Hot Jupiter formation in dense stellar clusters: A Monte Carlo model applied to 47 Tucanae

Abstract

We study the efficiency of high-e migration as a pathway for Hot Jupiter formation in the dense globular cluster 47 Tuc. Gravitational N-body simulations are performed to investigate the orbital evolution of star-planet systems due to dynamical stellar perturbations. Planetary systems that have been scattered into orbits of sufficiently high eccentricity can undergo tidal circularisation, with Hot Jupiter formation being one possible stopping condition. We also account for the possibility of (i) ionisation due to high-energy encounters, (ii) tidal disruption of the planet by tidal forces inside the Roche limit and (iii) Warm Jupiter formation. The orbital evolution of a population of cold Jupiter progenitors, with initial semi-major axes between 1-30 au, is simulated over 12 Gyr using a simplified dynamical model of 47 Tuc. Our computational treatment of dynamical encounters yields an overall HJ occurrence rate of F_HJ = 5.9 x 10^-4 per cluster star (a 51 per cent enhancement relative to the analytic baseline). The probability of Hot Jupiter formation is highest in the core and falls off steeply beyond a few parsecs from the centre of the cluster, where the stellar density is too low to drive efficient eccentricity diffusion. The code can be found here: https://github.com/James-Wirth/HotJupiter.