Supernova Kick Modeling of GW151226’s Progenitor

Binary black holes that form in isolation need to survive two supernova (SN) explosions. Such explosions may impart a natal kick onto the remnant black hole and cause the black hole spin to become misaligned with the orbital angular momentum. The constraint on GW151226’s spin mis-alignment provides a constraint on the first supernova kick imparted on the progenitor, assuming subsequent binary interactions do not significantly affect the spin mis-alignment thereafter. Here, we investigate if gravitational-wave emission from the natal kick on the binary affects the resulting spin-misalignment. We model the transition from the pre-SN binary to post-SN binary with an equation of motion that accounts for the finite timescales of the SN mass loss and natal kick. We then compare the post-SN binary properties with and without gravitational radiation reaction.