Mass quadrupole degeneracy of binary systems and Lagrange three-body systems

Abstract

It has been found that a binary system and a linearly stable Lagrange three-body system can have identical mass quadrupole waveforms up to the coalescence time. Here, we analyze the mass quadrupole degeneracy, specializing to cases when the binary has asymmetric masses. We find that as the difference between the masses of the binary grows larger, the waveform match between degenerate systems decreases below the standard threshold of 0.97 for the Advanced LIGO. The waveform matches in each polarization mode are symmetric functions of the mass ratio difference of the binary. However, an interesting feature we observed is that the waveform matches in each polarization mode are symmetric about different points.