Numerical simulation of time delay interferometry for eLISA/NGO

eLISA/NGO is a new gravitational wave detection proposal with arm length of 10⁶ km and one interferometer down-scaled from LISA. Just like LISA and ASTROD-GW, in order to attain the requisite sensitivity for eLISA/NGO, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for LISA and ASTROD-GW with one arm dysfunctional by using the CGC 2.7 ephemeris. The results are well below their respective limits in which the laser frequency noise is required to be suppressed. In this paper, we follow the same procedure to simulate the time delay interferometry numerically. To do this, we work out a set of 1000-day optimized mission orbits of the eLISA/NGO spacecraft starting on 1 January 2021 using the CGC 2.7 ephemeris framework. We then use the numerical method to calculate the residual optical path differences in the second-generation TDI solutions as in our previous papers. The maximum path length difference, for all configurations calculated, is below 13 mm (43 ps). It is well below the limit in which the laser frequency noise is required to be suppressed for eLISA/NGO. We compare and discuss the resulting differences due to the different arm lengths for various mission proposals—eLISA/NGO, an NGO-LISA-type mission with a nominal arm length of 2 × 10⁶ km, LISA and ASTROD-GW.