Dynamical Tides Research Articles

Resonant tides in binary neutron star mergers: Analytical-numerical relativity study

Resonant excitations of $f$-modes in binary neutron star coalescences influence the gravitational waves (GWs) emission in both quasicircular and highly eccentric mergers and can deliver information on the star interior. Most models of resonant tides are built using approximate, perturbative approaches and thus require to be carefully validated against numerical relativity (NR) simulations in the high-frequency regime. We perform detailed comparisons between a set of high-resolution NR simulations and the state of the art effective one body (EOB) model ${\tt TEOBResumS}$ with various tidal potentials and including a model for resonant tides. For circular mergers, we find that $f$-mode resonances can improve the agreement between EOB and NR, but there is no clear evidence that the tidal enhancement after contact is due to a resonant mechanism. Tidal models with $f$-mode resonances do not consistently reproduce, at the same time, the NR waveforms and the energetics within the errors, and their performances is comparable to resummed tidal models without resonances. For highly eccentric mergers, we show for the first time that our EOB model reproduces the bursty NR waveform to a high degree of accuracy. However, the considered resonant model does not capture the $f$-mode oscillations excited during the encounters and present in the NR waveform. Finally, we analyze GW170817 with both adiabatic and dynamical tides models and find that the data shows no evidence in favor of models including dynamical tides. This is in agreement with the fact that resonant tides are measured at very high frequencies, which are not available for GW170817 but might be tested with next generation detectors.

The tidal excitation ofrmodes in a solar-type star orbited by a giant planet companion and the effect on orbital evolution I: the aligned case

ABSTRACTIt has been suggested that tidal interaction is important for shaping the orbital configurations of close orbiting giant planets. The excitation of propagating waves and normal modes (dynamical tide) will be important for estimating time-scales for orbital evolution. We consider the tidal interaction of a Jupiter mass planet orbiting a solar-type primary. Tidal and rotational frequencies are assumed comparable making the effect of rotation important. Although centrifugal distortion is neglected, Coriolis forces are fully taken into account. We focus in detail on the potentially resonant excitation of r modes associated with spherical harmonics of degrees three and five. These are mostly sited in the radiative core but with a significant response in the convective envelope where dissipation occurs. Away from resonance significant orbital evolution over the system lifetime is unlikely. However, tidal interaction is enhanced near resonances and the orbital evolution accelerated as they are passed through. This speed up may be sustained if near resonance can be maintained. For close orbits with primaries rotating sufficiently rapidly, this could arise from angular momentum loss and stellar spin-down through a stellar wind bringing about significant orbital evolution over the system lifetime.

Relativistic Correction to the r-mode Frequency in Light of Multimessenger Constraints

The r-mode oscillations of rotating neutron stars are promising candidates for continuous gravitational-wave (GW) observations. The r-mode frequencies for slowly rotating Newtonian stars are well known and independent of the equation of state (EOS), but for neutron stars several mechanisms can alter the r-mode frequency for which the relativistic correction is dominant and relevant for most of the neutron stars. The most sensitive searches for continuous GWs are those for known pulsars for which GW frequencies are in targeted narrow frequency bands of a few hertz. In this study, we investigate the effect of several state-of-the-art multimessenger constraints on the r-mode frequency for relativistic, slowly rotating, barotropic stars. Imposing these recent constraints on the EOS, we find that the r-mode frequency range is slightly higher than that from the previous study and the narrowband frequency range can increase by up to 25% for the most promising candidate PSR J0537−6910 depending on the range of compactness. We also derive universal relations between r-mode frequency and dimensionless tidal deformability that can be used to estimate the dynamical tide of the r-mode resonant excitation during the inspiral signal. These results can be used to construct the parameter space for r-mode searches in GW data and also constrain the nuclear EOS following a successful r-mode detection.

