Modern tidal interaction models for rapid binary population synthesis: I. Methods

TL;DR

This paper delivers a unified, frequency- and structure-aware tidal prescription implemented in COMPAS to enable rapid binary population synthesis. By combining equilibrium tides (viscous dissipation in convective envelopes) with dynamical tides from internal gravity waves and inertial waves, the authors capture strong, structure-dependent dissipation that can differ by up to several orders of magnitude from traditional Z77-type prescriptions. The fiducial model shows 1–2 order-of-magnitude enhancements in equilibrium tides and 1–7 orders of magnitude enhancements in dynamical tides for many evolutionary stages, yielding more efficient circularization and synchronization in several regimes while preserving consistency with detailed simulations within an order of magnitude. This framework paves the way for population-level predictions of orbital evolution, spins, and gravitational-wave progenitor properties; a follow-up paper applies it to compact-object binaries and their merger rates.

Abstract

In this work, we present an updated prescription of contemporary tidal dissipation theory adapted for rapid binary population synthesis. Our simplified expressions encode the dependence of tidal dissipation on stellar structure, stratification, and tidal forcing frequency, while remaining computationally efficient. We implement these prescriptions in the rapid population synthesis code COMPAS, and demonstrate the self-consistent coupling of tides with stellar evolution and binary properties such as orbital periods, spins, and eccentricities for several representative binary systems. When compared with commonly used tidal prescriptions, our equilibrium tidal dissipation efficiencies can be stronger by 1-2 orders of magnitude for low mass main sequence and giant type stars, and dynamical tides can be stronger by 1-7 orders of magnitude due to the explicit dependence on internal stellar structure and the presence of inertial wave dissipation. Despite our simplistic approach, our models agree with detailed stellar simulations to within an order of magnitude across tidal dissipation mechanisms.

Figures (11)

• Figure 1: Overview of tidal effects considered in this work, for stars with various internal structures. Convective envelopes may experience a combination of equilibrium tides from viscous dissipation, dynamical tides from internal gravity wave (IGW) dissipation, and dynamical tides from inertial wave (IW) dissipation. Boundaries between radiative and convective zones may excite dynamical tides from IGWs and IWs, which are dissipated in the radiative and convective zones of the star, respectively. In our models, convective cores do not experience tidal dissipation.
• Figure 2: Evolutionary tracks of $e$ and $P_{\rm orb}$ under equilibrium tides for $0.3M_\odot+0.3M_\odot$ binaries, over a grid of initial orbital periods and initial eccentricities. Each binary is initialized on a grid in the $P_{\rm orb}-e$ plane, and we plot the orbital period and eccentricity of each binary for every time step in COMPAS. The colors depict the age of each evolutionary snapshot in years. The binaries are only evolved up to 14 Gyr, approximately the age of the Universe. The top panel shows the period-eccentricity evolution under our fiducial tidal model, and the bottom panel shows evolution under the Z77 model. None of the binaries evolve meaningfully in this plane over their simulated lifetimes with the Z77 model.
• Figure 3: Stellar and tidal evolution for a 0.3 $M_\odot$ + 0.3 $M_\odot$ binary with $P_{\rm orb, ZAMS}~=~2$ days and $e_{\rm ZAMS}=0.1$. The binary is simulated for 14 Gyr, the approximate age of the Universe.
• Figure 4: Time evolution of $e$ and $P_{\rm orb}$ for $1M_\odot+1M_\odot$ binaries over a grid of initial orbital periods and initial eccentricities, with our fiducial tides model (top panel) and the Z77 tides model (bottom panel). Each binary is initiated at a grid point, and the colors depict the age of each simulation snapshot in yr. The binaries are only evolved up to their MS lifetimes (approximately 10 Gyr) in this section.
• Figure 5: Stellar and tidal evolution for a 1 $M_\odot$ + 1 $M_\odot$ binary with $P_{\rm orb, ZAMS}$=10 days and $e_{\rm ZAMS}=0.5$. The binary is simulated until the end of MS, at roughly 10 Gyr.