Resonance locking and tidal evolution in rotating γ-Doradus binaries

In binary systems, studying tidal interactions is key to understanding the evolution of binary populations. From a theoretical standpoint, the primary dissipation process occurring in stars with radiative envelopes is believed to be radiative damping of high-radial-order tidally excited oscillations, which is in agreement with observations of most binary systems. However, recent studies have suggested that outside this dissipation regime, dynamical tides can act in the opposite manner (a phenomenon known as `inverse tides'), and resonance locking could significantly impact the orbital evolution of binary systems. While the basic theoretical principles behind inverse tides are understood, previous studies have primarily used simplified models that assume that resonance locking with a single oscillation mode occurs in order to assess its impact over long timescales without evaluating its feasibility or determining the orbital and rotational conditions under which locking should occur. We aim to study inverse tides and resonance locking by simultaneously including the effect of all the forcing frequencies and accounting for the effect of the rotation on the forced oscillations. We have developed an orbital evolution code that is coupled to a stellar oscillation code to compute on the fly the impact of dynamical tides on the rotational and orbital evolution of binary systems including multiple simultaneous forcing frequencies. We find that resonance locking can be stable over a long period of time and a source of long-term exchange of angular momentum for rapidly rotating stars (with rotation greater than 15% of the critical rotation). Long-term locking can increase the total angular momentum of a fast-rotating star by approximately 70$%$ during the main sequence. For slow-rotating stars, resonance locking can slow down the rotational evolution of the system over most of the main-sequence phase, even in the presence of strong tidal interactions. Inverse tides and resonance locking are mechanisms capable of preserving a signature of the initial stellar rotation in binary systems, even when non-resonant tidal interactions are expected to be strong. This mechanism efficiently drives asynchronisation in binary systems where significant discrepancies already exist between the orbital and rotational frequencies.