Impact of updated multipole Love numbers and f -Love universal relations in the context of binary neutron stars

Neutron star (NS) equation of state (EoS) insensitive relations or universal relations (UR) involving neutron star bulk properties play a crucial role in gravitational-wave astronomy. Considering a wide range of equations of state originating from (i) phenomenological relativistic mean field models, (ii) realistic EoS models based on different physical motivations, and (iii) polytropic EoSs described by spectral decomposition method, we update the EoS-insensitive relations involving NS tidal deformability (Multipole Love relation) and the UR between f-mode frequency and tidal deformability (f-Love relation). We analyze the binary neutron star (BNS) event GW170817 using the frequency domain TaylorF2 waveform model with updated universal relations and find that the additional contribution of the octupolar electric tidal parameter and quadrupolar magnetic tidal parameter or the change of multipole Love relation has no significant impact on the inferred NS properties. However, adding the f-mode dynamical phase lowers the 90% upper bound on $\tilde{\Lambda}$ by 16-20% as well as lowers the upper bound of NSs radii by $\sim$500m. The combined URs (multipole Love and f-Love) developed in this work predict a higher median (also a higher 90% upper bound) for $\tilde{\Lambda}$ by 6% and also predict higher radii for the binary components of GW170817 by 200-300m compared to the URs used previously in the literature. We further perform injection and recovery studies on simulated events with different EoSs in $\rm A+$ detector configuration as well as with third generation (3G) Einstein telescope. In agreement with the literature, we find that neglecting f-mode dynamical tides can significantly bias the inferred NS properties, especially for low mass NSs. However, we also find that the impact of the URs is within statistical errors.

Transit duration and timing variations from binary planets

ABSTRACT Systems of two gravitationally bound exoplanets orbiting a common barycentre outside their physical radii (‘binary planets’) may result from tidal capture during planet–planet scattering. These objects are expected to form in tight orbits of just a few times their summed radii due to dynamical tides. As a result of their close proximity, their transits overlap heavily, leading to the deceptive illusion of a single planet of larger effective size, an effect compounded in the presence of noisy data and/or long integration times. We show that these illusory single-component transits, dubbed ‘chimera transits’, exhibit large-amplitude transit duration variation (TDV) effects of the order of hours, as well as smaller transit timing variations (TTVs). We compute an analytical approximation for the transit duration upper bound, assuming binary planets with low impact parameter and orbits coplanar with the stellarcentric orbit. We verify the accuracy of our expressions against dynamical simulations of binary Jupiters using the luna algorithm, and provide a python code for numerical calculations of the TDV signal in binary planet systems (github.com/joheenc/binary-planet-transits). Additionally, chimera transits from binary planets exhibit TTVs of detectable amplitude and high frequency, falling within the recently identified exomoon corridor. Due to their anomalous shapes, depths, and durations, such objects may be flagged as false positives, but could be clearly surveyed for in existing archives.

Can the stellar dynamical tide destabilize the resonant chains of planets formed in the disk?

AbstractEvolution models of planetary systems find that resonant chains of planets often arise from the formation within protoplanetary disks. However, the occurrence of observed resonant chains, such as the notable TRAPPIST-1 system, is relatively low. This suggests that the majority of these chains become destabilized after the dissipation of the protoplanetary disk. Stellar tides, especially the wavelike dynamical tide, could be proposed as potential contributors to the destabilization of resonant chains. The dissipation of the dynamical tide, because of the frequency-dependant tidal excitation of stellar oscillation eigenmodes, potentially leads to a boost in migration for the close-in planets and disrupts the fragile stability of resonant chains. Thus, we investigate the influence of the stellar dynamical tide on multi-planet systems with taking their dissipation into account in the N-body code Posidonius. Notably, this research represents the first exploration of the impact of frequency-dependent dynamical tides on multi-planet systems.

Periastron precession effect of f -mode dynamical tides on gravitational waves from eccentric double white dwarfs

The dynamical tide can play an important role in the orbital motion of close eccentric double white dwarf binaries. As the launching of the space-based gravitational-wave detector, the Laser Interferometer Space Antenna (LISA), is just around the corner, detection of gravitational wave signals from such systems is anticipated. In this paper, we discuss the influence of the dynamical tide on eccentric orbits, focusing on the effect on periastron precession. We show that, in orbits with a high eccentricity, resonance can cause a large precession when a harmonic of the orbital frequency matches the natural frequencies of the normal modes of the star. In contrast to the case with circular orbits, each mode can encounter multiple resonances with different harmonics and these resonant regions can cover about 10% of the frequency space for orbits with close separations. In this case, the tidal precession effect is distinct from the other contributions and can be identified with LISA if the signal-to-noise ratio is high enough. However, within the highly eccentric-small separation region, the dynamical tide causes chaotic motion and the gravitational wave signal becomes unpredictable. Even not at resonance, the dynamical tide can contribute up to 20% of the precession for orbits close to Roche-lobe filling separation with low eccentricities and LISA can resolve these off-resonant dynamical tide effects within the low eccentricity-small orbital separation region of the parameter space. For lower mass systems, the dynamical tide effect can degenerate with the uncertainties of the eccentricity, making it unmeasurable from the precession rate alone. For higher mass systems, the radiation reaction effect becomes significant enough to constrain the eccentricity, allowing the measurement of the dynamical tide.

