Effectiveness of null time-delay interferometry channels as instrument noise monitors in LISA

We present a study of the use and limits of the time-delay interferometry null channels for in-flight estimation of the Laser Interferometer Space Antenna instrumental noise. The paper considers how the two main limiting noise sources, test-mass acceleration noise and interferometric phase measurement noise, propagate through different time-delay interferometry channels: the Michelson combination X that is the most sensitive to gravitational waves, then the less-sensitive combinations α, and finally the null channel ζ. We note that the null channel ζ, which is known to be equivalent to any null channel, not only has a reduced sensitivity to the gravitational waves, but also features a larger degree of cancellation of the test mass acceleration noise relative to the interferometry noise. This severely limits its use in quantifying the low-frequency instrumental noise in the Michelson X combination, which is expected to be dominated by acceleration noise. However, we show that one can still use in-flight noise estimations from ζ to put an upper bound on the considered noises entering in the X channel, which allows one to distinguish them from a strong stochastic gravitational wave background.