The Measurement of Dynamic Tidal Contribution to Apsidal Motion in Heartbeat Star KIC 4544587

TL;DR

This study quantifies the contribution of dynamic tides to apsidal motion in the heartbeat star KIC 4544587 using Kepler data, revealing that dynamic tides account for nearly half of the observed apsidal motion.

Contribution

It introduces a method to measure dynamic tide effects on apsidal motion quantitatively using high-precision photometric data.

Findings

Dynamic tides contribute approximately 44% to the total apsidal motion.

The measured apsidal motion rate from observations is 42.97 mrad yr$^{-1}$.

The dynamic tide contribution is comparable to the Newtonian term.

Abstract

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 $19.05\pm 1.70$ 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.