Time delay interferometry with minimal null frequencies and shortened time span

Abstract: In Paper I, we introduced the hybrid Relay, an alternative second-generation time-delay interferometry (TDI) configuration designed to minimize null frequencies and enhance gravitational wave (GW) analysis for massive binary black holes (MBBHs). In Paper II, we further improved its noise characterization performance by replacing its null stream with a more stable channel, $C^{12}_3$. In this work, we present a novel TDI scheme, PD4L, which features minimal null frequencies and a reduced time span. Unlike the hybrid Relay or the second-generation Michelson which require delays up to $7L$ (with $L$ denoting the light-travel time between spacecraft), the PD4L uses delays no longer than $3L$, corresponding to a total time span of $4L$. This compact structure yields several advantages: 1) reducing data margins at segment boundaries, 2) mitigating aliasing in the high frequency regime, and 3) shortening the signal tails caused by long span. To evaluate PD4L's performance, we perform parameter inference for chirping GW signals from coalescing MBBHs. Our results show that the PD4L outperforms the hybrid Relay in the high frequency band and performs comparably at low frequencies. Moreover, PD4L's null stream exhibits the same minimal null frequencies as its science channels and maintains a more stable noise spectrum than $C^{12}_3$. While the noise spectra of its science channels are slightly less stable than those of the hybrid Relay, PD4L can still reliably infer noise parameters for data durations of up to four months. These results suggest PD4L as a promising TDI scheme, particularly well-suited for analyzing GW signal in the higher-frequency domain.