Planet-star interactions with precise transit timing

Context. Hot Jupiters on extremely short-period orbits are expected to be unstable due to tidal dissipation and spiral toward their host stars. That is because they transfer the angular momentum of the orbital motion through tidal dissipation into the stellar interior. Although the magnitude of this phenomenon is related to the physical properties of a specific star-planet system, statistical studies show that tidal dissipation might shape the architecture of hot Jupiter systems during the stellar lifetime on the main sequence. Aims. The efficiency of tidal dissipation remains poorly constrained in star-planet systems. Stellar interior models show that the dissipation of dynamical tides in radiation zones could be the dominant mechanism driving planetary orbital decay. These theoretical predictions can be verified with the transit timing method. Methods. We acquired new precise transit mid-times for five planets. They were previously identified as the best candidates for which orbital decay might be detected. Analysis of the timing data allowed us to place tighter constraints on the orbital decay rate. Results. No statistically significant changes in their orbital periods were detected for all five hot Jupiters in systems HAT-P-23, KELT-1, KELT-16, WASP-18, and WASP-103. For planets HAT-P-23 b, WASP-18 b, and WASP-103 b, observations show that the mechanism of the dynamical tidal dissipation probably does not operate in their host stars, preventing their orbits from rapidly decaying. This finding aligns with the models of stellar interiors of F-type stars, in which dynamical tides are not fully damped due to convective cores. For KELT-16 b, the span of transit timing data was not long enough to verify the theoretical predictions. KELT-1 b was identified as a potential laboratory for studying the dissipative tidal interactions of inertial waves in a convective layer. Continued observations of those two planets may provide further empirical verification of the tidal dissipation theory.

Influence of tidal dissipation on outcomes of binary–single encounters between stars and black holes in stellar clusters

ABSTRACT In the cores of dense stellar clusters, close gravitational encounters between binary and single stars can frequently occur. Using the tsunami code, we computed the outcome of a large number of binary–single interactions involving two black holes (BHs) and a star to check how the inclusion of orbital energy losses due to tidal dissipation can change the outcome of these chaotic interactions. Each interaction was first simulated without any dissipative processes and then we systematically added orbital energy losses due to gravitational wave emission [using post-Newtonian (PN) corrections] and dynamical tides and recomputed the interactions. We find that the inclusion of tides increases the number of BH–star mergers by up to 75 per cent; however, it does not affect the number of BH–BH mergers. These results highlight the importance of including orbital energy dissipation due to dynamical tides during few-body encounters and evolution of close binary systems within stellar cluster simulations. Consistent with previous studies, we find that the inclusion of PN terms increases the number of BH–BH mergers during binary–single encounters. However, BH–star mergers are largely unaffected by the inclusion of these terms.

F -mode imprints on gravitational waves from coalescing binaries involving aligned spinning neutron stars

The excitation of $f$-mode in a neutron star member of coalescing binaries accelerates the merger course, and thereby introduces a phase shift in the gravitational waveform. Emphasising on the tidal phase shift by aligned, rotating stars, we provide an accurate, yet economical, method to generate $f$-mode-involved, pre-merger waveforms using realistic spin-modulated $f$-mode frequencies for some viable equations of state. We find for slow-rotating stars that the dephasing effects of the dynamical tides can be uniquely, EOS-independently determined by the direct observables (chirp mass ${\cal M}$, symmetric ratio $\eta$ and the mutual tidal deformability ${\tilde \Lambda}$), while this universality is gradually lost for increasing spin. For binaries with fast rotating members ($\gtrsim800\text{ Hz}$) the phase shift due to $f$-mode will exceed the uncertainty in the waveform phase at reasonable signal-to-noise ($\rho=25$) and cutoff frequency of $\gtrsim400\text{ Hz}$. Assuming a high cutoff frequency of $10^3\text{ Hz}$ and fast ($\gtrsim800\text{ Hz}$) members, a significant phase shift of $\gtrsim100$ rads has been found. For systems involving a rapidly-spinning star (potentially the secondary of GW190814), neglecting $f$-mode effect in the waveform templates can therefore lead to considerable systemic errors in the relevant analysis. In particular, the dephasing due to $f$-mode is larger than that caused by equilibrium tides by a factor of $\sim5$, which may lead to a considerably overestimated tidal deformability if dynamical tidal contribution is not accounted. The possibility of accompanying precursors flares due to $f$-mode excitation is also discussed.

