Algorithm for TDI numerical simulation and sensitivity investigation

Abstract

In this work, we introduce a generic algorithm to numerically determine the time delays and spacecraft positions for a time-delay interferometry (TDI) channel in the dynamical case, and streamline the calculations by implementing an SC layout-time delay diagram. We select 11 second-generation TDI channels constructed from four approaches and evaluate their performances including gravitational wave responses, noise levels, and averaged sensitivities under a numerical LISA orbit. The results show that the interference paths of selected TDI channels are well matched and the laser frequency noise should be suppressed under the secondary noise. The channels show various sensitivities in the range of [0.1 mHz, 0.3 Hz], and the major differences appear in the frequency region lower than 20 mHz. The optimal channel A2 or E2 combined from second-generation Michelson TDI channels (X1, X2, and X3) achieves the best sensitivity in the selected channels for the frequency lower than 50 mHz, while the Sagnac α1 channel shows the worse sensitivity. Multiple channels show better sensitivities at some characteristic frequencies compared to the fiducial X1 channel. The Michelson-type channels would have identical sensitivities considering noise level changes with the GW response. The joint A2 + E2 + T2 observation not only enhances the sensitivity of the X1 channel by a factor of √ 2 to 2 but also improves the capacity of sky coverage.

Observing gravitational wave polarizations with LISA-TAIJI network

“…The Michelson X channel spacecraft (S/C) layout-time delay diagram is shown in Fig. 2 as generated in [36]. Following the diagram, the…”

“…2. The S/C layout-time delay diagrams for Michelson X channels as generated in [36]. expression of measurements in the X channel will be [37].…”

Alternative LISA-TAIJI networks

“…For the space-borne GW missions, time-delay interferometry (TDI) is essential to suppress the laser frequency noise and achieve targeting sensitivity. The sensitivities for the different TDI channels have been evaluated numerically in our recent works [38,39]. With implementing the TDI, the GW response is combined from the response of each evolved single link.…”

“…η ji are the combined observables from S/Cj to S/Ci [46][47][48], and the specific expressions for this work are defined in [39]. By assuming the dominant laser frequency noises are sufficiently suppressed, the acceleration noise and optical path noise in η ij become the primary noise sources after TDI process.…”

“…And the power spectrum density (PSD) of a TDI channel S n,TDI is obtained by implementing the numerical algorithm developed in [38,39].…”