A simple model captures a distinct “direct wave” in black-hole mergers, separate from quasinormal ringing
This paper shows that a compact analytic model called Backwards One Body (BOB) naturally reproduces a recently identified non‑quasinormal contribution to the gravitational-wave signal from black‑hole mergers. That contribution, called the “direct wave,” is thought to come from prompt emission as one black hole plunges into the other. Using an analytic potential and a filter technique, the authors demonstrate that BOB can isolate and match this direct wave close to the peak of the signal.
Background: after two black holes merge, the remnant emits ringing signals that are usually modeled as a sum of quasinormal modes (QNMs). QNMs are linear ringing patterns set by the remnant’s mass and spin. Recent work found evidence for an extra, non‑QNM component — the direct wave — that cannot be written as a simple sum of these modes. The BOB model was built from the behavior of lightlike paths near the remnant’s unstable circular orbit (the “light ring”), and it predicts an amplitude that follows a hyperbolic‑secant (sech) shape in time. BOB is economical: it matches numerical waveforms with few free parameters and works especially well near the waveform peak.
What the authors did: first they used the Pöschl–Teller potential, a common analytic stand‑in for the true black‑hole potential, to show that the pole contributions of QNMs can reproduce the sech amplitude profile BOB predicts. In that calculation they make controlled approximations: they treat a certain hypergeometric factor as slowly varying and they assume the source term that excites prograde QNMs is roughly the same across overtones. Second, they applied rational filters — frequency‑domain tools that remove QNM content without fitting — to both numerical relativity (NR) News waveforms and to BOB waveforms. For the NR News they removed a set of modes (seven prograde, two retrograde and a (3,2) mode as in prior work). For BOB they tried two filter strategies: removing the same explicit QNMs, and removing the even prograde QNMs implied by BOB’s built‑in overtone structure in the eikonal limit.