The LISA Optimal Sensitivity

TL;DR

This paper identifies optimal interferometric combinations for LISA, enhancing sensitivity to gravitational waves by up to a factor of approximately 1.73, especially in specific frequency bands, compared to a single Michelson interferometer.

Contribution

The authors introduce a method to synthesize interferometric combinations in LISA, achieving optimal sensitivity improvements over traditional Michelson configurations.

Findings

Sensitivity gain of √2 in the long-wavelength band.

Broadened and slightly better than √2 sensitivity in the mid-band.

Oscillatory sensitivity improvement up to √3 at high frequencies.

Abstract

The multiple Doppler readouts available on the Laser Interferometer Space Antenna (LISA) permit simultaneous formation of several interferometric observables. All these observables are independent of laser frequency fluctuations and have different couplings to gravitational waves and to the various LISA instrumental noises. Within the functional space of interferometric combinations LISA will be able to synthesize, we have identified a triplet of interferometric combinations that show optimally combined sensitivity. As an application of the method, we computed the sensitivity improvement for sinusoidal sources in the nominal, equal-arm LISA configuration. In the part of the Fourier band where the period of the wave is longer than the typical light travel-time across LISA, the sensitivity gain over a single Michelson interferometer is equal to $\sqrt{2}$. In the mid-band region, where the LISA Michelson combination has its best sensitivity, the improvement over the Michelson sensitivity is slightly better than $\sqrt{2}$, and the frequency band of best sensitivity is broadened. For frequencies greater than the reciprocal of the light travel-time, the sensitivity improvement is oscillatory and $\sim \sqrt{3}$, but can be greater than $\sqrt{3}$ near frequencies that are integer multiples of the inverse of the one-way light travel-time in the LISA arm.