Time evolution of the binary semi-major axis for two additional preliminary simulations with H/R = 0.07 (black solid line) and H/R = 0.1 (red dashed line), both with α = 0.1 and N_p = 10⁶ (and otherwise the same parameters as the simulations presented in Sect. 3). Both of these cases show the binary orbit decaying with time, suggesting that the critical value of H/R that divides binary expansion or contraction is larger than the value of 0.04 reported by Tiede et al. (2020) when α ≈ 0.1, and is also parameter dependent (see Sects. 2 and 4). For the simulated parameters, these simulations suggest that the critical H/R is ≈0.1 − 0.2, as indicated by the small (but still negative) da/dt for the H/R = 0.1 case seen at t ≳ 100t_b.