Geometric approach for the modified second generation time delay interferometry

TL;DR

This paper employs a geometric approach combined with a ternary search algorithm to analyze and identify modified second-generation TDI combinations, enhancing the understanding of laser noise suppression in space-based gravitational wave detectors.

Contribution

It introduces a geometric method to investigate modified second-generation TDI combinations, providing a clearer physical interpretation and identifying new solutions.

Findings

Recovered forty second-generation TDI solutions.

Identified nine modified second-generation TDI solutions.

Elaborated on differences based on arm length change rates.

Abstract

The time delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of the space-based gravitational wave detection, namely, the distances between spacecraft are governed by the orbit dynamics and thus can not be held constant. Among different implementations, the geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to the first and the modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation about the synthesis of the virtual optical paths. In this paper, the geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between the second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the sixteen-link combinations, forty second-generation TDI solutions are recovered, among which nine of them are identified as the modified second-generation ones.