Prospects for detecting exoplanets around double white dwarfs with LISA and Taiji

Recently, Tamanini & Danielski (2019) discussed the possibility to detect circumbinary exoplanets (CBPs) orbiting double white dwarfs (DWDs) with the Laser Interferometer Space Antenna (LISA). Extending their methods and criteria, we discuss the prospects for detecting exoplanets around DWDs not only by LISA, but also by Taiji, a Chinese space-borne gravitational-wave (GW) mission which has a slightly better sensitivity at low frequencies. We first explore how different binary masses and mass ratios affect the abilities of LISA and Taiji to detect CBPs. Second, for certain known detached DWDs with high signal-to-noise ratios, we quantify the possibility of CBP detections around them. Third, based on the DWD population obtained from the Mock LISA Data Challenge, we present basic assessments of the CBP detections in our Galaxy during a 4-year mission time for LISA and Taiji. Our results show that LISA can detect $\sim 6000$ new systems at most, while as a comparison, Taiji can detect about $50\%$ more events. We discuss the constraints on the detectable zone of each system, as well as the distributions of the inner/outer edge of the detectable zone. Based on the DWD population, we further inject three different planet distributions with an occurrence rate of $50\%$ and constrain the total detection rates. We finally briefly discuss the prospects for detecting habitable CBPs around DWDs with a simplified model. These results can provide helpful inputs for upcoming exoplanetary projects and help analyze planetary systems after the common envelope phase.