Probing evolution of binaries influenced by the spin-orbit resonances

Abstract

We evolve isolated comparable mass spinning compact binaries experiencing Schnittman's post-Newtonian spin-orbit resonances in an inertial frame associated with $j_0$, the initial direction of the total angular momentum. We argue that accurate gravitational wave (GW) measurements of the initial orientations of the two spins and orbital angular momentum from $j_0$ should allow us to distinguish between the two possible families of spin-orbit resonances. Therefore, these measurements have the potential to provide direct observational evidence of possible binary formation scenarios. The above statements should also apply for binaries that do not remain in a resonant plane when they become detectable by GW interferometers. The resonant plane, characterized by the vanishing scalar triple product involving the two spins and the orbital angular momentum, naturally appears in the one parameter family of equilibrium solutions, discovered by Schnittman. We develop a prescription to compute the time-domain inspiral templates for binaries residing in these resonant configurations and explore their preliminary data analysis consequences.

26 pages, 9 figures, 1 table, v2: revised version incorporating referee's comments

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