[Paper Review] Revisiting time delay interferometry for unequal-arm LISA and TAIJI

G. Wang, Wei-Tou Ni|arXiv (Cornell University)|Aug 13, 2020

Pulsars and Gravitational Waves Research64 references4 citations

TL;DR

This paper revisits time delay interferometry (TDI) for unequal-arm LISA and TAIJI missions, using numerical orbital data to evaluate first-generation TDI configurations. It finds that TDI's T channels diverge from equal-arm performance at low frequencies (below 10 mHz), with sensitivity degraded by laser path mismatches due to arm length inequality; residual laser noise exceeds mission requirements unless laser stability is improved by 1–2 orders of magnitude.

ABSTRACT

Three spacecraft of LISA/TAIJI mission follow their respective geodesic trajectories, and their interferometric arms are unequal and time-varying due to orbital dynamics. Time-delay interferometry (TDI) is proposed to suppress the laser frequency noise caused by the unequal-arm. By employing the numerical orbit, we investigate the sensitivity of the first-generation TDI configurations and their corresponding optimal A, E, and T channels. The sensitivities of T channels from Michelson and Monitor/Beacon configurations diverge from the equal-arm case in frequencies lower than 10 mHz, and their performances vary with the inequality of the arm lengths. The mismatches of the laser beam paths are evaluated in a dynamic case, and the residual laser noise in the first-generation TDI could not satisfy the mission requirement.

Motivation & Objective

• To assess the sensitivity of first-generation TDI configurations (A, E, T channels) in unequal-arm LISA and TAIJI missions using numerical orbital data.
• To investigate how arm length inequality and time-varying orbital dynamics affect laser noise suppression in TDI channels.
• To quantify the impact of laser beam path mismatches on residual laser noise in TDI, particularly in the T channel.
• To determine whether first-generation TDI can meet mission-level noise requirements under realistic unequal-arm conditions.
• To evaluate the feasibility of using first-generation TDI for millihertz-band gravitational wave detection with current laser stability.

Proposed method

• Uses numerical ephemeris-based orbits for LISA and TAIJI, derived from solar system barycentric dynamics, to model time-varying arm lengths.
• Applies first-generation TDI formalism to construct optimal A, E, and T channels, with analytical expressions for time-delayed combinations of interferometric measurements.
• Models three noise sources: laser frequency noise, acceleration noise, and optical metrology noise, with frequency-dependent power spectral densities (PSDs).
• Calculates GW response functions for each TDI channel using the time-delayed interferometric combinations, incorporating directional and polarization-dependent signal responses.
• Numerically evaluates laser beam path mismatches in TDI channels by comparing round-trip path lengths across interferometric arms, quantifying residual laser noise from these mismatches.
• Synthesizes average sensitivity by weighting the GW response function with the total noise PSD, including contributions from laser, acceleration, and optical noise.

Experimental results

Research questions

• RQ1 How does arm length inequality in LISA and TAIJI affect the sensitivity of first-generation TDI channels, particularly the T channel?
• RQ2 To what extent do path mismatches in TDI laser beams degrade residual laser noise performance in unequal-arm configurations?
• RQ3 How do the sensitivities of the A, E, and T channels in first-generation TDI deviate from the equal-arm case in the low-frequency band (<10 mHz)?
• RQ4 Can first-generation TDI suppress laser noise sufficiently to meet mission requirements in unequal-arm scenarios, or is second-generation TDI necessary?
• RQ5 What laser stability improvement (in Hz/√Hz) is required to mitigate residual laser noise due to path mismatches in TAIJI and LISA?

Key findings

• The T channel in first-generation TDI shows significant sensitivity degradation compared to the equal-arm case at frequencies below 10 mHz, especially due to arm length inequality.
• Laser path mismatches in the TDI channels increase residual laser noise, which exceeds mission requirements unless laser stability is improved by 1–2 orders of magnitude to 0.3–3 Hz/√Hz.
• For TAIJI, with 20% longer arms and 20% higher relative velocities than LISA, the residual laser noise is approximately 40% higher than in LISA due to increased path mismatch.
• The sensitivity of the T channel is more susceptible to arm length inequality than the A and E channels, making it less reliable as a null stream for noise characterization at low frequencies.
• The mismatch of laser beam paths decreases with shorter arm lengths and lower relative velocities, suggesting that shorter-arm missions (e.g., AMIGO with 10⁴ km arms) may achieve sufficient laser noise suppression with first-generation TDI.
• Second-generation TDI is shown to be a viable alternative to overcome residual laser noise, as previously demonstrated in related numerical studies, and is recommended for future missions with high arm inequality.