Receiving Exoplanet Messages with Gravitational-wave Carriers: The Gravitational-wave Radial Velocity Method

Abstract Gravitational-wave (GW) radial velocity (RV) may offer a new method for detecting exoplanets, one that would primarily target planets orbiting GW-emitting, ultracompact, post-main-sequence stellar objects such as white dwarfs, neutron stars, and black holes. In this work we show that while similar to electromagnetic-based RV, this GW-based method depends on the “phase modulation index” (PMI), a parameter that is more sensitive to high-mass, long-period exoplanets. We investigate the potential of GW RV for GW sources in both the mid-frequency spectrum (where the upcoming LISA mission will operate) and the high-frequency spectrum (where the current LIGO–Virgo–KAGRA (LVK) observatories operate). Remarkably, we find that the PMI increases by a factor of ∼ O 1 0 4 − 1 0 6 going from the mid-frequency to the high-frequency GW spectrum, which results in a greater redistribution of observed power due to the exoplanet’s presence. By analyzing the power content of the observed GW signal, we derive analytic expressions to predict the GW carrier frequency power loss due to the exoplanet and the signal-to-noise ratio of the GW source and the exoplanet. We also explore the effects of the additional Doppler effect caused by the motion of the GW observatory and the potential for GW source parameter bias introduced by the presence of an undetected exoplanet. All of this helps us better understand where the GW RV method may work best in the exoplanet mass–period discovery space.