Inferring spin tilts at formation from gravitational wave observations of binary black holes: Interfacing precession-averaged and orbit-averaged spin evolution

Two important parameters inferred from the gravitational wave signals of binaries precessing black holes are spin tilt angles, i.e., angles at which holes' axes inclined with respect to binary's orbital angular momentum. The LIGO-Virgo parameter estimation analyses currently provide tilts a fiducial reference frequency, often lowest frequency used in data analysis. However, most astrophysically interesting quantities when binary was formed, can be significantly different those for strongly binaries. formally infinite separation good approximation formation many channels and computed efficiently using precession-averaged evolution. Here, we present new code computing infinity that combines evolution orbit-averaged high frequencies illustrate its application GW190521 other hole detections O3a. We have empirically determined transition between produce given accuracy. also regularized equations order obtain accuracy very close-to-equal-mass encountered practice. This additionally allows us investigate singular equal-mass limit expressions, where find an approximate scaling $1/(1 - q)$ mass ratio $q$.