Directional pre-sensitivity of the laser interferometer space antenna

The space-based Laser Interferometry Space Antenna (LISA) is a gravitational waves observatory currently under development. It comprises three spacecraft, each traveling in a heliocentric orbit that is weakly eccentric and inclined. Gravitational waves comprise two polarization components. They will be detected by conducting interferometric Doppler measurements between the LISA spacecraft. Among other factors, the signal strength of the Doppler measurements will depend on the location of the GW source, the GW polarization angle, and the orbits of the spacecraft. Thus, the signal strength of the Doppler measurements will vary over time. For given spacecraft orbits, we derive bounds on the signal strength that are functions of the source location. These bounds are simple, explicit expressions, and we refer to them as the directional pre-sensitivity. Using the directional pre-sensitivity, we construct a metric for the relative change in the signal strength depending on the source location and the spacecraft orbits. We illustrate how this formalism can be used to assess the signal strength for several examples of chosen orbits.