Dynamical friction can flip the hierarchical three-body system

In recent years, the long-term effects of non-linear perturbations were found to be important for the evolution of the hierarchical triple system, which, for the central third body of a larger mass, can significantly suppress the occurrences of orbital flip that changes the sign of angular momentum of inner binary. However, as the third-body mass increases significantly, the ambient dark matter spike becomes much more dense, rendering the effect of dynamical friction non-negligible. In this work, we take the dynamical friction into account for the first time in the hierarchical triple system up to the octupole order and find that the suppressed occurrences of orbital flip could be recovered, and as the spike index increases, the number of flips could increase over a period of time; meanwhile, as both the inner and outer semi-major axes increase while keeping their ratio fixed, the number of flips could also increase over the same number of outer orbital periods, making the detection of orbital flip a potential probe of the dark matter via observations of either electromagnetic waves or gravitational waves.