Fig. 1
From: Orbital evolution of a circumbinary planet in a gaseous disk
Semi-major axis \(a_{\mathrm {p}}\) and critical radius \(r_{\mathrm {crit}}\) calculated using Eq. (1) (Quarles et al. 2018) in observed circumbinary planet systems (except for Kepler-47c, and Kepler-47d, which are not the innermost planets of the system). The solid blue line represents \(a_{\mathrm {p}} = r_{\mathrm {crit}}\) and the area under this line, which is colored in purple, represents dynamically unstable area. Most of the observed planets’ semi-major axes are lined up just above the critical radius