be completely or close to being completely unstable. The rest of the eight systems had regions of both stability and instability that at times were due to rather interesting phenomena, co-orbital arrangements or suspected mean-motion orbital resonance for example. We looked more closely at HD 219828, HD 37605, HIP 67851 and Teegarden's Star. HD 219828 had a large gap between the two known planets, but due to the highly elliptical orbit of its known outer planet, which engulfed the orbital range of the hypothetical planet, it was found to be incapable of hosting an additional planet. HD 37605 was suspected to demonstrate mean-motion orbital resonance after the introduction of the hypothetical planet, though the studies did not confirm the hypothesis. HIP 67851 and Teegarden's Star were both suspected to show co-orbital configurations in the presence of the hypothetical planet. The hypothetical planet in HIP 67851 was found to be a quasi satellite of its known outer planet, while Teegarden's Star c was found to be in a Trojan co-orbital arrangement with the speculative planet. The situation of Teegarden's Star b with respect to the introduced planet could not be assessed with certainty. One possibility is that it is in a horseshoe orbit with the introduced planet.