Impact of Dynamical Tides on the Reconstruction of the Neutron Star Equation of State.

Gravitational waves (GWs) from inspiraling neutron stars afford us a unique opportunity to infer the as-of-yet unknown equation of state of cold hadronic matter at supranuclear densities. During the inspiral, the dominant matter effects arise due to the star's response to their companion's tidal field, leaving a characteristic imprint in the emitted GW signal. This unique signature allows us to constrain the cold neutron star equation of state. At GW frequencies above ≳800 Hz, however, subdominant tidal effects known as dynamical tides become important. In this Letter, we demonstrate that neglecting dynamical tidal effects associated with the fundamental (f) mode leads to large systematic biases in the measured tidal deformability of the stars and hence in the inferred neutron star equation of state. Importantly, we find that f-mode dynamical tides will already be relevant for Advanced LIGO's and Virgo's fifth observing run (∼2025)-neglecting dynamical tides can lead to errors on the neutron radius of O(1 km), with dramatic implications for the measurement of the equation of state. Our results demonstrate that the accurate modeling of subdominant tidal effects beyond the adiabatic limit will be crucial to perform accurate measurements of the neutron star equation of state in upcoming GW observations.

Prospects for distinguishing dynamical tides in inspiralling binary neutron stars with third generation gravitational-wave detectors

Tidal effects in gravitational-wave (GW) observations from binary neutron star mergers have the potential to probe ultra-dense matter and shed light on the unknown nuclear equation of state of neutron stars. Tidal effects in inspiralling neutron star binaries become relevant at GW frequencies of a few hundred Hz and require detectors with exquisite high-frequency sensitivity. Third generation GW detectors such as the Einstein Telescope or Cosmic Explorer will be particularly sensitive in this high-frequency regime, allowing us to probe neutron star tides beyond the adiabatic approximation. Here we assess whether dynamical tides can be measured from a neutron star inspiral. We find that the measurability of dynamical tides depends strongly on the neutron star mass and equation of state. For a semi-realistic population of 10,000 inspiralling binary neutron stars, we conservatively estimate that on average $\mathcal{O}(50)$ binaries will have measurable dynamical tides. As dynamical tides are characterised not only by the star's tidal deformability but also by its fundamental ($f$-) mode frequency, they present a possibility of probing higher-order tidal effects and test consistency with quasi-universal relations. For a GW170817-like signal in a third generation detector network, we find that the stars' $f$-mode frequencies can be measured to within a few hundred Hz.

Dynamical tides in superfluid neutron stars

ABSTRACT We study the tidal response of a superfluid neutron star in a binary system, focussing on Newtonian models with superfluid neutrons present throughout the star’s core and the inner crust. Within the two-fluid formalism, we consider the main aspects that arise from the presence of different regions inside the star, with particular focus on the various interfaces. Having established the relevant theory, we determine the tidal excitation of the most relevant oscillation modes during binary inspiral. Our results suggest that superfluid physics has a negligible impact on the static tidal deformation. The overwhelming contribution to the Love number is given by, as for normal matter stars, the ordinary fundamental mode (f mode). Strong entrainment, here described by a phenomenological expression, which mimics the large effective neutron mass expected at the bottom of the crust, is shown to have a significant impact on the superfluid modes, but our results for the dynamical tide are nevertheless similar to the static limit: the fundamental modes are the ones most significantly excited by the tidal interaction, with the ordinary f mode dominating the superfluid one. We also discuss the strain built up in the star’s crust during binary inspiral, showing that the superfluid f mode may (depending on entrainment) reach the limit where the crust breaks, although it does so after the ordinary f mode. Overall, our results suggest that the presence of superfluidity may be difficult to establish from binary neutron star gravitational-wave signals.

