An Empirical Fit for Viscoelastic Simulations of Tertiary Tides

Abstract

Tertiary tides (TTs), or the continuous tidal distortion of the tertiary in a hierarchical triple system, can extract energy from the inner binary, inducing within it a proclivity to merge. Despite previous work on the subject, which established that it is significant for certain close triple systems, it is still not a well-understood process. A portion of our ignorance in this regard stems from our inability to integrate a simulation of this phenomenon into conventional stellar evolution codes, since full calculations of these tidal interactions are computationally expensive on stellar evolution timescales. Thus, to attain a better understanding of how these TTs act on longer timescales, an empirical expression of its effects as a function of parameters of the triple system involved is required. In our work, we evaluate the rate at which TTs extract energy from the inner binary within a series of constructed hierarchical triple systems under varying parameters, and study the rate at which the inner binary orbital separation shrinks as a function of those parameters. We find that this rate varies little with the absolute values of the masses of the three component objects, but is very sensitive to the mass ratio of the inner binary $q$, the tertiary radius $R_3$, the inner binary orbital separation $a_1$, the outer orbital separation $a_2$, and the viscoelastic relaxation time of the tertiary $\tau$. More specifically, we find that the percentage by which $a_1$ shrinks per unit time can be reasonably approximated by (1/$a_1$)(d$a_1$/d$t$)=$\left(2.22\times 10^{-8}{\mathrm{yrs}}^{-1}\right)4q{\left(1+q\right)}^{-2}(R_3/100{\mathrm{R}}_{\odot }{)}^{5.2}(a_1/0.2\mathrm{AU}{)}^{4.8}(a_2/2\mathrm{AU}{)}^{-10.2}$ $(\tau /0.534\mathrm{yrs}{)}^{-1.0}$. We also provide tests of how precise this fitting function is.

arXiv comment8 pages, 15 figures, 3 tables

References in corpus (12)

• Evolution of binary stars and the effect of tides on binary populations
• MESA Isochrones and Stellar Tracks (MIST) 0: Methods for the construction of stellar isochrones
• Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity
• The Eccentric Kozai-Lidov Effect and Its Applications
• The Equilibrium-Tide Model for Tidal Friction
• Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology
• Dynamical masses, absolute radii and 3D orbits of the triply eclipsing star HD 181068 from Kepler photometry
• On the equilibrium figure of close-in planets and satellites
• Secular and tidal evolution of circumbinary systems
• Tidally Induced Oscillations and Orbital Decay in Compact Triple-Star Systems
• Tidal Love numbers and moment-Love relations of polytropic stars
• Numerical Modelling of Tertiary Tides

Cited by in corpus (5)

• Multiple Stellar Evolution: a population synthesis algorithm to model the stellar, binary, and dynamical evolution of multiple-star systems
• A Catalogue of Potential Post Common Envelope Binaries
• Compact Binary Coalescences: Astrophysical Processes and Lessons Learned
• Stellar Triples as a Source for Ba Stars
• BH-BH mergers with & without EM counterpart: A model for stable tertiary mass transfer in hierarchical triple systems