Algorithm for TDI numerical simulation and sensitivity investigation

TL;DR

This paper presents a numerical algorithm for TDI channel simulation and sensitivity analysis, comparing multiple channels for gravitational wave detection with LISA, and identifying optimal configurations for enhanced sensitivity and sky coverage.

Contribution

Introduces a generic numerical algorithm for TDI channel determination and sensitivity evaluation, analyzing multiple second-generation TDI channels for gravitational wave detection.

Findings

Optimal TDI channel A₂ achieves the best sensitivity.

Joint A₂+E₂+T₂ improves sensitivity and sky coverage.

Sensitivity varies across channels and frequencies, especially below 20 mHz.

Abstract

We introduce a generic algorithm to determine the time delays and spacecraft (S/C) positions to compose any time-delay interferometry (TDI) channel in the dynamical case and evaluate its sensitivity by using a full numerical method. We select 11 second-generation TDI channels constructed from four approaches and investigate their gravitational wave responses, noise levels, and averaged sensitivities under a numerical LISA orbit. The sensitivities of selected channels are various especially for frequencies lower than 20 mHz. The optimal channel A$_2$ (or equivalently E$_2$) combined from second-generation Michelson TDI channels (X$_1$, X$_2$, and X$_3$) achieves the best sensitivity among the channels, while the Sagnac $\alpha_1$ channel shows the worse sensitivity. Multiple channels show better sensitivities at some characteristic frequencies compared to the fiducial X$_1$ channel. The joint $\mathrm{A_2+E_2+T_2}$ observation not only enhances the sensitivity of the X$_1$ channel by a factor of $\sqrt{2}$ to 2 but also improves the capacity of sky coverage.