Tidal Dissipation Due to Inertial Waves Can Explain the Circularization Periods of Solar-type Binaries

Abstract Tidal dissipation is responsible for circularizing the orbits and synchronizing the spins of solar-type close binary stars, but the mechanisms responsible are not fully understood. Previous work has indicated that significant enhancements to the theoretically predicted tidal dissipation rates are required to explain the observed circularization periods (P circ) in various stellar populations and their evolution with age. This was based partly on the common belief that the dominant mechanism of tidal dissipation in solar-type stars is turbulent viscosity acting on equilibrium tides in convective envelopes. In this paper, we study tidal dissipation in both convection and radiation zones of rotating solar-type stars following their evolution. We study equilibrium tide dissipation, incorporating a frequency-dependent effective viscosity motivated by the latest hydrodynamical simulations, and inertial wave (dynamical tide) dissipation, adopting a frequency-averaged formalism that accounts for the realistic structure of the star. We demonstrate that the observed binary circularization periods can be explained by inertial wave (dynamical tide) dissipation in convective envelopes. This mechanism is particularly efficient during pre-main-sequence phases, but it also operates on the main sequence if the spin is close to synchronism. The predicted P circ due to this mechanism increases with the main-sequence age in accordance with observations. We also demonstrate that both equilibrium tide and internal gravity-wave dissipation are unlikely to explain the observed P circ, even during the pre-main sequence, based on our best current understanding of these mechanisms. Finally, we advocate more realistic dynamical studies of stellar populations that employ tidal dissipation due to inertial waves.

A model for spin–orbit commensurability and synchronous starspot activity in stars with close-by planets

Context. The rotation period of some planet-hosting stars appears to be in close commensurability with the orbital period of their close-by planets. In some cases, starspots rotating with a commensurable period have been detected, while the star displays latitudinal differential rotation. Aims. A model is proposed to interpret such a phenomenon based on the excitation of resonant oscillations in the interior magnetic field of the star by a component of the tidal potential with a very low frequency in the reference frame rotating with the star. Methods. A magnetic flux tube located in the overshoot layer of the star is assumed in order to study the excitation of the resonant oscillations in the magnetostrophic regime. The model considers a planet on a circular oblique orbit, and the growth timescale of the oscillations is estimated. To keep the system in resonance with the exciting potential despite the variations in the magnetic field or tidal frequency, a self-regulating mechanism is proposed. Results. The model is applied to ten systems and proves capable of accounting for the observed close commensurability in eight of them by assuming a magnetic field between 102 and 104 G. Systems with distant low-mass planets, such as AU Mic and HAT-P-11, cannot be interpreted by the proposed model. Conclusions. Consequences for the spin–orbit evolution of the systems, including the dynamical tides and gyrochronology of planet-hosting stars, are discussed together with the effects on the chromospheric features produced by star–planet magnetic interactions.

CORALIE radial-velocity search for companions around evolved stars (CASCADES)

Context. Increasing the number of detected exoplanets is far from anecdotal, especially for long-period planets that require a long duration of observation. More detections imply a better understanding of the statistical properties of exoplanet populations, and detailed modelling of their host stars also enables thorough discussions of star–planet interactions and orbital evolution of planetary systems. Aims. In the context of the discovery of a new planetary system, we aim to perform a complete study of HD 29399 and its companion by means of radial-velocity measurements, seismic characterisation of the host-star, and modelling of the orbital evolution of the system. Methods. High-resolution spectra of HD 29399 were acquired with the CORALIE spectrograph mounted on the 1.2-m Swiss telescope located at La Silla Observatory (Chile) as part of the CASCADES survey. We used the moments of the cross-correlation function profile as well as the photometric variability of the star as diagnostics to distinguish between stellar and planetary-induced signals. To model the host star we combined forward modelling with global and local minimisation approaches and inversion techniques. We also studied the orbital history of the system under the effects of both dynamical and equilibrium tides. Results. We present the detection of a long-period giant planet. Combining these measurements with photometric observations by TESS, we are able to thoroughly model the host star and study the orbital evolution of the system. We derive stellar and planetary masses of 1.17 ± 0.10 M⊙ and 1.59 ± 0.08 MJup, respectively, and an age for the system of 6.2 Gyr. We show that neither dynamical nor equilibrium tides have been able to affect the orbital evolution of the planet. Moreover, no engulfment is predicted for the future evolution of the system.

