Resonance locking and tidal evolution in rotating γ-Doradus binaries

Abstract

In binary systems, studying tidal interactions is key to understanding the evolution of binary populations. 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. 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. 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. This mechanism efficiently drives asynchronisation in binary systems where significant discrepancies already exist between the orbital and rotational frequencies.

Figures (16)

• Figure 1: Comparison of $1/m\ \mathrm{d}\sigma/\mathrm{d}t - \left(\mathrm{d}\Omega_{\mathrm{rot}}/\mathrm{d}t\right)_{\mathrm{evo}}$ (red curve) with $\left(\mathrm{d}\Omega_{\mathrm{rot}}/\mathrm{d}t\right)_{\mathrm{tides}}$ for a retrograde mode ($\ell=2$, $m=2$, $k=-2$, $n=30$, $\Omega{\mathrm{rot}}=0.2\ \Omega_{\mathrm{crit}}$; left) and a prograde mode ($\ell=2$, $m=-2$, $k=2$, $n=20$, $\Omega_{\mathrm{rot}}=0.05\ \Omega_{\mathrm{crit}}$; right). Forcing frequencies have been normalised by the dynamical timescale, $\tau_{\mathrm{dyn}}$. Blue segments represent unstable mode regions; orange curves represent stable regions. Arrows show the direction of mode evolution and spin trends. Red dots mark resonance locking points. Animated versions of this figure illustrating the various possible initial configurations and outcomes are provided in \ref{['apdx_animation_locking']}.
• Figure 2: Illustration of the principle behind the multi-layer filter system used to compute the dynamical tides with the on-the-fly solving method for a $\gamma$-Doradus star with a mass of $1.5M_\odot$.
• Figure 3: Evolution of the orbital frequency (top panel), eccentricity (middle panel), and stellar angular momentum (bottom panel) as a function of system age obtained with TREMOR. Two initial stellar rotation rates were considered: $\Omega_{\mathrm{rot}}/\Omega_{\mathrm{crit}} = 0.2$ and $0.3$. The initial eccentricity was set to $0.1$, and the initial orbital period of the system is $3.14$ days.
• Figure 4: Evolution of the surface rotation velocity (top panel), the stellar rotation rate normalised by the critical rotation rate (middle panel), and the stellar angular momentum (bottom panel) as a function of system age, as computed with TREMOR. Two initial stellar rotation rates are considered: $\Omega_{\mathrm{rot}}/\Omega_{\mathrm{crit}} = 0.2$ and $0.3$. The initial eccentricity was set to 0.1, and the initial orbital period is 3.14 days. The black track corresponds to the evolution predicted by single-star models.
• Figure 5: Evolution of the surface rotation velocity (top panel), the stellar rotation rate over the critatical rotation rate (middle panel), and stellar angular momentum (bottom panel) as a function of system age obtained with TREMOR. Two initial stellar rotation rates were considered: $\Omega_{\mathrm{rot}}/\Omega_{\mathrm{crit}} = 0.2$ and $0.3$. The initial eccentricity was set to $0.55$, and the initial orbital period of the system is $12.57$ days. The black track corresponds to the evolution predicted by single stars models.