Prospects of Constraining Equilibrium Tides in Low-mass Binary Stars

Abstract The dynamical evolution of short-period low-mass binary stars (with mass M &lt; 1.5 M ⊙ , from formation to the late main sequence, and with orbital periods less than ∼10 days) is strongly influenced by tidal dissipation. This process drives orbital and rotational evolution that ultimately results in circularized orbits and rotational frequencies synchronized with the orbital frequency. Despite the fundamental role of tidal dissipation in binary evolution, constraining its magnitude (typically parameterized by the tidal quality factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">Q</mml:mi> </mml:math> ) has remained discrepant by orders of magnitude in the existing literature. Recent observational constraints from time-series photometry (e.g., Kepler, K2, TESS), as well as advances in theoretical models to incorporate a more realistic gravitational response within stellar interiors, are invigorating new optimism for resolving this long-standing problem. To investigate the prospects and limitations of constraining tidal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">Q</mml:mi> </mml:math> , we use global sensitivity analysis and simulation-based inference to examine how the initial conditions and tidal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">Q</mml:mi> </mml:math> influence the observable orbital and rotational states. Our results show that, even under the simplest and most tractable models of tides, the path toward inferring <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">Q</mml:mi> </mml:math> from individual systems is severely hampered by inherent degeneracies between tidal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">Q</mml:mi> </mml:math> and the initial conditions, even when considering the strongest possible constraints (i.e., binaries with precise masses, ages, orbital periods, eccentricities, and rotation periods). Finally, as an alternative, we discuss how population synthesis approaches may be a more promising path forward for validating tidal theories.