Tidally tilted and triaxial pulsators: astrophysical applications

Tidally tilted and triaxial pulsators: astrophysical applications G. Handler 1R. Jayaraman 2,3 D. W. Kurtz 4,5 S. A. Rappaport 2J. Fuller 6V. Zhang 7 1Nicolaus Copernicus Astronomical Center 2MIT Kavli Institute for Astrophysics 3Cornell University 4North West University 5University of Central Lancashire 6California Institute of Technology 7Center for Astrophysics | Harvard & Smithsonian Introduction Observations by TESS [1] have demonstrated the existence of a novel class of pulsating stars in binaries. Such stars, referred to as “tidally tilted” pulsators, have their pulsation axes pulled into alignment with the tidal axis by the strong tidal forces from a close binary companion. Thus the pulsations are seen from all possible aspect angles over an orbital cycle which allows for mode identification [2], typically a rather difficult problem in asteroseismology. To date, a handful of such systems have been discovered, and we are working to understand the broader population of these systems and how they fit into the asteroseismic landscape. Tidally Tilted Pulsators The first TTP was discovered in March 2020 as part of a review of the TESS light curves by citizen surveyors. The light curve and periodogram of HD 74423 [3], which shows that the pulsations are clearly split into a multiplet (whose components are spaced by νorb) are shown in Figure 1. 2350 2352 2354 2356 2358 2360 Time (TJD) 0.98 0.99 1.00 1.01 1.02 Normalized Flux 7.5 8.0 8.5 9.0 9.5 10.0 Frequency (d 1) 0 1 2 3 4 5 6 7 8 Fourier amplitude 1e 6 1 1 orb 1+orb 12orb Figure 1. Left: A snippet of the TESS light curve for HD 74423, which shows that the pulsation amplitude reaches a maximum at the deeper ellipsoidal light minimum. Right: The tidally tilted pulsations manifest as a multiplet in the periodogram. Several TTPs have been discovered since HD 74423. Here we mention three that have highlighted unique aspects of these systems: CO Cam [4] exhibited strong tidal trapping of its pulsations, with the L1side pulsating more strongly than the L3side of the primary star. TIC 63328020 [5] was the first TTP with significant evidence of a history of prior mass transfer, with the currently-pulsating star being rejuvenated through an earlier accretion episode. HD 265435 [6], where the subdwarf B component exhibited TTPs, demonstrated that TTPs can be found in evolved stars. Properties of the TTPs were also able to constrain the system’s evolutionary stage. For TTPs, the échelle diagram—which plots the pulsation frequency against the modulus of the pulsational with respect to the orbital frequency—is a useful tool to characterize the pulsations. TTPs create ridges in échelle diagrams; see, e.g., the échelle for HD 265435 in Fig. 2. Figure 2. Échelle diagram for HD 265435, which exhibited over 25 tidally tilted modes. This is a zoom in on the full échelle to highlight a subset of these modes, which exhibit several components in their respective multiplets. Reproduced from [6]. Tri-Axial Pulsators Inspections of short-cadence TESS data revealed a class of tri-axial pulsators, which exhibit `= 1 modes about the x,y, and zaxes [7, 8], are visualized below and have been explained theoretically by [9]. Figure 3. Flux perturbations arising from dipole triaxial pulsations (adapted from [9]). In addition to newly-identified `= 1 modes, [9] also predicted quadrupole (`= 2) modes, which appear as tidally tilted standing waves (“Fuller modes” for short) on the surface of the star: Figure 4. Flux perturbations arising from quadrupole Fuller modes (adapted from [9]). We have recently reported a star, the primary of EL CMi, with two dipole trixial modes and one quadrupole Fuller mode [10]: Figure 5. Left: Folded light curve, amplitude and phase variability of a Y10xmode in EL CMi over its orbital period of ∼1 day from three TESS Sectors (red, black, blue). Middle: The same, but for the Y10ymode. Right: The same for the Y22−mode which shows four amplitude maxima and ∼πphase shifts per orbit. Figure adapted from [10]. The use of eclipse mapping The computations by [9] showed that the runs of pulsation amplitude and phase of Y10xand Y21−as well as Y10yand Y21+ over the orbit are indistinguishable. However, in the case of eclipses, the spatial filtration effect serves to resolve this degeneracy; the modes can be distinguished: Figure 6. Left: Amplitude and phase variability of a simulated Y10xand a simulated Y21−mode over the orbital period. Right: The same but for simulated Y10yand Y21+ modes, respectively. References [1] Ricker et al. 2015, JATIS 1, 014003 [6] Jayaraman et al. 2022, ApJ 928, L14 [2] Reed et al. 2005, ApJ 634, 602 [7] Zhang et al. 2024, MNRAS 528, 3378 [3] Handler et al. 2020, NatAs 4, 684 [8] Jayaraman et al. 2024, ApJ 975, 121 [4] Kurtz et al. 2020, MNRAS 494, 5118 [9] Fuller et al. 2025, ApJ 979, 80 [5] Rappaport et al. 2021, MNRAS 503, 254 [10] Handler et al., submitted to A&A TASC 9 / KASC 16 Workshop – ISTA Klosterneuburg July 7–11, 2025 ger[email protected]