LISA for Cosmologists: Calculating the Signal-to-Noise Ratio for Stochastic and Deterministic Sources

Abstract

We present the steps to forecast the sensitivity of the Laser Interferometer Space Antenna (LISA) to both a stochastic gravitational wave background and deterministic wave sources. We show how to use these expressions to estimate the precision with which LISA can determine parameters associated with these sources. Tools are included to enable easy calculation of the signal-to-noise ratio and draw sensitivity curves. Benchmark values are given for easy comparison and checking of methods in the case of two worked examples. The first benchmark is the threshold stochastic gravitational wave background ${\Omega }_{GW}{h}^2$ that LISA can observe. The second is the signal-to-noise ratio that LISA would observe for a binary black hole system identical to GW150914, radiating 4 years before merger.

arXiv commentV2: added 'monotone' example (white-dwarf binary ZTFJ1539) and other minor changes to match published version. 15 page, 4 figures, comments welcome, Mathematica notebook outlining main calculations at https://doi.org/10.5281/zenodo.3341817

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