We propose a data processing technique that allows searches for a stochastic background of gravitational radiation with data from a single detector. Our technique exploits the difference between the coherence time of the gravitational wave (GW) signa
l and that of the instrumental noise affecting the measurements. By estimating the auto-correlation function of the data at an off-set time that is longer than the coherence time of the noise {underbar {but}} shorter than the coherence time of the GW signal, we can effectively enhance the power signal-to-noise ratio (SNR) by the square-root of the integration time. The resulting SNR is comparable in magnitude to that achievable by cross-correlating the data from two co-located and co-aligned detectors whose noises are uncorrelated. Our method is general and it can be applied to data from ground- and space-based detectors, as well as from pulsar timing experiments.
We previously showed how the measurements of some eighteen time series of relative frequency or phase shifts could be combined (1) to cancel the phase noise of the lasers, (2) to cancel the Doppler fluctuations due to non-inertial motions of the six
optical benches, and (3) to remove the phase noise of the onboard reference oscillators required to track the photodetector fringes, all the while preserving signals from passinggravitational waves. Here we analyze the effect of the additional noise due to the optical modulators used for removing the phase fluctuations of the onboard reference oscillators. We use a recently measured noise spectrum of an individual modulator to quantify the contribution of modulator noise to the first and second-generation Time-Delay Interferometric (TDI) combinations as a function of the modulation frequency. We show that modulator noise can be made smaller than the expected proof-mass acceleration and optical-path noises if the modulation frequencies are larger than $approx 682$ MHz in the case of the unequal-arm Michelson TDI combination $X_1$, $approx 1.08$ GHz for the Sagnac TDI combination $alpha_1$, and $approx 706$ MHz for the symmetrical Sagnac TDI combination $zeta_1$. These modulation frequencies are substantially smaller than previously estimated and may lead to less stringent requirements on the LISAs oscillator noise calibration subsystem.
