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Register a new userThe Measurement of Dynamic Tidal Contribution to Apsidal Motion in Heartbeat Star KIC 4544587
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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.
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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.
Heartbeat stars are eccentric (e > 0.2) ellipsoidal variables whose light curves resemble a cardiogram. We present the observations and corresponding model of KIC 3749404, a highly eccentric (e = 0.66), short period (P = 20.3 d) heartbeat star with tidally induced pulsations. A binary star model was created using PHOEBE, which we modified to include tidally induced pulsations and Doppler boosting. The morphology of the photometric periastron variation (heartbeat) depends strongly on the eccentricity, inclination and argument of periastron. We show that the inclusion of tidally induced pulsations in the model significantly changes the parameter values, specifically the inclination and those parameters dependent on it. Furthermore, we determine the rate of apsidal advance by modelling the periastron variation at the beginning and end of the 4-yr Kepler data set and dividing by the elapsed time. We compare the model with the theoretical expectations for classical and general relativistic apsidal motion and find the observed rate to be two orders of magnitude greater than the theoretical rate. We find that the observed rate cannot be explained by tidally induced pulsations alone and consequently hypothesise the presence of a third body in the system.
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.
The light curve of KIC 8462852, a.k.a Boyajians Star, undergoes deep dips the origin of which remains unclear. A faint star $approx$2arcsec to the east was discovered in Keck/NIRC2 imaging in Boyajian et al. (2016), but its status as a binary, and possible contribution to the observed variability, was unclear. Here, we use three epochs of Keck/NIRC2 imaging, spanning five years, in JHK near-infrared bands to obtain 1-mas precision astrometry. We show that the two objects exhibit common proper motion, measure a relative velocity of $mu=0.14pm0.44$ mas yr$^{-1}$ ($mu=0.30pm0.93$ km s$^{-1}$) and conclude that they are a binary pair at $880pm10$ AU projected separation. There is marginal detection of possible orbital motion, but our astrometry is insufficient to characterize the orbit. We show that two other point sources are not associated with KIC 8462852. We recommend that attempts to model KIC 8462852 As light curve should revisit the possibility that the bound stellar companion may play a role in causing the irregular brightness variations, for example through disruption of the orbits of bodies around the primary due to long-term orbital evolution of the binary orbit.
We present the analysis of KIC 8164262, a heartbeat star with a high-amplitude (~1 mmag), tidally resonant pulsation (a mode in resonance with the orbit) at 229 times the orbital frequency and a plethora of tidally induced g-mode pulsations (modes excited by the orbit). The analysis combines Kepler light curves with follow-up spectroscopic data from the Keck telescope, KPNO (Kitt Peak National Observatory) 4-m Mayal telescope and the 2.7-m telescope at the McDonald observatory. We apply the binary modelling software, PHOEBE, to the Kepler light curve and radial velocity data to determine a detailed binary star model that includes the prominent pulsation and Doppler boosting, alongside the usual attributes of a binary star model (including tidal distortion and reflection). The results show that the system contains a slightly evolved F star with an M secondary companion in a highly eccentric orbit (e = 0.886). We use the results of the binary star model in a companion paper (Fuller et al., 2017) where we show that the prominent pulsation can be explained by a tidally excited oscillation mode held near resonance by a resonance locking mechanism.
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