Theoretical and observed quality factor of gravitational quadrupoles

Useful insights into the complicated physics of gravitational waves can often be drawn from approximations to analogous physics of electromagnetic waves. Here, we present a gravitational form of the electromagnetic Chu limit that sets bounds on the achievable Q (quality factor) relating the ratio of stored energy to radiated energy in the underlying fields. In particular, we answer two fundamental physics questions: (1) what is the theoretical Q for gravitational quadrupole radiation sources, and (2) can gravitational Q be observed from recent measured astronomical data? Gravitational Q is shown to follow an inverse seventh-order power law, and gravitational-wave data is used to find observed values of Q for GW170817. Inasmuch as electromagnetic Q serves a central role in design and analysis of electrically-small antennas, the proposed gravitational Q offers the potential for a similar utility in the design and analysis of gravitationally-small detectors and quadrupoles.