Searching for gravitational waves via Doppler tracking by future missions to Uranus and Neptune

Abstract

ABSTRACT The past year has seen numerous publications underlining the importance of a space mission to the ice giants in the upcoming decade. Proposed mission plans involve a ∼10 yr cruise time to the ice giants. This cruise time can be utilized to search for low-frequency gravitational waves (GWs) by observing the Doppler shift caused by them in the Earth–spacecraft radio link. We calculate the sensitivity of prospective ice giant missions to GWs. Then, adopting a steady-state black hole binary population, we derive a conservative estimate for the detection rate of extreme mass ratio inspirals (EMRIs), supermassive black hole (SMBH), and stellar mass binary black hole (sBBH) mergers. We link the SMBH population to the fraction of quasars fbin resulting from Galaxy mergers that pair SMBHs to a binary. For a total of 10 40-d observations during the cruise of a single spacecraft, $\mathcal {O}(f_\mathrm{bin})\sim 0.5$ detections of SMBH mergers are likely, if Allan deviation of Cassini-era noise is improved by ∼102 in the 10−5 − 10−3 Hz range. For EMRIs the number of detections lies between $\mathcal {O}(0.1) \ \mathrm{ and} \ \mathcal {O}(100)$. Furthermore, ice giant missions combined with the Laser Interferometer Space Antenna (LISA) would improve the localization by an order of magnitude compared to LISA by itself.