Tidally trapped pulsations in binary stars

Abstract

A new class of pulsating binary stars was recently discovered, whose pulsation amplitudes are strongly modulated with orbital phase. Stars in close binaries are tidally distorted, so we examine how a star’s tidally induced asphericity affects its oscillation mode frequencies and eigenfunctions. We explain the pulsation amplitude modulation via tidal mode coupling such that the pulsations are effectively confined to certain regions of the star, e.g., the tidal pole or the tidal equator. In addition to a rigorous mathematical formalism to compute this coupling, we provide a more intuitive semi-analytic description of the process. We discuss three resulting effects: 1. Tidal alignment, i.e., the alignment of oscillation modes about the tidal axis rather than the rotation axis; 2. Tidal trapping, e.g., the confinement of oscillations near the tidal poles or the tidal equator; 3. Tidal amplification, i.e., increased flux perturbations near the tidal poles where acoustic modes can propagate closer to the surface of the star. Together, these phenomena can account for the pulsation amplitude and phase modulation of the recently discovered class of “tidally tilted pulsators.” We compare our theory to the three tidally tilted pulsators HD 74423, CO Cam, and TIC 63328020, finding that tidally trapped modes that are axisymmetric about the tidal axis can largely explain the first two, while a non-axisymmetric tidally aligned mode is present in the latter. Finally, we discuss implications and limitations of the theory, and we make predictions for the many new tidally tilted pulsators likely to be discovered in the near future.

GG Carinae: discovery of orbital-phase-dependent 1.583-day periodicities in the B[e] supergiant binary

“…Kurtz et al (2020) find a similar result in CO Cam, finding that four modes are trapped by the tidal potential of the companion. Fuller et al (2020) presents evidence of a similar process occurring in TIC 63328020. The authors explain the amplitude modulation in these systems as being due to the pulsation axis of the variable component to be aligned with the line of apsis of the binary which cause the pulsations to have a larger amplitude on one hemisphere of the star, either the hemisphere facing towards or away from the companion.…”

A tidally tilted sectoral dipole pulsation mode in the eclipsing binary TIC 63328020

“…Both HD 74423 and CO Cam were designated as 'single-sided pulsators' because they show enhanced pulsation amplitude on the L 1 side of the star facing the secondary, as explained by Fuller et al (2020). In this paper, we report the discovery of the third single-sided pulsator, TIC 63328020, which is different from the two systems studied earlier.…”

“…In reality, the tidal distortion induces coupling between modes of different spherical degree l, modifying the perturbed flux distribution at the surface, and sometimes 'tidally trapping' the oscillations on one side of the star. The theoretical groundwork for this type of analysis was laid by Fuller et al (2020).…”

Asteroseismology of Close Binary Stars: Tides and Mass Transfer

“…Also some important factors have not been included. For example, detailed calculations in Fuller et al (2020) only considered the effect of static tidal distortion on the mode eigenfrequencies and eigenfunctions and ignored the effect of Coriolis force. Close binaries with circular/synchronized orbits are easier to follow up observationally.…”

“…Subsequent discoveries include CO Cam by Kurtz et al (2020) and TIC 63328020 by Rappaport et al (2021). Fuller et al (2020) used the more general operatorperturbation method in Dahlen and Tromp (1998) and modeled the stellar response to the static tides by decomposing it into free-oscillation eigenfunctions. Thus, they obtained not only tidally perturbed eigenfrequencies, but also eigenfunctions.…”