Characterization of time delay interferometry combinations for the LISA instrument noise

Time delay interferometry (TDI) is a postprocessing technique used in the Laser Interferometer Space Antenna (LISA) to reduce laser frequency noise by building an equal-arm interferometer via combining time-shifted raw phase measurements. The set of so-called second generation TDI variables that sufficiently suppress laser frequency noise considering realistic LISA orbital dynamics has recently been expanded by a large number of additional solutions. In this paper, we characterize these new TDI channels by relating them to the well-known first generation variables alpha, beta, gamma, and zeta. We compute explicitly how each second generation variable can be approximated as a linear combination of these four first generation variables and show numerically that these approximations are accurate enough to model the noises not suppressed by TDI. We use these results to discuss how the newly found channels might be advantageous to use for the LISA data analysis. In addition, we demonstrate that newly found variants of the variable zeta significantly outperform the ones previously known from the literature.