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We examine the reasons for discrepancies between two alternative approaches to modeling small-amplitude tides in binary systems. The direct solution (DS) approach solves the governing differential equations and boundary conditions directly, while the modal decomposition (MD) approach relies on a normal-mode expansion. Applied to a model for the primary star in the heartbeat system KOI-54, the two approaches predict quite different behavior of the secular tidal torque. The MD approach exhibits the pseudosynchronization phenomenon, where the torque due to the equilibrium tide changes sign at a single, well-defined, and theoretically predicted stellar rotation rate. The DS approach instead shows “blurred” pseudosynchronization, where positive and negative torques intermingle over a range of rotation rates. We trace a major source of these differences to an incorrect damping coefficient in the profile functions describing the frequency dependence of the MD expansion coefficients. With this error corrected, some differences between the approaches remain; however, both are in agreement that pseudosynchronization is blurred in the KOI-54 system. Our findings generalize to any type of star for which the tidal damping depends explicitly or implicitly on the forcing frequency.

We describe new functionality in the GYRE stellar oscillation code for modeling tides in binary systems. Using a multipolar expansion in space and a Fourier-series expansion in time, we decompose the tidal potential into a superposition of partial tidal potentials. The equations governing the small-amplitude response of a spherical star to an individual partial potential are the linear, non-radial, nonadiabatic oscillation equations with an extra inhomogeneous forcing term. We introduce a new executable,gyre_tides, that directly solves these equations within the GYRE numerical framework. Applying this to selected problems, we find general agreement with results in the published literature but also uncover some differences between our direct solution methodology and the modal decomposition approach adopted by many authors. In its present formgyre_tidescan model equilibrium and dynamical tides of aligned binaries in which radiative diffusion dominates the tidal dissipation (typically, intermediate- and high-mass stars on the main sequence). Milestones for future development include incorporation of other dissipation processes, spin–orbit misalignment, and the Coriolis force arising from rotation.

We present 18 yr of OGLE photometry together with spectra obtained over 12 yr revealing that the early Oe star AzV 493 shows strong photometric (ΔI< 1.2 mag) and spectroscopic variability with a dominant, 14.6 yr pattern and ∼40 day oscillations. We estimate the stellar parametersT_eff= 42,000 K,$\log L/L_{\odot }=5.83\pm 0.15$,M/M_⊙= 50 ± 9, andvsini= 370 ± 40 km s⁻¹. Direct spectroscopic evidence shows episodes of both gas ejection and infall. There is no X-ray detection, and it is likely a runaway star. The star AzV 493 may have an unseen companion on a highly eccentric (e> 0.93) orbit. We propose that close interaction at periastron excites ejection of the decretion disk, whose variable emission-line spectrum suggests separate inner and outer components, with an optically thick outer component obscuring both the stellar photosphere and the emission-line spectrum of the inner disk at early phases in the photometric cycle. It is plausible that AzV 493’s mass and rotation have been enhanced by binary interaction followed by the core-collapse supernova explosion of the companion, which now could be either a black hole or a neutron star. This system in the Small Magellanic Cloud can potentially shed light on OBe decretion disk formation and evolution, massive binary evolution, and compact binary progenitors.