Tracing the evolution of precessing binary black holes on eccentric orbits

The angles between the spins and orbital angular momentum, or tilts, of binary black holes are vital for distinguishing different astrophysical formation channels. However, the tilts observed when the binary enters the frequency band of ground-based gravitational-wave detectors can differ significantly from the tilts at formation. Therefore, evolving a binary backward in time from detection to formation is essential for understanding its origins. It is necessary to generalize the existing codes for this evolution to include eccentricity, since dynamical formation channels can result in non-negligible eccentricities at detection. We have developed a code to evolve eccentric and precessing binary black holes to formation using orbit-averaged post-Newtonian equations at small orbital separations and precession-averaged equations at large orbital separations. This code gives systematic errors in tilts that are lower than the anticipated statistical errors for observations in the LVK’s fifth observing run. We study how the parameters of eccentric binaries at some reference frequency affect their tilts at formation. The inclusion of eccentricity in this evolution is even important for cases where the eccentricity at detection is well below our current ability to measure it.