Improving the sensitivity of LISA

It has been shown in several recent papers that the six Doppler data streams obtained from a triangular LISA configuration can be combined by appropriately delaying the data streams for cancelling the laser frequency noise. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. A rigorous and systematic formalism using the powerful techniques of computational commutative algebra was developed, which generates in principle all the data combinations cancelling the laser frequency noise. The relevant data combinations form a first module of syzygies. In this paper, we use this formalism to advantage for optimizing the sensitivity of LISA by analysing the noise and signal covariance matrices. The signal covariance matrix is calculated for binaries whose frequency changes at most adiabatically and the signal is averaged over polarizations and directions. We then present the extremal SNR curves for all the data combinations in the module. They correspond to the eigenvectors of the noise and signal covariance matrices. A LISA ʹnetworkʹ SNR is also computed by combining the outputs of the eigenvectors. We show that substantial gains in sensitivity can be obtained by employing these strategies. The maximum SNR curve can yield an improvement up to 70% over the Michelson, mainly at high frequencies, while the improvement using the network SNR ranges from 40% to over 100%.