The importance of live binary evolution in numerical simulations of binaries embedded in circumbinary discs

The shrinking of a binary orbit driven by the interaction with a gaseous circumbinary disc, initially advocated as a potential way to catalyze the binary merger, has been recently debated in the case of geometrically thick (i.e. with $H/R\gtrsim 0.1$) discs. However, a clear consensus is still missing mainly owing to numerical limitations, such as fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc. In this work, we asses the importance of evolving the binary orbit by means of hydrodynamic simulations performed with the code {\sc gizmo} in meshless-finite-mass mode. In order to model the interaction between equal mass circular binaries and their locally isothermal circumbinary discs, we enforce hyper-Lagrangian resolution inside the cavity. We find that fixing the binary orbit ultimately leads to an overestimate of the gravitational torque that the gas exerts on the binary, and in an underestimate of the torque due to the accretion of material onto the binary components. Furthermore, we find that the modulation of the accretion rate on the binary orbital period is strongly suppressed in the fixed orbit simulation, while it is clearly present in the live binary simulations. This has potential implications for the prediction of the observable periodicities in massive black hole binary candidates.