Orbital and Pulsation Analysis of 42 Heartbeat Stars Discovered in TESS Data

TL;DR

This study expands the census of heartbeat stars by reporting 42 new HBSs discovered in TESS data and constraining their orbital properties using the K95$^+$ and PHOEBE models. It detects tidally excited oscillations in ten systems, deriving pulsation phases and modal identifications dominated by $l=2$ modes with $m=0$ or $\,\pm2$, while noting a few departures that hint at nonadiabatic or traveling-wave behavior. The paper also identifies a $\\gamma$ Dor$-$type pulsator among the sample and discusses the eccentricity–period relation and the location of HBSs in the Hertzsprung–Russell diagram, revealing selection effects that favor hotter, more luminous systems in the TESS era. Overall, the results enhance understanding of tidal interactions in eccentric binaries and demonstrate TESS’s effectiveness for discovering massive HBSs and TEOs, with implications for binary evolution and asteroseismology.

Abstract

Heartbeat stars (HBSs) are ideal laboratories for studying the formation and evolution of binary stars in eccentric orbits and their mutual tidal interactions. We present 42 new HBSs discovered based on TESS-SPOC and QLP data. Their physical parameters have been obtained through modeling with appropriate models. Subsequently, Tidally excited oscillations (TEOs) are detected in ten systems, and their pulsation phases and modes are identified. Most pulsation phases can be explained by the dominant being spherical harmonic degree $l=2$ and azimuthal order $m=0$ or $\pm2$. For TIC 156846634, the harmonic with large deviation ($>3σ$) from the expected adiabatic phase can be expected to be a traveling wave or significantly nonadiabatic. The harmonic numbers $n$ = 16 in TIC 184413651 may not be considered as a TEO candidate due to its large deviation ($>2σ$) from the adiabatic expectation. Moreover, TIC 92828790 shows no TEOs but exhibits a significant $γ$\,Dor-type pulsation. The eccentricity-period ($e-P$) relation also shows a positive correlation between eccentricity and period, as well as the existence of orbital circularization. The Hertzsprung-Russell diagram shows that TESS HBSs have higher temperatures and greater luminosities than Kepler HBSs, possibly due to selection effects. This significantly enhances the detectability of massive HBSs and those containing TEOs.

Figures (7)

• Figure 1: Fit results of TIC 16791467. The K95$^+$ model (solid red line) fitted to the phase-folded light curve (black dots) in the top panel. The lower panel shows the residuals of the fit. The dashed red line indicates a zero point. The unit of $T_{0p}$ is TBJD=BJD$-$2,457,000. Note: The plot shows phases 0$-$2 to make the fitting results clear, and phases 1$-$2 is an exact copy of phases 0$-$1.
• Figure 2: Corner plot of the MCMC fit procedure for TIC 16791467. Red vertical lines indicate the median values of the presented histograms for each parameter. Black vertical dashed lines show 1 $\sigma$ uncertainties.
• Figure 3: The analytic procedure for TIC 184413651. Panel (a): The K95$^+$ model (solid red line) fitted to the phase-folded light curve (black dots). Panel (b): The residuals of the fit in panel (a), and the blue dots are medians in 0.01 phase bins. Panel (c): The Fourier spectrum of the residuals from panel (b). The red and blue vertical dashed lines represent the orbital harmonics n; the blue lines indicate that they are harmonic TEOs. The solid red line shows the level of S/N = 4.0. Panel (d): The pulsation phases of the TEOs. The gray, light blue, and green strips indicate the $m=0,+2$, and $-2$ modes, respectively. The phases of the $m=+2,-2$ modes are shown next to the strips. The width of the strips results from the uncertainties of $T_{0p}$ and $\omega$. The blue circle represents a TEO with its harmonic number $n$; the error bar corresponds to the uncertainty of its phase. In this system, the $n$ = 9 harmonic is close to $m=0$ mode. The $n$ = 16 harmonic shows a large deviation ($>2\sigma$) from the adiabatic expectations. Given its lower amplitude, it may not be considered as a TEO candidate.
• Figure 4: The analytic procedure for TIC 92828790. Panel (a1): The K95$^+$ model (solid red line) fitted to the phase-folded light curve (black dots). Panel (a2): The residuals of the fit in panel (a1). The blue dots are medians in 0.01 phase bins. Panel (b1): The frequency spectrum of the light curve shown in panel (a1). Panel (b2): The frequency spectrum of the residuals shown in panel (a2). Panels (b1) and (b2): The solid red line shows the amplitudes at $S/N$ = 4.0 as a function of frequency; the red vertical dashed lines represent the orbital harmonics $n$.
• Figure 5: The eccentricity-period ($e-P$) diagram. Red stars indicate the TESS HBSs in this work. Orange pluses indicate the TESS HBSs from 2021AA...647A..12K2024ApJ...974..278L2024MNRAS.534..281L. Blue circles represent the positions of the Kepler HBSs reported in 2023ApJS..266...28L. The two black dashed curves mark an eccentricity-period relation of $e=\sqrt{1-(P_0/P)^{2/3}}$, which is the expected functional form assuming conservation of angular momentum. The two curves use $P_0$ of 2 and 12 days.