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Register a new userListening to the heartbeat: Tidal Asteroseismology in action
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Zhao Guo
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We briefly review the current status of the study of tidally excited oscillations (TEOs) in heartbeat binary stars. Particular attention is paid to correctly extracting the TEOs when the Fourier spectrum also contains other types of pulsations and variabilities. We then focus on the theoretical modeling of the TEO amplitudes and phases. Pulsation amplitude can be modeled by a statistical approach, and pulsation phases can help to identify the azimuthal number m of pulsation modes. We verify the results by an ensemble study of ten systems. We discuss some future prospects, including the secular evolution and the non-linear effect of TEOs.
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This paper summarizes the project work on asteroseismology at the ERASMUS+ GATE 2020 Summer school on space satellite data. The aim was to do a global asteroseismic analysis of KIC 5006817 and quantify its stellar properties using the high-quality, state of the art space missions data. We employed the aperture photometry to analyze the data from the Kepler space telescope and the Transiting Exoplanet Survey Satellite (TESS). Using the lightkurve Python package, we have derived the asteroseismic parameters and calculated the stellar parameters using the scaling relations. Our analysis of KIC 5006817 confirmed its classification as a heartbeat binary. The rich oscillation spectrum facilitate estimating power excess ($ u_{rm max}$) at 145.50$pm$0.50 $mu$Hz and large frequency separation ($Delta u$) to be 11.63$pm$0.10 $mu$Hz. Our results showed that the primary component is a low-luminosity, red-giant branch star with a mass, radius, surface gravity, and luminosity of 1.53$pm$0.07 M$_odot$, 5.91$pm$0.12 R$_odot$, 3.08$pm$0.01 dex, and 19.66$pm$0.73 L$_odot$, respectively. The orbital period of the system is 94.83$pm$0.05 d.
Apsidal motion is a gradual shift in the position of periastron. The impact of dynamic tides on apsidal motion has long been debated, because the contribution could not be quantified due to the lack of high quality observations. KIC 4544587 with tidally excited oscillations has been observed by textit{Kepler} high-precision photometric data based on long time baseline and short-cadence schema. In this paper, we compute the rate of apsidal motion that arises from the dynamic tides as $19.05pm 1.70$ mrad yr$^{-1}$ via tracking the orbital phase shifts of tidally excited oscillations. We also calculate the procession rate of the orbit due to the Newtonian and general relativistic contribution as $21.49 pm 2.8$ and $2.4 pm 0.06$ mrad yr$^{-1}$, respectively. The sum of these three factors is in excellent agreement with the total observational rate of apsidal motion $42.97 pm 0.18$ mrad yr$^{-1}$ measured by eclipse timing variations. The tidal effect accounts for about 44% of the overall observed apsidal motion and is comparable to that of the Newtonian term. Dynamic tides have a significant contribution to the apsidal motion. The analysis method mentioned in this paper presents an alternative approach to measuring the contribution of the dynamic tides quantitatively.
We characterize the extreme heartbeat star system MACHO 80.7443.1718 in the LMC using TESS photometry and spectroscopic observations from the Magellan Inamori Kyocera Echelle (MIKE) and SOAR Goodman spectographs. MACHO 80.7443.1718 was first identified as a heartbeat star system in the All-Sky Automated Survey for SuperNovae (ASAS-SN) with $P_{rm orb}=32.836pm0.008,{rm d}$. MACHO 80.7443.1718 is a young (${sim}6$~Myr), massive binary, composed of a B0 Iae supergiant with $M_1 simeq 35 M_odot$ and an O9.5V secondary with $M_2 simeq 16 M_odot$ on an eccentric ($e=0.51pm0.03$) orbit. In addition to having the largest variability amplitude amongst all known heartbeats stars, MACHO 80.7443.1718 is also one of the most massive heartbeat stars yet discovered. The B[e] supergiant has Balmer emission lines and permitted/forbidden metallic emission lines associated with a circumstellar disk. The disk rapidly dissipates at periastron which could indicate mass transfer to the secondary, but re-emerges immediately following periastron passage. MACHO 80.7443.1718 also shows tidally excited oscillations at the $N=25$ and $N=41$ orbital harmonics and has a rotational period of 4.4 d.
We present a new method for constraining the Milky Way halo gravitational potential by simultaneously fitting multiple tidal streams. This method requires full three-dimensional positions and velocities for all stars to be fit, but does not require identification of any specific stream or determination of stream membership for any star. We exploit the principle that the action distribution of stream stars is most clustered when the potential used to calculate the actions is closest to the true potential. Clustering is quantified with the Kullback-Leibler Divergence (KLD), which also provides conditional uncertainties for our parameter estimates. We show, for toy Gaia-like data in a spherical isochrone potential, that maximizing the KLD of the action distribution relative to a smoother distribution recovers the true values of the potential parameters. The precision depends on the observational errors and the number of streams in the sample; using KIII giants as tracers, we measure the enclosed mass at the average radius of the sample stars accurate to 3% and precise to 20-40%. Recovery of the scale radius is precise to 25%, and is biased 50% high by the small galactocentric distance range of stars in our mock sample (1-25 kpc, or about three scale radii, with mean 6.5 kpc). About 15 streams, with at least 100 stars per stream, are needed to obtain upper and lower bounds on the enclosed mass and scale radius when observational errors are taken into account; 20-25 streams are required to stabilize the size of the confidence interval. If radial velocities are provided for stars out to 100 kpc (10 scale radii), all parameters can be determined with 10% accuracy and 20% precision (1.3% accuracy in the case of the enclosed mass), underlining the need for ground-based spectroscopic follow-up to complete the radial velocity catalog for faint halo stars observed by Gaia.
Asteroseismology is the determination of the interior structures of stars by using their oscillations as seismic waves. Simple explanations of the astrophysical background and some basic theoretical considerations needed in this rapidly evolving field are followed by introductions to the most important concepts and methods on the basis of example. Previous and potential applications of asteroseismology are reviewed and future trends are attempted to be foreseen.
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