The construction and use of LISA sensitivity curves

TL;DR

This paper develops methods to construct and interpret LISA sensitivity curves for the mHz GW band, enabling quick assessment of source detectability. It provides an analytic model for the LISA noise, combining instrumental, acceleration, and confusion noises into an effective spectrum $S_n(f)$ with $L = 2.5$ Gm and $f_* = 19.09$ mHz, and discusses the transfer function ${\cal R}(f)$. It covers both sky-averaged and sky-dependent SNR calculations for binary sources using PhenomA waveforms, including visualization with $h_{\rm eff}$ against $S_n$ and using $h_c(f)$ for complex sources like EMRIs. The work provides public tooling and emphasizes how detector geometry and the galactic foreground noise shape sensitivity and source visibility across the sky.

Abstract

The Laser Interferometer Space Antenna (LISA) will open the mHz band of the gravitational wave spectrum for exploration. Sensitivity curves are a useful tool for surveying the types of sources that can be detected by the LISA mission. Here we describe how the sensitivity curve is constructed, and how it can be used to compute the signal-to-noise ratio for a wide range of binary systems. We adopt the 2018 LISA Phase-0 reference design parameters. We consider both sky-averaged sensitivities, and the sensitivity to sources at particular sky locations. The calculations are included in a publicly available {\em Python} notebook.

Figures (11)

• Figure 1: A plot taken from the LISA L3 mission proposal showing the expected sensitivity (green line) and a variety of possible sources (various colors) in units of dimensionless characteristic strain.
• Figure 2: The signal transfer function ${\cal R}(f)$ for the combination of two Michelson-style LISA data channels, and the analytic fit from equation (\ref{['Rfit']}).
• Figure 3: The amplitude spectral density of the noise, and the corresponding sensitivity curve, found by dividing $P_n(f)$ by ${\cal R}(f)$. The analytic fit to $S_{n}(f)$ given in equation (\ref{['Sn']}) is also shown.
• Figure 4: The amplitude spectral density of the galactic noise, $S_c^{1/2}$, and the full sensitivity curve combining the instrument noise and the galactic confusion noise, $S_n^{1/2}$, for a 4-year mission lifetime.
• Figure 5: The amplitude spectral density of the noise $\sqrt{P_n}$, and the amplitude sensitivity curve $\sqrt{S_n}$ are plotted against the raw strain spectral density $\sqrt{S_h}$ and the effective strain spectral density $h_{\rm eff}$ for an equal mass black hole binary at $z=3$ with source frame total mass $M = 10^6 \, M_{\odot}$. This system is so bright that even its raw amplitude will be visible in the detector. However, the effective amplitude $h_{\rm eff}$ that appears in the numerator of the SNR calculation better communicates the true brightness of the source. The area between the $h_{\rm eff}$ curve and the $S_n^{1/2}$ curve roughly corresponding to the optimal SNR of 2626. Note that this graph differs slightly from the one shown in Figure 1, which plots dimensionless characteristic strain $h_c(f) = \sqrt{f S(f)}$ rather than strain spectral density $\sqrt{S}$.