| 其他摘要 | Heartbeat stars (HBSs) are a class of detached binary systems in highly eccentric orbits. During the periastron passage, the strong tidal interaction due to the close distance will cause the ellipsoidal distortion of the components, and produce strong mutual irradiation effects and Doppler booming and other effects, which will make the luminosity of the system suddenly change, and the shape of its light curve is similar to the ”heartbeat” in the electrocardiogram. Thus, their name derives from the presence of a heartbeat signature in their light curves. HBSs are ideal laboratories to study the formation and evolution of binary stars in eccentric orbits and to explore the internal structural changes of components under strong tidal action; it is also a class of important objects to study the properties of tidally excited oscillations (TEOs) and to search for special celestial bodies, etc. Therefore, they are important and valuable in scientific research. Although theoretical work on HBSs is extensive, they have not been detected by ground-based telescopes due to the small amplitude and short duration of the light variations. It was not until the release of long-period, high-precision photometric data from the Kepler space telescope that the tiny changes in the light curves were discovered and began to be studied. In this paper, more than 100 HBSs have been analyzed and studied, mainly using Kepler photometric data and stellar atmospheric parameters from the LAMOST and Gaia surveys. A set of effective approaches to fit the light curve of all types of HBSs (eclipsed or not) has been compiled. A Fourier spectrum analysis program has been developed to support the automatic analysis of large volume data, to analyze the TEOs and their phases and modes, and to extract the frequencies in the Fourier spectrum. The main research results of this thesis are as follows: 153 HBSs without eclipsing in Kirk et al. catalog have been modeled by using the K95+ model based on the Markov Chain Monte Carlo (MCMC) method. Orbital parameters of more than 100 systems are obtained for the first time. An empirical equation has been proposed for the relationship between the upper limit of eccentricity and the orbital period in systems with orbital periods less than 10 days based on the eccentricity-period (e−P) relation. The e−P relation also reveals the existence of orbital circularization in HBSs. In this work we have compiled a set of well-established fitting methods that can be used to fit HBSs without eclipsing.The Fourier spectra of these systems are further analyzed based on the previous work. The TEOs of 21 HBSs have been newly analyzed and presented. Twelve of these HBSs show prominent TEOs (signal-to-noise ratio of the harmonics 𝑆/𝑁 ≥ 10). The relation between the orbital eccentricities and the harmonic number of the TEOs shows a positive correlation. Furthermore, the distribution of HBSs with TEOs in the Hertzsprung-Russell (H-R) diagram shows that TEOs are more visible in hot stars with surface effective temperatures 𝑇 ≳ 6500 K. The relation between the orbital periods and the harmonic number also shows a positive correlation. The relatively short period corresponds to strong tidal forces that can more easily form TEOs. A set of analytic procedures to examine the harmonic and anharmonic TEOs in their Fourier spectra has been compiled.Based on the orbital parameters of candidate TEOs from the two previous works, the pulsation phases and amplitudes of TEOs in fourteen Kepler HBSs have been determined. The pulsation phases of most systems can be explained by the dominant 𝑙 = 2, 𝑚 = 0, or ±2 spherical harmonic, assuming that the spin and orbital axes are aligned and that the pulsations are adiabatic and standing waves. The large deviations occur in two systems, which can be explained by the spin-orbit misalignment. Other large deviations in five other systems suggest that these harmonics should not be considered TEO candidates, or that they should be expected to be travelling waves rather than standing waves. In addition, we suggest that the apsidal motion could cause large deviations in TEO phases from theoretical values.The eclipsing HBS KIC 7914906 with hybrid pulsations has been studied. The parameters, including orbital period, eccentricity, inclination, argument of periastron, mass ratio, effective temperatures and relative radii, are derived based on the PHOEBE model and MCMC method. The secondary component has a lower mass and a larger radius, indicating that it may have evolved off the main sequence. The Fourier spectral analysis shows that the object exhibits the TEOs, 𝛾 Dor and 𝛿 Sct hybrid pulsations. We also examine the rotation period of one component. In this work we have compiled the fitting methods for eclipsing HBSs. |
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