Theoretical investigation of the occurrence of tidally excited oscillations in massive eccentric binary systems

Astronomical Institute, University of Wrocław, Kopernika 11, 51-622 Wrocław, Poland
e-mail: kolaczek@astro.uni.wroc.pl

Received: 16 October 2022
Accepted: 31 December 2022

Abstract

Context. Massive and intermediate-mass stars reside in binary systems at a much higher rate than low-mass stars. At the same time, binaries containing massive main-sequence (MS) component(s) are often characterised by eccentric orbits, and can therefore be observed as eccentric ellipsoidal variables (EEVs). The orbital phase-dependent tidal potential acting on the components of EEVs can induce tidally excited oscillations (TEOs), which can affect the evolution of the binary system.

Aims. We investigate how the history of resonances between the eigenmode spectra of the EEV components and the tidal forcing frequencies depends on the initial parameters of the system, limiting our study to the MS. Each resonance is a potential source of TEO. We are particularly interested in the total number of resonances, their average rate of occurrence, and their distribution in time.

Methods. We synthesised 20 000 evolutionary models of the EEVs across the MS using Modules for Experiments in Stellar Astrophysics (MESA) software for stellar structure and evolution. We considered a range of masses of the primary component from 5 to 30 M_⊙. Later, using the GYRE stellar non-adiabatic oscillations code, we calculated the eigenfrequencies for each model recorded by MESA. We focused only on the l = 2, m = 0, +2 modes, which are suspected of being dominant TEOs. Knowing the temporal changes in the orbital parameters of simulated EEVs and the changes in the eigenfrequency spectra for both components, we were able to determine so-called resonance curves, which describe the overall chance of a resonance occurring and therefore of a TEO occurring. We analysed the resonance curves by constructing basic statistics for them and analysing their morphology using machine learning methods, including the Uniform Manifold Approximation and Projection (UMAP) tool.

Results. The EEV resonance curves from our sample are characterised by a striking diversity, including the occurrence of exceptionally long resonances or the absence of resonances for long evolutionary times. We find that the total number of resonances encountered by components in the MS phase ranges from ∼10² to ∼10³, mostly depending on the initial eccentricity. We also noticed that the average rate of resonances is about an order of magnitude higher (∼10² Myr⁻¹) for the most massive components in the assumed range than for EEVs with intermediate-mass stars (∼10¹ Myr⁻¹). The distribution of resonances over time is strongly inhomogeneous, and its shape depends mainly on whether the system is able to circularise its orbit before the primary component reaches the terminal-age main sequence (TAMS). Both components may be subject to increased resonance rates as they approach the TAMS. Thanks to the low-dimensional UMAP embeddings performed for the resonance curves, we argue that their morphology changes smoothly across the resulting manifold for different initial EEV conditions. The structure of the embeddings allowed us to explore the whole space of resonance curves in terms of their morphology and to isolate some extreme cases.

Conclusions. Resonances between tidal forcing frequencies and stellar eigenfrequencies cannot be considered rare events for EEVs with massive and intermediate-mass MS stars. On average, we should observe TEOs more frequently in EEVs that contain massive components than those that contain intermediate-mass ones. The TEOs will be particularly well pronounced for EEVs whose component(s) are close to the TAMS, which calls for observational verification. Given the total number of resonances and their rates, TEOs may play an important role in the transport of angular momentum within massive and intermediate-mass stars (mainly near the TAMS).