Characterization of Time Delay Interferometry combinations for the LISA instrument noise

Abstract

Time delay interferometry (TDI) is a post-processing technique used in the Laser InterferometerSpace Antenna (LISA) to reduce laser frequency noise by building an equal-arm interferometer via combining time-shifted raw phase measurements. Many so-called 2nd generation TDI variables have been found that sufficiently suppress laser frequency noise considering realistic LISA orbital dynamics.In this paper, we want to investigate the relationships between these different TDI channels to understand the optimal approach for recovering all information from the raw phase measurements.It is already well known from the literature that the entire space of TDI solutions can be generated out of the 4 combinations α, β, γ, and ζ, at least under the approximation of three different but constant constellation arms (1st generation TDI). We apply this result to a core subset of the 2nd generation combinations reported in the literature, for which we compute explicitly how they can be approximated in terms of these 4 generators and show numerically that these approximations are accurate enough to model the noises not suppressed by TDI. Finally, we identify multiple possible 2nd generation representatives of α, β, γ, and ζ, and discuss which might be ideal to use for the LISA data analysis. In addition, we demonstrate that newly found variants of the variable ζ significantly out-perform the ones previously known from the literature.

Charactering instrumental noises and stochastic gravitational wave signals from combined time-delay interferometry

“…If the performances of six test masses and optical benches and fully identical, the acceleration noise and optical path noise could be precisely characterized by three or fewer TDI channels [21][22][23]. However, in the realistic case, the performance of instruments on each spacecraft may differ from each other, and these noises should be characterized individually by combing multiple TDI outputs [24][25][26][27].…”

Geometric approach for the modified second generation time delay interferometry

“…In Ref. [33], Hartwig and Muratore characterized geometric TDI channels in terms of the first generation TDI variables.…”