Optimizing the directional sensitivity of LISA

It was shown in a previous work that the data combinations canceling laser frequency noise constitute a module---the module of syzygies. The cancellation of laser frequency noise is crucial for obtaining the requisite sensitivity for the Laser Interferometer Space Antenna (LISA). In this work, we show how the sensitivity of LISA can be optimized for a monochromatic source---a compact binary---whose direction is known, by using appropriate data combinations in the module. A stationary source in the barycentric frame appears to move in the LISA frame and our strategy consists of coherently tracking the source by appropriately switching the data combinations so that they remain optimal at all times. Assuming that the polarization of the source is not known, we average the signal over the polarizations. We find that the best statistic is the ``network'' statistic, in which case LISA can be construed as two independent detectors. We compare our results with the Michelson combination, which has been used for obtaining the standard sensitivity curve for LISA, and with the observable obtained by optimally switching the three Michelson combinations. We find that for sources lying in the ecliptic plane, the improvement in signal-to-noise ratio (SNR) increases from 34% at low frequencies to nearly 90% at around 20 mHz. Finally, we present the signal-to-noise ratios for some known binaries in our Galaxy. We also show that, if at low frequencies SNRs of both polarizations can be measured, the inclination angle of the plane of the orbit of the binary can be estimated.