The effect of frequency mismatch to orbital synchrony of two double white dwarfs

Abstract

In 2018, the possibility of synchronization of the orbital motions of two gravitational wave emitters was first investigated. They found that two double white dwarfs may be able to lock their orbital frequencies together through the assistance of intrabinary mass transfer. Their analysis was centered around the synchronized state where the orbital frequencies are nearly identical. This work extends their investigation by lifting this approximation to cater for different frequency mismatches. Through an energy relation, we found that the coefficients of the potential equation give the preliminary conditions for the choices of the parameters and initial conditions for synchronization capture. We also found that the capture time for synchrony significantly increases with increased frequency mismatch.