Effect of filters on the time-delay interferometry residual laser noise for LISA

The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. Laser frequency noise enters the interferometric measurements and dominates the expected gravitational signals by many orders of magnitude. Time-delay interferometry (TDI) is a technique that reduces this laser noise by synthesizing virtual equal-arm interferometric measurements. Laboratory experiments and numerical simulations have confirmed that this reduction is sufficient to meet the scientific goals of the mission in proof-of-concept setups. In this paper, we show that the on-board antialiasing filters play an important role in TDI’s performance when the flexing of the constellation is accounted for. This coupling was neglected in previous studies. To reach an optimal reduction level, filters with vanishing group delays must be used on board or synthesized off-line. We propose a theoretical model of the residual laser noise including this flexing-filtering coupling. We also use two independent simulators to produce realistic measurement signals and compute the corresponding TDI Michelson variables. We show that our theoretical model agrees with the simulated data with exquisite precision. Using these two complementary approaches, we confirm TDI’s ability to reduce laser frequency noise in a more realistic mission setup. The theoretical model provides insight on filter design and implementation.

Figure 1

Conventions for labeling spacecraft, MOSAs, lasers, optical benches, and arms. Primed indices are used for arms pointing clockwise, and for MOSAs and optical benches receiving light clockwise.

Figure 2

Main steps of the analysis chain.

Figure 3

Levels for different filter terms $K_{\mathcal{F}}$. Dotted lines correspond to leading-order expansions.

Figure 4

Original optical design used in LISACode simulations. Four interferometric measurements per spacecraft are performed: the science signals $s_i$ and $s_i^{\prime }$, along with the reference signals ${\tau }_i$ and ${\tau }_i^{\prime }$.

Figure 5

New split interferometry optical design used in LISANode simulations. Six interferometric measurements per spacecraft are performed: the science signals $s_i$ and $s_i^{\prime }$, the test-mass signals ${\epsilon }_i$ and ${\epsilon }_i^{\prime }$, along with the reference signals ${\tau }_i$ and ${\tau }_i^{\prime }$.

Figure 6

Power spectral density of the residual laser frequency noise in the Michelson $X_1$ channel. The LISACode and LISANode simulations use realistic Keplerian orbits, while the theoretical model uses armlengths varying linearly with time. Secondary noises are shown in red and indicate the target level of laser frequency noise suppression.

Figure 7

Power spectral density of the residual laser frequency noise in the Michelson $X_2$ channel. The LISACode and LISANode simulations use realistic Keplerian orbits, while the theoretical model uses armlengths varying linearly with time. Secondary noises are shown in red and indicate the target level of laser frequency noise suppression.