Radiatively inefficient accretion flows induced by gravitational-wave emission before massive black hole coalescence

We study an accretion flow during the gravitational-wave driven evolution of binary massive black holes. After the binary orbit decays due to an interaction with a massive circumbinary disk, the binary is decoupled from the circumbinary disk because the orbital-decay timescale due to emission of gravitational wave becomes shorter than the viscous timescale evaluated at the inner edge of circumbinary disk. During the subsequent evolution, the accretion disk, which is truncated at the tidal radius because of the tidal torque, also shrinks as the orbital decay. Assuming that the disk mass changed by this process is all accreted, the disk becomes radiatively inefficient when the semi-major axis is several hundred Schwarzschild radii. The high-energy radiations, in spite of a low bolometric luminosity, are emitted from an accretion disk around each black hole long before the black hole coalescence as well as the gravitational wave signals. The synchrotron process can notably produce potentially observable radio emissions at large distances if there is a strong, dipole magnetic field around each black hole. In unequal mass-ratio binaries, step-like light variations are seen in the observed light curve because the luminosity is higher and its duration time are shorter in the radio emission by the disk around the secondary black hole than those of the primary black hole. Such a precursor would be unique to not a single black hole system but a binary black hole system, and implies that binary black holes finally merge without accretion disks.

💡 Research Summary

The paper investigates the evolution of accretion flows around binary massive black holes (MBHs) during the final stage of orbital decay driven by gravitational‑wave (GW) emission. Initially, the binary interacts with a massive circumbinary disk, which supplies gas to the black holes on a viscous timescale τvis. As the orbit shrinks, the GW‑driven decay timescale τGW eventually becomes shorter than τvis at a separation of a few hundred Schwarzschild radii (RS). At this “decoupling” point the circumbinary disk can no longer follow the binary, and each black hole retains its own mini‑disk truncated at the tidal radius rt≈(Mi/Mtotal)1/3 a. Because rt shrinks together with the binary separation, the mass contained in the mini‑disk is forced inward and is assumed to be completely accreted.

Using mass‑conservation and energy‑balance arguments, the authors calculate the surface density Σ and temperature T of the shrinking disks. The accretion rate drops dramatically to Ṁ∼10‑3–10‑5 ṀEdd, driving the radiative efficiency η down to ≲10‑4. Consequently the bolometric luminosity becomes very low, yet the ion temperature remains ∼10^9 K, characteristic of a radiatively inefficient accretion flow (RIAF). In an RIAF most of the dissipated energy is stored in ions rather than radiated away, so the flow is optically thin and geometrically thick.

A key insight is that, if each black hole is threaded by a strong dipolar magnetic field (B≈10^4–10^5 G), the hot electrons in the RIAF will emit synchrotron radiation. The predicted radio flux density at ν≈1–10 GHz can reach 0.1–1 mJy even for sources at several hundred Mpc, making the emission detectable with current and upcoming radio facilities (e.g., VLA, SKA). Because the secondary (lower‑mass) black hole’s mini‑disk is smaller and denser, its synchrotron burst is shorter (days to weeks) but brighter than that of the primary. This produces a step‑like feature in the observed light curve: a rapid rise and fall associated with the secondary, followed by a longer, weaker component from the primary. Such a precursor is unique to binary systems and would not appear in single‑black‑hole accretion.

The authors argue that simultaneous detection of this radio precursor and the GW signal would allow independent constraints on binary parameters: total mass, mass ratio, magnetic field strength, and the viscous α‑parameter of the disks. Moreover, the disappearance of electromagnetic emission at the moment of coalescence would confirm that the final merger proceeds without a substantial accretion disk, a scenario difficult to infer from GW data alone.

Finally, the paper outlines future work: (1) high‑resolution numerical simulations to capture non‑linear disk‑binary interactions, (2) more realistic magnetic‑field configurations, and (3) coordinated observing campaigns that combine GW detectors (e.g., LISA) with wide‑field radio surveys. By establishing a clear electromagnetic precursor, this study opens a new avenue for multimessenger astronomy of massive black‑hole mergers.