[Paper Review] LISA Sensitivity and SNR Calculations

S. Babak, M. Hewitson+1 more|arXiv (Cornell University)|Aug 2, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy15 references61 citations

TL;DR

The note derives LISA's noise PSD, sensitivity curve, and SNR calculations, matching the Science Requirement Document and detailing both 4-link and 6-link configurations.

ABSTRACT

This Technical Note (LISA reference LISA-LCST-SGS-TN-001) describes the computation of the noise power spectral density, the sensitivity curve and the signal-to-noise ratio for LISA (Laser Interferometer Antenna). It is an applicable document for ESA (European Space Agency) and the reference for the LISA Science Requirement Document.

Motivation & Objective

• Define a sky- and polarization-averaged LISA sensitivity curve consistent with the SciRD.
• Model instrumental noise with two primary components (OMS displacement noise and test-mass acceleration noise).
• Derive the GW response (X-Michelson) and its averaging over sky, polarization, and frequency regimes.
• Present methods to compute SNR for black hole binaries and connect sensitivity to GW strain.
• Provide long-wavelength approximations and semi-analytic vs numerical methods for response and sensitivity.

Proposed method

• Formulate SNR^2 as 4 Re integral over frequency of |X(f)|^2 / S_n(f).
• Define sensitivity S_h(f) = S_n(f) / <|R_L|^2> (averaged antenna response).
• Model noise PSD with S_n(f) components: S_OMS and S_acc with frequency scalings (Equations 9–13).
• Derive TDI X-1.5 and X-2.0 noise PSDs under different armlength approximations (Equations 17–20).
• Compute GW response for X-Michelson, including polarization basis, and average using F_X^+, F_X^× (Equations 32–40).
• Provide long-wavelength limit expressions for S_h and discuss multi-TDI configurations (X, Y, Z; A, E, T).

Experimental results

Research questions

• RQ1 How can one compute a sky- and polarization-averaged LISA sensitivity curve that is consistent with the SciRD?
• RQ2 What is the impact of the two dominant noise components (OMS and acceleration) on the LISA sensitivity across frequency?
• RQ3 How does the GW response of X-Michelson TDI depend on armlength assumptions and how can it be averaged analytically or numerically?
• RQ4 How can SNR be computed for compact binaries (e.g., BH binaries) using the SPA waveforms and averaged over sky/polarization?
• RQ5 What are the appropriate long-wavelength approximations for LISA sensitivity and how do they compare to full numerical results?

Key findings

• The sensitivity model reproduces the SciRD curve within the adopted arm-response conventions for a 6-link configuration with 2.5 Gm arms.
• Two primary noise components (OMS displacement noise and test-mass acceleration noise) dominate the instrumental noise model, with specified frequency dependences.
• Analytic and semi-analytic treatments for the averaged GW response show consistency with numerical simulations for X-1.5 and X-2.0 TDIs across a range of frequencies.
• The long-wavelength limit provides practical approximations for S_h and shows agreement with more detailed calculations, including a 6-link factor adjustment.
• Tables compare PSDs and response values at representative frequencies, validating the analytical expressions against numerical tools like LISACode and LISANode.
• A framework is provided to compute SNR for BH binaries using SPA waveforms, including averaging over sky, polarization, and inclination.