A Catalog of Binary Black Holes in Eccentric Orbits

Displayed below is a subset of LIGO–Virgo–KAGRA (LVK) binary black holes (BHs) from O1, O2, O3 and O4a re-analyzed with an waveform model which includes the effect of orbital eccentricity [1, 2, 3, 4].

We plot the BH dynamics and h₊ waveform by assuming the maximum-a-posteriori (MAP) point from the posterior. The dynamics are calculated using the effective-one-body (EOB) framework [5]. We are assuming spins aligned (or anti-aligned) with the orbital angular momentum. This is displayed by a spinning white tick on the border of the black hole. The size of the black holes is determined by the mass assuming a Schwarzschild radius. When the black holes merge, we compute the remnant final spin and mass using numerical relativity fits [6, 7, 8, 9]. Hover any event name to see the posterior distribution in mass, spin, and eccentricity.

We are measuring the eccentricity and starting the EOB evolution at an detector frame frequency of 10Hz. However, the displayed orbit and waveform is from when the GW enters the LVK band (20 Hz).

The background mesh represents the spacetime as seen by an observer co-moving with the center of mass. Each black hole deforms the mesh—in the near zone—using an approximate Kerr solution (a visualization shortcut for the strong-field region, we cannot do numerical relativity with javascript)! Outside the orbital radius—the wave zone—the mesh is tidally displaced via the geodesic deviation equation in the trasvere-traceless (TT) gauge: δx = ½(h+ x + h× y), δy = ½(−h+ y + h× x), evaluated at the retarded time tret = t − (r − rorbit)/c with a 1/r radiative falloff.

Prior re-weighting. The prior on eccentricity stongly affects the recovered eccentricity. We can set a a sharp two-bin population prior at e = 0.05 (0.05 is effectively quasicircular at O1-O4 LVK sensitivity [10]). Pick the fraction f of events you expect to be eccentric; the per-event posterior weights are multiplied by (1−f) / 0.1 for e < 0.05 samples and f / 0.9 for e > 0.05 (the original pe prior was a uniform prior on e ∈ [0, 0.5]). The displayed orbit then becomes the MAP sample under the new prior. The more robust way to do this is also to let the events inform the recovered population rates/prior (see) Ref. [1].