Modulation-assisted time-delay interferometric ranging for LISA

Laser Interferometer Space Antenna LISA represents the next frontier in gravitationalwave GW astronomy targeting the detection of millihertz gravitational signals Central to LISAs operation is the nanosecondprecision estimation of the light travel times LTTs between its constituent spacecraft Precise LTT estimates are critical for suppressing dominant laser noise with timedelay interferometry TDI and ensuring the required sensitivity to GW signals The baseline method is to modulate a pseudorandom noise PRN code on the laser beams exchanged between the spacecraft Timedelay interferometric ranging TDIR was proposed as a simpler alternative LTT estimation method TDIR LTT estimates are chosen to minimize the TDI residual noise over the full LISA frequency band TDIR can be used in case of PRN failure or to calibrate the biases of the PRN method In this study we introduce modulationassisted TDIR MATDIR an enhanced variant of TDIR that significantly improves LTT estimation precision and resilience MATDIR achieves this by modulating the laser phase at specific frequencies close to 1Hz thereby artificially elevating the laser phase content relative to secondary unsuppressed noises This modulation strategy not only enhances the signaltonoise ratio for TDIR but also mitigates the impact of GW signals and instrumental artifacts enabling more reliable LTT estimates with reduced integration times We develop the theoretical framework of MATDIR incorporating the full constellation of three spacecraft laser locking and multiple Michelson TDI combinations Analytical predictions confirmed by numerical simulations indicate that MATDIR can achieve LTT estimates comparable to the 1mrms at fs 4 Hz of the PRNbased baseline method We therefore suggest that the possibility to modulate lasers is added to the laser system requirements of LISA