The Lost Meaning of Jupiter’s High-degree Love Numbers

Abstract NASA’s Juno mission recently reported Jupiter’s high-degree (degree ℓ, azimuthal order m = 4, 2) Love number k 42 = 1.289 ± 0.063 (1σ), an order of magnitude above the hydrostatic k 42 obtained in a nonrotating Jupiter model. After numerically modeling rotation, the hydrostatic k 42 = 1.743 ± 0.002 is still 7σ away from the observation, raising doubts about our understanding of Jupiter’s tidal response. Here, we use first-order perturbation theory to explain the hydrostatic k 42 result analytically. We use a simple Jupiter equation of state (n = 1 polytrope) to obtain the fractional change in k 42 when comparing a rotating model with a nonrotating model. Our analytical result shows that the hydrostatic k 42 is dominated by the tidal response at ℓ = m = 2 coupled into the spherical harmonic ℓ, m = 4, 2 by the planet’s oblate figure. The ℓ = 4 normalization in k 42 introduces an orbital factor (a/s)2 into k 42, where a is the satellite semimajor axis and s is Jupiter’s average radius. As a result, different Galilean satellites produce a different k 42. We conclude that high-degree tesseral Love numbers (ℓ > m, m ≥ 2) are dominated by lower-degree Love numbers and thus provide little additional information about interior structure, at least when they are primarily hydrostatic. Our results entail important implications for a future interpretation of the currently observed Juno k 42. After including the coupling from the well-understood ℓ = 2 dynamical tides (Δk 2 ≈ −4%), Jupiter’s hydrostatic k 42 requires an unknown dynamical effect to produce a fractional correction Δk 42 ≈ −11% in order to fit Juno’s observation within 3σ. Future work is required to explain the required Δk 42.

Inferring the dense nuclear matter equation of state with neutron star tides

During the late stages of a neutron star binary inspiral finite-size effects come into play, with the tidal deformability of the supranuclear density matter leaving an imprint on the gravitational-wave signal. As demonstrated in the case of GW170817—the first direct detection of gravitational waves from a neutron star binary—this can lead to strong constraints on the neutron star equation of state. As detectors become more sensitive, effects which may have a smaller influence on the neutron star tidal deformability need to be taken into consideration. Dynamical effects, such as oscillation mode resonances triggered by the orbital motion, have been shown to contribute to the tidal deformability, especially close to the neutron star coalesence, where current detectors are most sensitive. We calculate the contribution of the various stellar oscillation modes to the tidal deformability and demonstrate the (anticipated) dominance of the fundamental mode. We show what the impact of the matter composition is on the tidal deformability, as well as the changes induced by more realistic additions to the problem, e.g. the presence of an elastic crust. Finally, based on this formulation, we develop a simple phenomenological model describing the effective tidal deformability of neutron stars and show that it provides a surprisingly accurate representation of the dynamical tide close to merger.

Dynamical tides in eccentric binaries containing massive main-sequence stars: analytical expressions

ABSTRACT Tidal evolution of eccentric binary systems containing at least one massive main-sequence (MS) star plays an important role in the formation scenarios of merging compact-object binaries. The dominant dissipation mechanism in such systems involves tidal excitation of outgoing internal gravity waves at the convective-radiative boundary and dissipation of the waves at the stellar envelope/surface. We have derived analytical expressions for the tidal torque and tidal energy transfer rate in such binaries for arbitrary orbital eccentricities and stellar rotation rates. These expressions can be used to study the spin and orbital evolution of eccentric binaries containing massive MS stars, such as the progenitors of merging neutron star binaries. Applying our results to the PSR J0045-7319 system, which has a massive B-star companion and an observed, rapidly decaying orbit, we find that for the standard radius of convective core based on non-rotating stellar models, the B-star must have a significant retrograde and differential rotation in order to explain the observed orbital decay rate. Alternatively, we suggest that the convective core may be larger as a result of rapid stellar rotation and/or mass transfer to the B-star in the recent past during the post-MS evolution of the pulsar progenitor.

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

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 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 ± 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 ± 2.8 and 2.4 ± 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 ± 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.