Relativistic Tidal Dissipation and the Gravitational-wave Signal of a White Dwarf Orbiting an Intermediate-Mass Black Hole

Finding intermediate-mass black holes (IMBHs) and measuring their masses and spins are key to understanding massive black hole formation. White dwarf (WD)-IMBH binaries provide a unique probe because they emit both electromagnetic radiation and gravitational waves (GWs), thereby conveying richer information. However, such multi-messenger sources often enter the regime of strong gravity, where existing models fail to capture their relativistic dynamics. Here, we develop a fully relativistic model for the tidal response of a WD close to an IMBH and use it to study the secular orbital evolution as well as the GW signal. We find that for IMBHs more massive than 10^5 solar masses, tidal interaction becomes relativistic and sensitive to IMBH spin. The interaction generally dissipates binary orbital energy and angular momentum, but due to relativistic frame rotation, which reduces phase coherence across pericenter passages, the orbit-averaged tidal dissipation rate can be suppressed by up to about 50% relative to Newtonian predictions. Including tidal dissipation leads to more rapid damping of the orbital eccentricity, to the extent that the pericenter distance may even increase over time, potentially explaining quasi-periodic eruptions and secular orbital period growth. Such tidal effects accumulate into measurable phase and amplitude deviations in the GW signal. For typical space-based observations, the GW waveform mismatch can reach values of order 0.1 within 6 months. Our results indicate that relativistic tidal dissipation is both dynamically important and observationally essential for reliably predicting the multi-messenger signals of WD-IMBH systems.

💡 Research Summary

The paper presents a fully relativistic treatment of tidal dissipation (TD) in white‑dwarf (WD) – intermediate‑mass black‑hole (IMBH) binaries, a class of systems that are promising multi‑messenger sources because they emit both electromagnetic (EM) radiation and gravitational waves (GWs). Existing models largely rely on Newtonian tidal prescriptions, which break down when the pericenter distance of the orbit approaches a few tens of the IMBH’s gravitational radius (r_g). The authors therefore construct a practical model in a Fermi normal coordinate (FNC) frame that captures the quadrupolar tidal field of a Kerr black hole, includes frame‑dragging effects, and computes energy and angular‑momentum fluxes using the theory of g‑mode oscillations of the WD.

Key findings are:

1. Relativistic regime threshold – For IMBH masses ≳10⁵ M⊙, the tidal disruption radius (r_t) lies within ~10 r_g, placing the system firmly in the strong‑gravity regime. In this domain the tidal interaction becomes sensitive to the black‑hole spin.

2. Suppression of tidal dissipation – Frame dragging reduces phase coherence between successive pericenter passages. As a result, the orbit‑averaged TD rate can be up to ~50 % lower than the Newtonian prediction. This suppression is strongest for prograde orbits around rapidly spinning holes.

3. Competition with gravitational‑wave radiation – By comparing characteristic timescales t_GW and t_tide, the authors show that TD becomes comparable to GW back‑reaction when the pericenter distance is ≲10 r_g (k≲3). In this region TD can dominate the eccentricity damping, leading to rapid circularization.

4. Orbital evolution consequences – The enhanced TD damps the binary’s eccentricity much faster than GW emission alone, and can even cause the pericenter distance to increase over time (a “pericenter migration” effect). This behavior offers a natural explanation for the observed secular period growth in quasi‑periodic eruptions (QPEs) from galactic nuclei.

5. Impact on GW waveforms – Incorporating relativistic TD into the orbital evolution produces cumulative phase and amplitude deviations. For typical space‑based detectors (LISA, TianQin, Taiji), the waveform mismatch can reach ~0.1 after only six months of observation, implying that neglecting TD would lead to biased parameter estimation.

6. Spin dependence – Prograde spin lowers the effective angular‑momentum barrier, allowing deeper penetration before plunge, while simultaneously weakening the tidal tensor, thus requiring a smaller pericenter for tidal disruption. Retrograde spin has the opposite effect, shifting the plunge and disruption boundaries outward.

The paper also discusses the fate of the binary (tidal disruption vs. direct plunge) as a function of spin and eccentricity, showing that for a 0.6 M⊙ WD around a 10⁵ M⊙ IMBH, high prograde spin (a≳0.5) leads to disruption, whereas strong retrograde spin (a≲−0.3) leads to plunge.

In the discussion, the authors outline future extensions: inclusion of higher‑order multipoles, treatment of non‑axisymmetric WD structures, coupling to mass‑transfer and accretion physics, and long‑term hydrodynamic simulations to validate the semi‑analytic TD fluxes over many pericenter passages.

Overall, the study demonstrates that relativistic tidal dissipation is dynamically significant and observationally essential for accurately modeling the GW and EM signatures of WD‑IMBH binaries, and it provides the first quantitative framework needed for multi‑messenger analyses of these exotic systems.